Progetto IS-MANET
ISTI
Deliverable WP6D5
PROGETTO IS-MANET
DELIVERABLE WP6D5
September 2005
UNITA’ OPERATIVE:
ISTI – CNR/CNIT-Univ. of Genoa
WP6: Protocolli per l’interconnessione rete MANET/rete fissa
 WP6-T2: Realization of the interconnection: TCP transmissions
via satellite
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 WP6-T2:
ISTI
Deliverable WP6D5
Realization of the interconnection
TCP transmissions via satellite and resource allocations
This task aims at developing the interconnection between two
multihop MANETs via the satellite link. The multihop MANET has
been defined in Task 2 of WP5, and the satellite interconnection has
been experimented in Task 1 of WP6. The connection performance
parameters, in terms of delay, throughput, BER, etc, will be
measured.
This deliverable is divided in three Sections:
1. Section A contains an overview of the problems encountered when TCP data are
transmitted via satellite (ISTI);
2. Section B contains the results of an experiment aimed at evaluate the performance of
different versions of TCP when transmitted via satellite (CNIT);
3. Section C contains satellite bandwidth allocation algorithms and call admission control in
the presence of fading and multiple Services (ISTI, CNIT).
This work is part of
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SECTION A (ISTI)
1. Overview of TCP enhancements for wireless channels
The problems with TCP and wireless links have stimulated research on TCP enhancements.
Several solutions have been proposed to improve TCP performance both over wired and
wireless links, including satellite connections. Some suggestions focus on limited
modifications of standard procedures and tuning of TCP parameters, whereas others
envisage the adoption of procedures that substitute or add to the standard TCP algorithms.
The main problems regarding particularly satellites are depicted in RFC2488: Enhancing TCP
Over Satellite Channels using Standard Mechanisms, while RFC2760: Ongoing TCP
Research Related to Satellites is devoted to the relative research issues.
The number of proposals characterized by the introduction of major TCP modifications is
quite large, comprising TCP Vegas, TCP Peach, TCP Westwood, and TCP Hybla. Some
details to depict a general framework follow, while more details will be provided in the
following paragraphs for some of them.
TCP Vegas aims at preventing the congestion losses by exploiting a dynamic estimation of
the available bandwidth. Although positive results may be achieved in wired networks, neither
the performance penalisation suffered by long RTT connections, nor the cwnd spurious
reduction due to random errors are specifically addressed, leaving basically unresolved the
main problems posed by satellite connections.
TCP-Peach is based on the replacement of Slow Start and Fast Recovery algorithms with
Sudden Start and Rapid Recovery procedures, which rely on the introduction of dummy
segments to probe the bandwidth availability of the network. TCP-Peach requires all the
routers along the connection to implement some priority mechanism at the IP layer, in order
to discard dummy segments in presence of congestion.
Another interesting proposal is TCP Westwood, which introduces a modification of the Fast
Recovery algorithm called Faster Recovery. In contrast with the TCP standard, which halves
the congestion window after three duplicate ACKs and fixes the Slow Start threshold to it,
TCP Westwood attempts to select a Slow Start threshold more consistent with the actual
available bandwidth. Although it may offer several advantages in the presence of link errors, it
does not address the TCP bias against connections with long RTTs.
By contrast with TCP Westwood, TCP Hybla primarily aims at providing and assembling a set
of techniques to solve the RTT disparity problem. A key element is the modification of the
standard rules for the congestion window increase. The variations introduced to the
congestion control algorithms can be considered as an extension of the “Constant-Rate”
additive increase policy. TCP Hybla, although not specifically designed to counteract the
effect of random errors, provides good performance even in noisy channels, due to the speed
up of the cwnd growth granted by the enhanced congestion control policies.
CK-STP (Complete Knowledge-Satellite Transport Protocol) assumes that the bandwidth and
delay of the network are known, thus the TCP buffers on the receiver and sender sides are
tuned appropriately. The initial window is set to the bandwidth-delay product, the congestion
window value is not increased when the acknowledgments arrive and the TCP recovery
mechanism is modified, by entering Fast Retransmission as soon as a duplicated
acknowledgment arrives. At the end of the recovery phase, the congestion window value is
not reduced, so the transmission rate is unaffected. When a timer expires, the congestion
window is not reduced to one segment but, once the retransmission phase ends, the data
communication continues with the same data rate as before.
Recently, an important role is recognised for the Stream Control Transmission Protocol
(SCTP), which has been initially designed for the transportation of signalling packets and
progressively implemented as a transport protocol for reliable data communication. It is
closely related to the TCP, but cannot be considered simply as a TCP enhancement, because
it has been defined and implemented independently of the works related to the TCP.
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An alternative proposal to the aforementioned solutions is represented by the Delay Tolerant
Network (DTN) architecture, which is a work in progress within Internet Research Task Force
(IRTF). This solution is aimed at guaranteeing reliable data communication in environments,
where frequent disconnections are experienced such as in interplanetary and sensor
networks. It provides a bundling protocol working over the transport layer and aimed at
performing custody/ transfer operations. Concerning the transport layer issues developed in
this context, a point-to-point transport protocol is provided by the Licklider Transmission
Protocol (LTP). It has the capability of tolerating link interruption without data loss and of
imposing minimal overhead on low-capacity and/or asymmetric links. Further details are
presented in the following sections.
2. Spoofing and splitting
Under these general names are a series of techniques, also known under the label of
performance enhancing proxies, of which an overview can be found in RFC3135:
Performance Enhancing Proxies Intended to Mitigate Link-Related Degradations, which in
several ways change the semantics of the end-to-end TCP connection exploiting the use of
agents generally based at the edge of the wireless networks, that is, at the satellite earth
stations and at the wireless access points.
Spoofing refers to proxies that change the contents of the TCP packets on the fly. A typical
spoofing functionality is to exactly know the value of the pipe size (bandwidth * delay) and
adjust the receive window accordingly, in order to optimize the satellite channel usage.
Splitting refers to proxies that break the end-to-end semathics of TCP by masquerading to
each of the connection ends as its counterpart. This is a very general technique. For a
satellite link, it is possible to have a proxy at each earth station, while for wireless LANS a
proxy can be implemented at the access point.
3. TCP startup behaviour on long fat pipes without errors
Standard Newreno TCP has an appalling startup behaviour on geostationary satellite links
with ample bandwidth and no errors when the end points are appropriately tuned for high
transfer bandwidth. In this case, in fact, the receive window does not limit the connection
throughput, nor does the Slow Start threshold, which is commonly set to a very high initial
value. The Slow Start phase thus ends with a dramatic case of packets lost in the tens, or
even hundreds on several Mb/s-size links, when the congestion windows, after having grown
up to the bandwidth-delay product plus the link buffer size, doubles in one RTT, thus
overflowing the buffer. The subsequent recovery can be incredibly slow when the Slow-butSteady variant of the Newreno algorithm is implemented, as is the case witht he FullTCP ns-2
implementation, which is the same as the FreeBSD TCP.
In the case of the Slow but Steady variant of Newreno, in fact, the retransmission timer is
reset for every received partial ack. Since Newreno only recovers a single lost packet per
RTT, and since it never times out because at one packet per RTT it rarely encounters any
congestion, the recovery phase can easily last for minutes, a period during which the receiver
only sees a goodput of few packets per RTT.
We started studying this pathological behaviour after having observed it on ns-2, we
examined the implementation of Newreno in the FreeBSD and Linux kernels, and we started
experiments on the CNIT nominal 2 Mb/s errorless satellite link. Preliminary results show that
the Linux Newreno implementation does not behave as bad, mostly because it often happens
that a retransmitted packet is lost and the bad behaviour is interrupted by timeout. Sack on
Linux behaves much better after the timeout. Both exhibit time intervals of more than 10
seconds during which the goodput is reduced to a trickle.
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SECTION B (CNIT-Genoa)
1. TCP transmission experiments
1.1. Experimental setting
The performance evaluation of the different TCP implementations requires operating in a
controlled environment in order to assure, for each test, the repeatability of experiments. With
this aim, we decided to emulate the satellite link by using the facilities offered by the CNIT
National Laboratory for Multimedia Communications in Naples, Italy. The experimental setup
employed is depicted in Figure 1.
Figure 1. Experimental setup used to test the TCP implementations.
The LAN on the left consists of a set of hosts devoted to generate TCP traffic. According to
the specific test, up to ten connections can be running at the same time.
All the packets produced feed the router 1 (CISCO 3640), which conveys them to a serial
V.35 interface, adopting a HDLC protocol at the data link layer. The synchronous data flow is
fed as input to a Fairchild SM290 modem (modem 1), operating in quadrature phase-shift
keying (QPSK), at an information rate of 2048 kbit/s with a sequential FEC of 3/4. The
outgoing modulated signal is applied to a Channel Simulator (here used as a simple
programmable attenuator) and then added to a Gaussian noise, produced by a noise
generator. Both the attenuation and noise variance are suitably changed, to reproduce the
effects of real world fading as concerns the bit error probability observed at the receiver end.
In other words, on the basis of two recorded fading patterns, and on the assumption that the
uplink fading be perfectly compensated by an uplink power control, the Channel Simulator
and Noise source are controlled by the Fading Pattern Generator, in order to emulate the
behaviour of a real link, whose budget was derived according to the Italsat satellite
characteristics [Card95] (G/T=23 dB at the receiver, under the adopted parameter values).
After a delay of 250 ms, the corrupted signal feeds the receiver portion of a second modem,
which interfaces with the router 2. The latter communicates with a group of hosts, whose
mission is to sink TCP packets and to measure their statistics. Obviously, according to the
test to be carried out, both at the transmitter and receiver ends, specific Linux kernels were
booted in all the involved hosts. It should be highlighted that the return channel (i.e., the link
connecting the outgoing signal from modem 2 to the input of modem 1) introduces again a
delay of 250 ms, but it is not affected by errors. Although this does not permit to exactly
reproduce the actual operating conditions, the approximation so introduced can be
reasonably neglected, as the probability that a TCP “pure” acknowledgement packet be lost is
small, due to the limited length of this kind of packet. Indeed, the heavy and statistically
significant traffic is due to pay-loading packets, which always flow from TCP packet
generators (the hosts on the left) to packet receivers (the hosts on the right).
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1.2 Summary of the TCP implementations used
The four TCP implementations that have been compared [Dav05] are Westwood, Peach,
Complete Knowledge Satellite Transport Protocol (CK-STP) and the most common New
Reno.
The TCP Westwood [Ger01] algorithm (we have actually used Westwood+ [Mas04]) is
based on bandwidth end-to-end estimation (BWE). This is achieved by filtering the stream of
ACK packets. When three duplicated ACKs are received, both the congestion window (cwnd)
and the slow start threshold (ssthresh) are set to BWE * RTTmin, where RTTmin represents
the minimum measured round trip time. If a timeout occurs, ssthresh is set as just described
and cwnd is set equal to one. Upon normal ACKs’ reception, cwnd is increased according to
the Reno algorithm and the BWE is computed. It is clear that these adaptive settings
drastically reduce the congestion window in the presence of heavy congestion (low BWE), but
gently reduce it in the presence of light congestion. On the other hand, the original Reno TCP
implements a congestion window halving that does not take into account the specific
congestion status of the network.
New Reno [Flo99] is an improved version of Reno that avoids waiting for a retransmit timer
when multiple packets are lost from a window. The change concerns the sender's behaviour
during Fast Recovery, when a partial ACK is received that acknowledges some, but not all of
the packets that were outstanding. In New Reno, partial ACKs received during Fast Recovery
are treated as an indication that the packet immediately following the acknowledged one in
the sequence space has been lost, and should be retransmitted. Thus, when multiple packets
are lost from a single window of data, New-Reno can recover without a retransmission
timeout, retransmitting one lost packet per round-trip time until all of the lost packets from that
window have been retransmitted.
TCP Peach [Ak01] implements Congestion Avoidance and Fast Retransmit (the same as
Reno), and two new algorithms: Rapid Recovery and Sudden Start. These last two algorithms
are based on the use of dummy segments, low priority segments generated by the sender as
a copy of the last transmitted data packet. If a router is congested, it discards dummy
segments first, due to their low priority. On the contrary, the sender interprets the ACKs for
dummy segments as the evidence that there are unused resources on the link and,
accordingly, it can increase the transmission rate. The Sudden Start algorithm sets cwnd
equal to 1 at the beginning of a connection and, after the first data segment, it transmits rwnd1 dummy segments every T=RTT/rwnd, where rwnd is the maximum advertised window. This
will rapidly increase the congestion window. The Rapid Recovery algorithm acts as the
original Fast Recovery one, whenever a segment loss is detected after the reception of ndup
duplicated ACKs, setting the congestion window equal to cwnd/2. Moreover, in order to test
the network resources, the sender transmits n=cwnd dummy segments. The ACKs for dummy
segments will be received after the ACKs for lost data segments. After the reception of the
first cwnd/2 ACKs for dummy packets, each new ACK for a dummy packet will increase the
congestion window by one segment. As a result, if all dummy segments are ACKed to the
sender, the congestion window reaches the value it had before the segment loss was
detected.
The Complete Knowledge Satellite Transport Protocol (CK-STP, indicated in the following
simply as STP) [Mar01] is based on the TCP New Reno implementation, with the adoption of
the SACK option. The indication "Complete Knowledge" refers to the knowledge about the
physical characteristics of the satellite link, in terms of propagation delay and channel
bandwidth. Concerning the algorithms ruling the data transmission, some more words are
needed. Compared with TCP, this proposal assumes that all the losses experienced by the
satellite link are due exclusively to link errors, such as those caused by strong fading effects.
In this perspective, a constant transmission window set to the bandwidth-delay product is
employed, in order to fill the maximum channel bandwidth achievable by the data
communication. With respect to the TCP implementation, the “slow start” phase is no longer
entered, and for each received acknowledgement, the congestion window keeps its constant
value. As far as the loss detection is concerned, the arrival of only one duplicate
acknowledgement is necessary to trigger the recovery phase, which consists of retransmitting
the lost data segments. Once the recovery phase has terminated, the protocol continues
transmitting with the constant transmission window as set previously. Compared to the TCP
algorithms employed during the recovery phase, the congestion window is not subject to a
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shrinking operation, since only link errors are assumed and, consequently, the reduction of
the transmission window and hence of the data rate is no longer required. At last, also the
timeout management has been improved, in order to react effectively in the presence of a
noisy channel; once the TCP timer expires, the unacknowledged segments are retransmitted
and then the transmission goes on without entering the slow start phase.
1.3 Experimental results
A number of experiments have been performed on the testbed previously described, in
order to measure the throughput of the various TCP implementations and compare their
performance in different operating conditions [Dav05]. The throughput here is intended as the
number of successfully received segments at the socket interface (sometimes referred to as
goodput).
In order to investigate the behavior under real operating conditions, we have adopted a set
of fading attenuation values, which are taken from the results of the propagation experiment
carried out in Ka band on the Olympus satellite by the CSTS (Centro Studi sulle
Telecomunicazioni Spaziali) Institute, on behalf of the Italian Space Agency (ASI). The
attenuation samples considered were 1-second averages, expressed in dB, of the signal
power attenuation with respect to clear sky conditions. The adopted patterns A and B are
taken from data recorded at the Spino d’Adda (Northern Italy) station on September 21 and
23, 1992, respectively. Their behavior over a time window of 300 seconds can be found in
[Cel04]; here, we have used them over a longer time window (900 s), by replicating each
sample 3 times, in order to have a longer time scale for observing the TCP reaction. Fading
pattern A is milder, whereas B is quite severe, and produces a loss of receiver
synchronization for over 100 seconds, starting at 400 s.
Throughput [kbyte/s]
250
200
Westwood
New Reno
STP
Peach
600
700
150
100
50
0
100
200
300
400
500
Time [s]
800
900
Figure 2. Throughput vs. time of the different TCP implementations with only one
connection active over a noisy satellite link (fading pattern A).
All graphs are obtained by averaging the results of 5 repeated experiments (under the
same fading pattern), in order to increase their statistical significance. In all kernel
implementations adopted for the various protocols ([peach], [MPer] and [buff], for Peach, STP
and Westwood, respectively) the sender buffer dimension has been left untouched, with
respect to the native New Reno implementation for the Linux Kernel 2.4.18 (except for STP,
where the buffer dimension is one of the parameters to be set). Thus, in all cases, the sender
buffer per connection is 64 kbytes for New Reno, Westwood and Peach, whereas it is set at
320 kbytes for STP (independently of the number of connections).
Figs. 2-4 show the throughput behaviour (computed over successive 10 second windows),
under fading pattern A, of New Reno, STP, Westwood and Peach with 1, 2 and 5 TCP
connections, respectively, sharing the link at the same time. In the cases of 1 or 2
connections, it must be noted that the buffer dimension limits the channel utilization
achievable by all versions, with the exception of STP. It is therefore not surprising that STP
maintains the best behaviour, in terms of maximum overall throughput, in these cases. The
throughput of the other implementations improves with the number of connections, and is
superior to that of STP when 5 connections are active. For the sake of completeness, we
should however mention that we are using STP in the multiple connection case under a noncomplete-knowledge hypothesis (i.e., the parameter tuning is the same as with a single
connection), as no automatic adaptation feature is currently provided by the code. In principle,
if such automatic parameter adaptation could be devised in a changing environment with
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variable numbers of active connections, STP would be able to maintain the maximum
allowable utilization (at least on a noiseless channel). Another limit of the implementation of
STP we are currently testing is evidenced in Fig. 4 by the oscillating behaviour of the
aggregate throughput; this is a consequence of a lack of protection against unfairness,
caused by the aggressiveness of the individual connections (which can exhibit totally different
throughput patterns, as will be seen in subsequent graphs).
Among the other TCP implementations, the best performance is achieved by Westwood,
which also exhibits remarkable fairness.
300
Throughput [kbyte/s]
250
200
150
100
Westwood
50
0
100
200
New Reno
300
STP
400
500
Time [s]
Peach
600
700
800
900
Figure 3. Aggregate throughput vs. time of the different TCP implementations with 2
connections active over a noisy satellite link (fading pattern A).
300
Throughput [kbyte/s]
250
200
150
100
Westwood
50
0
100
200
New Reno
300
400
STP
500
Peach
600
700
800
900
Time [s]
Figure 4. Aggregate throughput vs. time of the different TCP implementations with 5
connections active over a noisy satellite link (fading pattern A).
250
Throughput [kbyte/s]
Westwood
New Reno
STP
Peach
200
150
100
50
0
100
200
300
400
500
Time [s]
600
700
800
900
Figure 5. Throughput vs. time of the different TCP implementations with only one
connection active over a noisy satellite link (fading pattern B).
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250
Throughput [kbyte/s]
Westwood
Reno
SDR
Peach
200
150
100
50
0
100
200
300
400
500
Time [s]
600
700
800
900
Figure 6. Aggregate throughput vs. time of the different TCP implementations with 2
connections active over a noisy satellite link (fading pattern B).
Figs. 5-7 show the throughput behaviour (computed over successive 10 second windows),
under fading pattern B, of New Reno, STP, Westwood and Peach with 1, 2 and 5 TCP
connections, respectively, sharing the link at the same time.
250
Throughput [kbyte/s]
Westwood
New Reno
STP
Peach
200
150
100
50
0
100
200
300
400
500
Time [s]
600
700
800
900
Figure 7. Aggregate throughput vs. time of the different TCP implementations with 5
connections active over a noisy satellite link (fading pattern B).
The deep fading situation depicted in these figures further evidences some differences
among the various implementations, particularly as regards the readiness in recovering after
an outage situation. Here again, the high aggregate throughput of STP is paid in terms of
fairness (in the sense explained above). Overall, TCP Westwood seems to represent the best
compromise.
100
Throughput [kbyte/s]
90
80
70
60
50
40
30
20
10
0
100
200
300
400
500
600
700
800
Time [s]
Figure 8. Throughput vs. time of three connections out of 5, measured during the
realization of a single experiment with STP, under fading pattern A.
Tests have been performed also over a noiseless satellite link; the results in terms of relative
behavior of the protocols are quite similar to those under fading pattern A, especially in the
first half of the observation period of the latter, where the fading attenuation is lighter.
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Finally, going back to the previous observation about fairness, we show in Figs. 8 and 9 two
instances of the sample paths of individual connections in STP and TCP Westwood,
respectively.
100
Throughput [kbyte/s]
90
80
70
60
50
40
30
20
10
0
100
200
300
400
500
600
700
800
Time [s]
Figure 9. Throughput vs. time of three connections out of 5, measured during the
realization of a single experiment with Westwood+, under fading pattern A.
References
[Card95] F. Carducci, M. Francesi, “The Italsat satellite system”, Int. J. Satell. Commun., vol. 13, pp.
49-81, 1995.
[Dav05] F. Davoli, G. Spanò, S. Vignola, S. Zappatore, “Performance measurements and comparison
of modified TCP control algorithms over rain-faded satellite channels”, Proc. 3rd Internat.
Workshop on Internet Performance, Simulation, Monitoring and Measurement (IPS-MoMe
2005), Warsaw, Poland, March 2005, pp. 215-220.
[Ger01] M. Gerla, A. M. Y. Sanadidi, R. Wang, A. Zanella, C. Casetti, S. Mascolo. “TCP Westwood:
Congestion Control using Bandwidth Estimation”, Proc. IEEE Globecom 2001, S. Antonio,
TX, Nov. 2001, pp. 1698-1702.
[Mas04] A. Dell’Aera, L. A. Grieco, S. Mascolo. “Linux 2.4 implementation of Westwood+ TCP with
rate-halving: a performance evaluation over the Internet”. Proc. IEEE Internat. Conf.
Commun. 2004 (ICC 2004), Paris. France, June 2004, pp. 2092-2096.
[Flo99] S. Floyd, and T. Henderson, New Reno Modification to TCP's Fast Recovery, RFC 2582, April
1999.
[Ak01] I. F. Akyildiz, G. Morabito, S. Palazzo. “TCP-Peach: a new congestion control scheme for
satellite IP networks. IEEE/ACM Trans. Networking, vol. 9, no. 3, pp. 307-321, June 2001.
[Mar01] M. Marchese. “TCP modifications over satellite channels: study and performance evaluation.
Internat. J. Satell. Commun. Network., vol. 19, no. 1, pp. 93-110, Jan./Feb. 2001.
[Cel04] N. Celandroni, F. Davoli, E. Ferro, S. Vignola, S. Zappatore, A. Zinicola, “An experimental
study on the quality of service of video encoded sequences over an emulated rain-faded
satellite channel, IEEE J. Select. Areas Commun., vol. 22, no. 2, pp. 229-237, Feb 2004.
[peach] http://www.diit.unict.it/users/apanto/peach.
[MPer] M. Marchese, Personal Communication.
[buff]
http://buffer.antifork.org
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SECTION C (ISTI & CNIT-Genoa)
RESOURCE ALLOCATION AND TCP TRANSMISSIONS VIA SATELLITE
Resource allocation is one of the main tasks of a network, where different users and services
must share a pool of common resources. In wireless networks, where bandwidth may be
relatively scarce with respect to cabled networks and environmental conditions may affect
channel quality, the dynamic control of allocated resources becomes a challenge. Typically,
control actions need to be exerted over a wide range of time scales, to cope with events that
may occur with intervals from milliseconds to minutes or hours. Quite a few works in the
literature ([1-4] in the satellite environment and [5-11] in different contexts, as some examples
among many others) have already been focused on optimal control choices, regarding CAC
and resource allocation. Satellite systems not only have to face variable load multimedia
traffic, but also variable channel conditions and large propagation delays. The variability in
operating conditions is due both to changes in the traffic loads and to the signal attenuation
on the satellite links, owing to bad atmospheric events, which particularly affect the
transmissions in the Ka band (20-30 GHz). It is therefore crucial to make use of adaptive
network management and control algorithms to maintain the Quality of Service (QoS) of the
transmitted data. The combined action among various layers of the network (from the
physical layer up to the application layer) might improve the performance of the overall
system, through a coordination of control actions, QoS mapping and cross-layer information
exchange for control purposes. However, this procedure is complex and difficult to obtain to
the widest possible extent, which would imply numerous cross-layer interactions and the
related exchange of signaling information. Moreover, architecting the layers, possibly with the
adoption of ad-hoc solutions, becomes of paramount importance in a situation of this type,
which may require the separation of the specific environment from the rest of the network
(e.g., by the introduction of performance-enhancing proxies or relay entities), in order to work
effectively. Much care has to be taken in these approaches, in order not to disrupt wise
layering principles, possibly leading to unstable system performance [12].
In the work summarized here, in order to obtain optimized policies for satellite bandwidth
allocation, we coordinate the actions taken in a satellite network at the physical layer (where
the fade countermeasure technique is applied) with the work that is done at the data link layer
(where the satellite bandwidth is allocated), thus obtaining a cross-layer optimization. Though
applied to a different traffic context, our approach follows the same philosophy as [1]. Besides
the cross-layer interaction, another feature characterizes our approaches, namely, a more or
less hierarchical multilevel structure of the bandwidth allocation and CAC strategies. These
aspects will carry over the various operative scenarios that we consider. Such scenarios may
be divided into two categories: one assumes the presence of both guaranteed performance
(inelastic, or Continuous Bit Rate, CBR) and best-effort (BE) traffic, without explicitly
characterizing the elastic behavior of the latter (as induced by TCP congestion control
mechanisms); the other considers only best-effort services, by explicitly modeling the effects
of TCP congestion control. Within these categories, a further subdivision regards the degree
of flexibility and adaptation of the bandwidth allocation: whereas CAC presumes the on-line
application of dynamic control strategies (and the same happens with fade countermeasures
at the physical layer), the bandwidth allocation may be effected in a more or less adaptive
fashion, according to the information available to the controllers and to their frequency of
intervention.
The report is organized as follows. In the next Section, we introduce the fade countermeasure
and the traffic models adopted. In the third Section, we treat the first case of mixed inelastic
and BE traffic. In doing so, we consider two different cases, depending on the kind of
information on channel conditions that is available for control adaptation purposes: i) the
static bandwidth allocation, based on the knowledge of long-term statistics (and, possibly, of
rough real-time information on weather conditions); the dynamic bandwidth allocation, based
on real-time measurements of fading attenuation levels. Section 4 is devoted to the analysis
of long-lived TCP connections, experiencing diverse fading conditions, and to their fair
bandwidth allocation, performed by taking into account the tradeoff between Bit Error Rate
(BER) and Information Bit Rate (IBR) upon TCP goodput. Section 5 presents and discusses
various numerical results, based both on analytical modeling and discrete event simulation.
Section 6 concludes the report, also giving some directions for further research.
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1. FADING AND TRAFFIC MODELS
1.1. Fading and fade countermeasure.
We consider a fully meshed satellite network that uses the Ka band (20-30 GHz) of a
geostationary satellite transponder as a bent-pipe channel, and we counteract the fade
attenuations of the signals, due to bad weather conditions, by applying adaptive FEC
(Forward Error Correction) codes and bit rates. This means that the fade is countered by
applying redundancy to the data before their transmission to the satellite, according to the
detected attenuation level of the signal. For the sake of simplicity, in order to avoid the use of
more complex traffic models, in all treatment involving the presence of inelastic CBR flows,
we assume that the attenuation experienced by each station is independent of the destination
of its traffic; this is the case where the fading is of the up-link-predominant type, or when all
the traffic sent by a station is addressed to destinations affected by the same environmental
conditions. This assumption will be relaxed when examining the case of bandwidth allocation
to TCP connections only.
A typical example of such a scenario may arise in handling a typical IS.MANET emergency
situation, caused by such a severe disaster that the terrestrial networks are unusable. Several
mobile ad-hoc networks (MANETs) may be set up, consisting of teams equipped with devices
for specific monitoring and data acquisition, plus a base camp, equipped with a satellite earth
station, which is in contact with the operative headquarters via a satellite link. The satellite
bandwidth is handled at the base camp (the master station), and distributed among the
MANETs according to optimization criteria. In each MANET, only one piece of equipment (the
traffic station) is able to make contacts with the base camp (to request and obtain the
bandwidth) and to transmit the data to headquarters, via a satellite link. In this scenario, it is
clear that all the traffic stations experience the same up-link fade, as they operate in the same
geographical area (restricted to a few square kilometers), and the same down-link fade, as all
the data are addressed to the headquarters.
Since the signal fade may vary in very short time intervals (even less than a second), in order
to avoid too many oscillations in applying the fade countermeasures according to each single
fade level variation, the measured value of the signal attenuation is categorized in a class f,
f=1,…,F, where F is the number of fade classes, equal for all the stations, so that the
countermeasure strategy adopted remains unchanged for all those levels of signal
attenuation that belong to the same class. Thus, for each type of traffic with a given Bit Error
Rate (BER) requirement, a fade class aggregates those fade levels that need the same data
redundancy (in order to keep the BER below a given threshold), expressed at station i by
(i)
redundancy coefficients rf , f=1, 2,…, F. They represent the ratio between the IBR in clear
sky and the IBR in the specific working condition. As non-guaranteed traffic and real-time
traffic usually have different QoS requirements in terms of BER, we indicate the respective
(i)
(i)
redundancies with rf , ng and rf , rt . The operative environment we refer to is a Multi-Frequency

Time Division Multiple Access (MF-TDMA) system, i.e., a network where the total capacity of
the satellite transponder is divided into carriers at different frequencies, each one accessed in
TDMA. We also assume that a traffic station cannot transmit at different frequencies in the

 Specific values of the redundancy coefficients and their computational
same temporal
slot.
procedure under a given link budget are also provided.
1.2. Traffic models and related performance indexes in the mixed (CBR/BE) traffic case.
As regards real-time, guaranteed-bandwidth traffic, it is modeled as Continuous Bit Rate
(CBR) guaranteed-bandwidth connections (voice or MPEG4 video), which may be carried
within some specific DVB (Digital Video Broadcasting) class [13]. The dynamics of interest
are at the connection level, and the relevant performance index is the call blocking probability
( Pblock ); this is the steady-state probability that an arriving call is refused because all the
bandwidth devoted to the real-time traffic is busy. Note that we assume that blocked calls are
lost (not re-attempted). For this type of traffic we adopt the usual birth-death model with
exponential distribution of call inter-arrival and duration times (Poissonian traffic). We assume
that all connections of station i belong to the same fade class, and have the same peak

rate B(i) ; then, we face a particular single-class case, where the expression of the blocking

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probability is given by the classical Erlang B loss formula [11]. At station i, given the Erlang
traffic intensity  (i)  (i)  (i) (where (i) [s-1] is the arrival rate of the connection requests,
and 1  (i) [s] is the average duration of each connection), and a desired upper bound on the
(i)
blocking probability  (i) , the maximum number of acceptable calls N max
is then derived as


(i)
N max

M


 (i)
M!


(i)
 maxM  N : Pblock
(M ) 
  (i) 
j
M
M 
 j0  (i) j! 


 
 
(1)
(i)
In this particular case, under a specific fading condition requiring redundancy rf , rt , the total

(i) (i)
(i)
bandwidth required to carry the maximum number of calls at station i would be B rf , rt N max .
More generally, a station might be in the multiclass case, where the connections that utilize a
given bandwidth portion have different statistical parameters and peakrates, and they belong
to different fade classes, as they may be addressed to destination stations that experience
 would require the
diverse down-link attenuations. Therefore, the transmission of the data
simultaneous application of different data redundancy values. In this multiclass case, which
we intend to analyze in a wider forthcoming study, the blocking probability would result from a
stochastic knapsack problem [11]. The situation can be kept always in the single class case if
the bandwidth is assigned separately per fading or traffic class inside the earth station.
As far as the best-effort traffic is concerned, we assume that it originates from non-real-time
data packets that are fragmented into fixed-size cells (ATM or DVB [13]) before transmission
on the satellite channel. This traffic stems from the aggregation of packet bursts, generated
by a high number of sources, and may include TCP/IP short-lived connections and UDP/IP
flows with no particular bandwidth reservation. At each station i, cells are queued in a finite
buffer of capacity Q(i). In this context, the quantity of interest is the cell loss probability ( Ploss)
in the queue of station i . In order to derive an approximate evaluation of this quantity, we
consider a discrete-time self-similar traffic model. This model represents the superposition of
on-off sources, whose active periods (bursts) have Pareto-distributed ‘on’ time
  c 1 , 1   2,
( Pr  

where  and c are the parameter of the 
discrete Pareto
distribution and its normalization constant, respectively). The detailed description of the
model, which yields an upper bound on Ploss, can be found in [14, 15]. Actually, various
possible models can be adopted to approximate the cell loss probability, given the statistical
characteristics of the burst generation and a fixed rate of extraction of cells from the buffer
[15, 16, 17]. A more specific formulation of Ploss is reported in the Appendix.
In our case, we have to take into
account that the extraction rate is determined by the residual
(i)
capacity Cnrt
(t) , available for the non-guaranteed traffic after serving all guaranteed-
(i)
bandwidth connections in progress
 at the required peak transmission rate B . Namely,
C (i)  B(i) r (i) (t)n(i) (t) if B(i) r (i) (t)n(i) (t)  C (i)
(i)
f ,rt
f ,rt
Cnrt (t)  
0
otherwise

where C

(i)
(2)

(i)
(i)
is the capacity allocated to station i , and n (t) and rf , rt (t) are the number of
guaranteed traffic connections in progress at time t, and the data redundancy factor applied to
them, respectively. Therefore, the residual bandwidth is a random variable; as a
consequence, the loss probability at fixed capacity can be considered only as conditional on
 be computed with respect to the
the number of connections in progress, and its average must
statistics of the Markov chain that describes the connection dynamics 1.
1
In computing the average, the fact that the time scales of the guaranteed and non-guaranteed traffic are widely
different can be exploited, in order to use independent stationary distributions for both. In other words, the
guaranteed traffic process is supposed to be quasi-stationary, so as to use the conditional Ploss expression at
June 2005
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Thus, the
(i)
Ploss

C
(i)
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P
loss that we consider is the average one,
(i)
, rf ,nrt , to stress the dependence on the allocated

from here on indicated as
bandwidth, as well as on the
redundancy coefficient for non-real-time traffic (see the Appendix for the detailed expression).
As previously mentioned, the real-time and the non-real-time traffic generally have different

QoS requirements in terms of BER (realistic values of BER indicate about 10 -4 for real-time
voice connections and MPEG4 video [20], and at least 10-7 for best-effort traffic).
Consequently, the redundancy to be applied to the latter is normally higher than the other
one. This redundancy factor further reduces the effective residual capacity. The dependence
on the redundancy factors, which are time-varying quantities, deserves a further comment. In
fact, all previously discussed calculations regarding the performance indexes have
considered the current values of these coefficients as lasting forever. Whereas this is true in
the “static” case (where, for the purpose of bandwidth allocation, the redundancies are
considered as unknown random values with known probabilities), it is not in the “dynamic”
case, where they are recomputed at each change of fade class. The resulting dynamic control
scheme is thus a sort of “open-loop feedback” repetitive control [21], where the initial time
continuously shifts ahead.
1.3. Traffic model for long-lived TCP connections
In this sub-section we outline the model used to derive analytical expressions of the goodput
of long-lived TCP connections, which is the performance measure to be used in the
bandwidth allocations to be considered in Section 4. For the sake of simplicity, we refer to a
single link. When a number of long-lived TCP sources share the same bottleneck-rate link, it
was empirically observed in [22] (by making use of simulation) that, if all connections have the
same latency, they obtain an equal share of the link bandwidth. This is strongly supported by
our simulations, as well [23]. As the latency introduced by a geostationary satellite is quite
high (more than half a second), it is reasonable to assume that the additional one introduced
by the satellite access network in the entire path is negligible with respect to the satellite one,
and that all connections have the same latency.
In order to avoid time consuming simulations, reasonable estimations can be constructed for
the goodput of a TCP Reno agent. A first relation that can be used is the one taken from [24],
which is estimated for infinite bottleneck rate, and thus it is valid far apart the approaching of
the bottleneck rate itself. Let  be the bottleneck (the satellite link) rate expressed in
segments/s, n the number of TCP sources, and  the delay between the beginning of the
transmission of a segment and the reception of the relative acknowledgement, when the
satellite link queue is empty. Moreover, let us assume the segment losses to be independent
with rate q . We have 
  cl 1/  , where cl is the channel latency. The TCP connections that

share the same link also share an IP 
buffer, inserted ahead of the satellite link, whose
capacity is at least equal to the product  . Let also b be the number of segments
acknowledged
received by the sender TCP, and To the timeout
 by each ACK segment

estimated by the sender TCP. Then, by exploiting the expression of the send rate derived in



for normalization
 and multiplying it by 1 q for a better approximation,
n
 as
the relative goodput (normalized to the bottleneck rate) can be expressed
[24], dividing it by
Tg 

1 q



3bq 
  2bq
 To min 1, 3
q(1  32 q 2 )


n 
3
8 


.
(3)
Relation (3) is rather accurate for high values of q , i.e., far apart the saturation of the
bottleneck link. For low values of q , it is found by simulation that, given a fixed value of cl , for



constant rate, and the non-guaranteed
traffic queue is supposed to reach steady-state between successive
jumps in
the Markov chain [18, 19].
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  5
fixed values of the parameter y  q    , the goodput has a limited variation with respect
n 
to individual variations of the parameters q ,  and n . Owing to the high number of
2
simulations needed to verify this observation, a fluid simulator (TGEP) has been employed
[25], which was validated by means of ns-2 [26], for values of y  1. Simulation results have
been obtained for thegoodput estimation, with a 1% confidence interval at 99% level, over a

 

range of values of
between 20 and 300, and n between 1 and 10. For 0  y  1, goodput
n
 more than 8% from their mean. We
values corresponding to the same y never deviate for
then interpolated such mean values with a 4-th order polynomial approximating function,
 with the least squared errors
whose coefficients have been estimated
 technique. Assuming a

constant cl , equal to 0.6 s (which takes into account half a second of a geostationary satellite
double hop, plus some processing time), in the absence of the so-called Delayed ACKs
option ( b 1), the polynomial interpolating function results to be

Tg  ao  a1 y  a2 y 2  a3 y 3  a4 y 4 ;
y 1
,
(4)

where ao  0.995; a1  0.11 [s 3 ]; a2  1.88 [s 6 ]; a3 1.98 [s 9 ]; a4  0.63 [s 12 ] .

For y  1, Tg  0.575. For y  1, we adopt relation (1), with b  1. The adoption of relation (2)
for y  1, instead of relation (1), with 1 as an upper limit, allows reducing the approximation
 error, which would otherwise reach 25%, within about 8%.
 Gaussian Noise (AWGN) channel (a
Ifwe assume to

 operate on an Additive White
reasonable approximation for geostationary satellites and fixed earth stations), the segment

loss rate q can be computed as [27]:
l
q 1 (1  pe le) s ,
(5)
where pe is the BER, ls is the segment length in bits, and le is the average error burst length
(ebl). We took pe data from the Qualcomm Viterbi decoder data sheet [28] (standard NASA
1/2 rate with constraint length 7 and derived punctured codes), while le was obtained through
in [27]. Since we needed
 numerical simulation

 to evaluate the BER and error burst
characteristics for BER values even less than 10-9, we resorted to extrapolation for some

points. The complete set of data is plotted versus Ec / N 0 (channel bit energy to one-sided

noise spectral density ratio) in [27]. In order to make q computations
easier, we interpolated
such data, and expressed pe and le analytically, as functions of the coding rates considered
and the Ec / N 0 ratio [23, 29]. The TCP goodput relative to the bottleneck rate is a decreasing

function of the segment loss rate q , which, in its turn, is a decreasing function of the coding
redundancy applied
 in agiven channel condition C / N 0 (carrier power to one-sided noise
spectral density ratio; see Section 5 for the relation between C / N 0 and Ec / N 0) and for a
given bit rate br . As already
 noted, the combination of channel bit rate and coding rate gives
rise to a “redundancy factor”, which, in 
this case where no ambiguity is possible, will be
indicated simply by rf . The absolute goodput of each TCP connection Tˆg is obtained by


multiplying
the relative value by the bottleneck rate, i.e.,


1 C
Tˆg  T g  T g 
n r
n
(6)
where C is the link rate in segments/s in clear sky conditions. The expression of the goodput
we have derived will be exploited in Section 4 in the bandwidth allocation among TCP
connections experiencing different fading conditions.

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Alternative analytical expressions of the TCP goodput and of the packet loss probability
caused by congestion, used to model the behaviour of TCP over geostationary satellite
channels, have been derived in [30], and have been used in the cost functions of control
mechanisms, such as the bandwidth allocation schemes in the presence of mixed guaranteed
performance and best-effort traffic, where long-lived TCP traffic flows are explicitly considered
(besides UDP and short-lived TCP connections). This approach is particularly useful when
the packet loss probability is the metric of the control rules [31].
2. BANDWIDTH ALLOCATION AND CAC IN THE PRESENCE OF
GUARANTEED BANDWIDTH AND BEST-EFFORT FLOWS
In many studies of resource allocation, a simple complete sharing (CS) policy is used, i.e.,
connections are admitted simply if sufficient resources are available at the time of the
request, without considering the importance of a connection when they are allocated. In the
complete sharing policy, the only constraint on the system is the overall capacity C. As an
almost opposite situation, in the set of policies of complete partitioning (CP) type, every class
of traffic is allocated a set of resources that can be used only by that class.
Other policies have been derived to provide optimized access to resources, and Ross [11]
provides an extensive discussion about a number of different solutions. Optimal approaches
should be based on Markov decision processes, given a certain cost functional to be
minimized (or maximized) as a performance index; however, they must take into detailed
account any allowable network state and state transition, which is impractical even for
networks of modest complexity. The functional form of the optimal policies is usually
unknown. Therefore, a set of generally suboptimal policies with fixed structure (which can be
often described by a set of parameters), have been developed, which are simpler to
implement and, in some special cases, do correspond to the optimal one: among others, the
above mentioned CP, trunk reservation (TR) [32], guaranteed minimum (GM) [36], and upper
limit (UL) policies [33, 34]. Comparisons have been made between these policies and the
optimal one. The results indicate that the CP, TR, GM, and UL policies outperform the CS
one when significant differences among classes exist in requirements for bandwidth and
offered load [35]. Obviously, once one of such fixed-structure policies has been selected,
parametric optimization can be adopted, in order to choose the “best” values of parameters
that minimize a given cost function (or maximize a performance index). This is the approach
we have taken. Moreover, whereas the presence of best-effort traffic is most often neglected
in this case, we take it explicitly into account when designing the cost function that determines
the bandwidth partitioning.
Our allocation policies fall in the CP category, but it is important to highlight that as the
partitions are adaptively changed in response to traffic or fading variations, they try to match
the traffic load and channel conditions as closely as possible. In this respect, the philosophy
of this approach is much in the same line as that of [18]; however, the major novelty
introduced here is in the cross-layer optimization, which stems from the explicit presence of
the redundancy factors representing the fade countermeasure in the cost function.
2.1. Local CAC
As we mentioned, all control schemes we are considering exhibit a hierarchical structure. A
lower level performs CAC (and implicit bandwidth allocation between CBR and BE traffic) at
each station within a given bandwidth, whereas a higher one is devoted to bandwidth
allocation (static or dynamic) among earth stations. The lower level allocation algorithm acts
with a faster timing than the upper one, and it is located at each earth station i. It shares the
bandwidth C (i) , allocated to station i, between guaranteed ( Crt(i) [bits/s]) and non-guaranteed
(i)
( Cnrt
[bits/s]) traffic, by imposing a constraint on the call blocking probability. It performs Call
Admission Control (CAC) of the incoming guaranteed calls and measures the statistics
necessary
for successive allocations.



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Given the bandwidth C (i) , allocated to station i, the lower level optimization problem evaluates
(i)
the threshold N max
as in (1), so that the call blocking probability be, if possible, below  (i) . If,
(i) (i)
(i)
(i)
at time t, B rf , rt (t)N max  C , the available bandwidth is shared between the CBR and BE
 a portion sufficient to guarantee the required QoS (represented by  (i) ) for
flows, assuring
(i)
CBRtraffic, and the CAC threshold is N max
; otherwise, all the bandwidth isassigned to the



. Both from the
(i) (i)

B
r
(t)


f
,
rt


guaranteed traffic, and the CAC threshold is given by 
C (i)

computational and the technological
point of view, it is simpler to assume that
C (i)   : C (i)  k  mbu,  k  N , C (i)  C , i.e., that the bandwidth is assigned in multiples
of some minimum bandwidth unit (mbu). It is worth noting that, owing to the dynamic fade

changes, there may be time intervals where the assigned bandwidth C (i) is insufficient to
carry the currently ongoing number of CBR connections in the station (i.e.,

C (i)  B(i) rf(i), rt (t)n (i) (t)); since we are considering inelastic traffic, in such situations one or
more ongoing calls would be dropped. This is a situation over which
 we have no direct control
(except immediate signaling to the master station in the dynamic case), and a good design
should minimize its probability.

2.2. Bandwidth allocation in the “static” case
We refer to the static case as one where, for the purpose of bandwidth allocation, fading is
not intended as instantaneous, but it is described by the probability that a certain station has
to be in a given range of fade values, owing to its geographical position. This is “a priori”
information, derivable from long-term statistics. It may be complemented by the knowledge of
a given station being either in “clear sky” or “rain” conditions, without any specification of the
actual fade level. The case of real-time knowledge and explicit usage of fading levels on the
part of the master station will be referred to as the “dynamic” one (note the earth stations are
always supposed to measure and utilize fading locally).
An upper level control scheme is implemented in the master (hub) station. It allocates the
available bandwidth C [bit/s] by assigning a portion C (i) [bits/s] of the total bandwidth to each
earth station i. The algorithms considered for the allocation in the static case have been the
OC-ABASC (Optimal Channel-Adaptive Bandwidth Allocation in Satellite Channels), and the
CAP-ABASC (Constrained Average Probability) method, indicated in the following simply as
CAP; both were introduced in [36, 37] and
 studied in a real case in [38]. The first method
does not take into account any degradation of the satellite link, as, instead, the CAP method
does. In the CAP method, the fading effect on the channel “seen” by station i is modeled as a
reduction of the capacity C (i) allocated. The real capacities utilized by station i’s real-time
(i)
(i)
rf(i), rt
and best-effort traffic may be written as Creal, rt  C
(i)
(i)
(i)
and Creal, nrt  Cnrt rf , nrt ,
(i)
(i)
(i)
(i)
respectively. To each value rf , rt ( rf , nrt ), a probability p f , rt ( p f , nrt ) is associated, which can
 long-term statistics. For a given geographical site, the latter are extracted
be derived from the
from the ITU-R interpolation formula 
[39], which estimates the
 attenuation exceeded for a
percentage p of an average year, when the attenuation A0.01 exceeded for 0.01% of a year is



known for the site. 
The CAP mechanism works as follows. A strong penalization is introduced if the average
(over
of the system is above the fixed threshold.
 the fading levels) call blocking probability

This is accounted for by a penalty function of the type:
 

(i)
0 if Pblock
C (i)   (i)
F (i) C (i)  

otherwise

 
(7)
(i)
Here,  is a sufficiently large number, and the function Pblock
() in (7) is defined as the call
blocking probability of station i, averaged over the fading levels:


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 
ISTI
 
F
(i)
(i)
(i)
(i)
÷(i)
Pblock
C (i)   p (i)
f , rt  Pblock N max C , rf , rt
f 1
Deliverable WP6D5

(8)
(i)
where Pblock
is given by the Erlang B formula as in (1) and



(i)
(i) (i)
(i)
÷
N max C , rf ,rt  min N max
,



 C (i) 


(i) (i) 
B
r

f , rt 



(9)
Then, one can define the following cost function for station i, as seen by the master station,



 
(i)
(i)
J (i) (C (i) )  Ploss
C (i) , rf(i),nrt  Fcap
C (i)
(10)
The goal of the master station is find the capacity assignments that minimize the expected

(i)
(with respect to the probability distribution p f , nrt ) global cost:
N
J(C (1) ,C (2) ,...,C ( N ) )  
i1
(i)
p (i)
C (i) , rf(i), nrt 
 
f , nrt  J 
F
f 1
(11)
under the constraints

 N
 C (i)  C
i1
 (i)
(i)
C  0, C  Cc , i  1,...,N
(12)

where
Cc is the maximum allowable information rate for each carrier.
Though the assignment considers a stationary situation with respect to the traffic, it can be
obviously repeated, in an adaptive fashion, whenever the traffic statistics would change.

2.3 Bandwidth allocation in the dynamic case.
This is the case of adaptive hierarchical control, where the bandwidth assignment not only
follows traffic variations adaptively, but also fading variations, of which the master station is
aware. In [40] we studied a centralized allocation policy based on the solution of a discrete
optimization problem, and we demonstrated that the combination of periodic (synchronous)
and event-driven (asynchronous) decisions on the bandwidth allocation gives the best results
in terms of call blocking and data loss probabilities of the entire system. The limit we found
was on the computational time required by the master to calculate the allocations. Actually,
this time can be considerably shortened, by introducing explicit constraints on the minimum
and maximum bandwidth assignments allowable in the optimization problem [41]. The
master’s optimization criterion, improved with respect to the one presented in [40] by the
introduction of constraints, is referred to as "Optimized Centralized" (OC). In OC, the master
adopts an allocation policy that is optimized for the whole system; the traffic stations can only
trigger a re-allocation procedure, without explicitly indicating a specific amount of bandwidth.
This is similar to the previously described static case, with a main difference regarding the
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use of fading information, which is now explicitly accounted for by the master station: the
redundancy coefficients used by the earth traffic stations are communicated in real time to the
master, which uses such measured realizations in the bandwidth allocation, rather than
computing expectations on the basis of the probability distributions derived from weather
forecast scenarios, as in (8) and (11) above. In addition to OC, we also investigate another
“dynamic” allocation policy, referred to as “Optimized Proportional” (OP), where the master
acts passively, only making assignments proportional to the requests received. Each of these
requests is the result of an optimal policy local to each traffic station, based on fading
measurements and predictions derived by traffic models.
We consider a control architecture which comprises three time scales: a) the time interval E
during which a fade class remains unchanged at station i (fade class time interval); b) the
time interval s during which each traffic station estimates its fade level (frame time interval); c)
the duration w of a traffic station’s data transmission (transmission window). The different
temporal time scales are depicted in Fig. 1.
Reschedu li ng
requ ired
E1
E2
FC x
eva luate fade level
FC x+1
frame y
trans mi ssionw indow
Fig. 1. Time intervals at station i. FC x stands for “Fade Class x”.
The master station re-computes the bandwidth assignments each time at least one traffic
station notifies that its fade class has changed, or each time a station enters or leaves the
network. The computation is done as if the allocations had to last forever; in principle this is
true, because the allocations remain unchanged when system conditions are stable. The
allocations are upper- and lower-limited. The constraint relevant to the minimum assignment
is specific to each single station i; namely, the already outstanding connections of station i
must be maintained, in order to prevent the relevant call dropping probability from reaching
unacceptable values. The constraint relevant to the maximum assignment is common to all
stations: the bandwidth assigned to a single station cannot exceed the single carrier capacity.
At station i, the number of supportable call connections depends on the bandwidth allocated
to the station, and on the call blocking and cell loss probability thresholds the station has
imposed.
In order to compute the allocations, the master utilizes the most recently received (at time t)
(i)
vectors v(i) (t) , simply indicated by v , (i=1, 2, …, N, where N is the number of stations),
which contain information relevant to each individual traffic station. This vector assumes
different meanings, according to the allocation policy adopted. When the OC policy is applied,
(i )
( i)
v
collects the mean real-time traffic intensity  [Erlang], the best-effort traffic burst
(i)
intensity burst [burst/s] and mean burst length  , together with the last redundancy
coefficients applied to data for the two types of traffic, and the current fade class indication. In
(i )
the OP policy, v represents the total bandwidth request, expressed in minimum bandwidth
units (mbu, which represents the minimum bandwidth granularity). This value is
comprehensive of the station’s need to accommodate both the real-time connections and the
best-effort traffic within the desired respective QoS requirements. The traffic stations only
know the separate values of the real-time and non-real-time traffic requests individually.
(i)
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(i )
In the OC case, on the basis of the last updated v
values, the master computes the
bandwidth to be allocated to each station, by minimizing a cost function relative to the whole
system.
In the OP case, the master simply assigns portions of bandwidth to the stations proportional
to the amount of the requests, up to the maximum bandwidth that can be allocated to each
station.
(i)
Whatever the allocation policy used, the master sends the capacities C , assigned to each
station i , in a reference burst (RB), which is transmitted at the beginning of each frame
interval s. The assigned capacity remains unaltered until a new reallocation is executed.
The fade class time interval is typical of each traffic station. It is the time interval between two
consecutive changes in the fade classes. The length of thistime interval is unpredictable: it
goes from 1 second (chosen as the minimum value) till the duration of the entire satellite
session. In this time interval, each traffic station performs its call admission control (CAC)
(i)
procedure. At each change of fade class, within the received capacity partition C , the
(i)
station i re-computes the threshold N max on the maximum number of acceptable call
connections, given the relevant bandwidth requirements (which depend on the data
redundancy needed), and the desired upper bound on the call blocking probability. This
threshold serves the purpose of the CAC, which is performed locally at 
each traffic station,
independent of the bandwidthallocation method used by the master. At each change of fade
(i)
class, station i sends the master the previously mentioned information vector v , thus
causing an immediate rescheduling procedure.

The frame s is a fixed time interval, in the order of ms. It begins with a reference burst (RB,
sent by the master) which contains the current bandwidth allocation plan of all stations in the
time-frequency space. In each frame s all stations measure their up- and down -link
attenuations. In order to filter out the background noise and the major part of the scintillation
effect [42], the attenuation values are averaged over an interval of 1 second to make
attenuation estimation. The attenuation values are used to compute the fade class of each
link (see Section 5) and the redundancy coefficients needed by each class of traffic. In the
(i)
OC case, this information is sent to the master in the vector v . The techniques used to
estimate the signal attenuation are beyond the scope of the present work; a possible method
can be found in [43].
By using the most recently measured attenuation value and the ensuing classification and
redundancy, each station transmits its data in the assigned transmission window w, according
to the received transmission time plan. Moreover, each station sends the master,
piggybacked with the data, the information on the latest fade level measured. As previously
stated, in order to allow the evaluation of the link-by-link fade classes, the master redistributes
this information within each RB. In general, the various data flows sent by a station may
experience different down-link fading conditions, according to their destination.
2.3.1. The Optimized Centralized strategy (OC)
In this strategy the traffic stations do not communicate explicit bandwidth requests to the
master station, but they send the previously defined information vector v ( i) at each change of
the current fade class.
To allocate the portions of bandwidth, the master computes a cost function, which takes into
account the costs pertaining to the single stations. As before, the goal is to obtain the “best”

bandwidth assignments, which represent the parameters to be optimized, while keeping the
system’s constraints satisfied. Indeed, the rationale behind the cost function is to set a penalty
on bandwidth assignments that would push the partition for real-time traffic at each station i
below the minimum bandwidth necessary for that station to satisfy its constraint imposed on
the call blocking probability. On the other hand, for bandwidth assignments that do not violate
this constraint, the loss probability of best-effort traffic is considered as a cost. The measured
values of the redundancy factors, as known to the master station, are used in the evaluation of
the cost. This allows taking into account the most recent channel characteristics, and
effectively binds the “layer 2” decision made here with the physical layer BER control, in a
cross-layer optimization, which is one of the main objectives of our approach. The cost
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function is computed exactly as in (8)-(12), with the exception that now all quantities are
calculated with respect to the current values of the redundancy coefficients, and the respective
probabilities are all 0, except for the value corresponding to the given realization, which is 1.
Note that, in this case, the upper bound  (i) is to be intended relatively to the blocking
(i)
probability stemming from the given value of rf , rt , rather than to the average. Additional
constraints
C (i)  n(i) (t)rf(i),rt (t)B , i 1,...,N

(13)

must be added to guarantee the continuation of connections in progress at the instant of
reallocation. It is worth noting that the minimization can be effected by means of Dynamic
Programming [11, 40, 41], since the cost function is separable in the discrete decision
variables. This is true for both the present dynamic case and the static one considered earlier,
but the issue is more relevant here, since calculations are likely to be much more frequent.
The algorithm reported in [11] has been suitably modified [41], to keep into account the
presence of the constraints. It is worth noting that the presence of constraints can greatly
reduce the search space, speeding up the computational time of the algorithm. For example, a
further reduction may be obtained by imposing the values of the previous assignments as the
upper bound for those stations that did not signal any increase of bandwidth need (i.e., no
deeper fade or higher traffic load), while the previous assignments can be imposed as lower
bounds for stations that signaled an increase of bandwidth need.
(i)
(i )
The problem admits at least one solution C  Copt, i  1, ..., N , if
N
( j)
B( j) rf( ,j)rt (t)  C ,
 N max
j1
where C is the total available bandwidth in the system. Otherwise, the master computes the
allocation as




(i)
(i) (i)


N
B
r
(t)
max
f
,
rt
C (i)  min C  N
, Cc 


N ( j) B( j) rf( ,j)rt (t)
  max

 j1



(14)
i.e., proportionally to the foreseen bandwidth need of real-time traffic.
2.3.2. The Optimized Proportional strategy (OP)
In this strategy, at each time frame the traffic stations send the master requests for explicit
bandwidth values. A request is issued for obtaining the minimum bandwidth necessary to
support both types of traffic of the station, under given QoS constraints on call blocking and
cell loss probabilities. The master simply assigns the bandwidth proportionally to the requests
received. The problem of how to compute the request is solved within each station. Various
methods may be applied. For example, the Erlang B formula may be used at station i to
compute the bandwidth required for real-time connections, while the bandwidth necessary for
the best-effort traffic transmissions can be obtained by considering a constraint imposed on
the average loss probability ( Plo(i)ss   (i) ). The latter can be easily derived, by considering the
expressions reported in the Appendix.
2.3.3. The Sensitivity Estimation Approach
The aforementioned optimization approaches act according to a parameter adaptive certainty
equivalent control. Namely, a mapping between the statistical behaviour of the system and
the parameters of the functional costs in (10), (11) must be periodically performed in real
time, in order to maintain good performance of the resource allocation algorithm. Each time a
change in the statistical behaviour of the system is detected, a call to an optimization
procedure guarantees the maintenance of the optimal resource allocation. Actually, it is
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necessary to periodically perform a mapping between the current state of the network (in
terms of traffic sources and fading levels) and the parameters of the employed closed form
functional costs.
Two drawbacks deteriorate the performance of such a strategy. The first one concerns the
presence of errors over the measures performed on line to estimate the current state of the
network. The second one regards the possibility that the current statistical behaviour of the
system does not conform to the hypotheses assumed a-priori to provide a particular closed
form expression of the performance index. On the other hand, it is also remarkable that
closed forms for important performance measures (e.g., mean delay and delay jitter of the
packets) are not always available (for example in the presence of self-similar traffic), and, in
general, it is difficult to assure that in a real application scenario some strict hypotheses are
verified. Moreover, the on-line implementation of Dynamic Programming in a real context may
become quite impractical, due to the well-known curse of dimensionality problem.
In this perspective, the application of algorithms, able to estimate the sensitivity of the
performance measure, may help in providing sub-optimal control decisions, without the
adoption of closed form functional costs and the application of computationally expensive
optimization techniques. Sensitivity estimation algorithms are based on the so-called
Perturbation Analysis (PA) technique. PA is a sensitivity estimation technique for Discrete
Event Systems (DESs). It is based on the observation of the sample paths followed by the
stochastic processes of a DES and gives an estimation of the derivative of the performance
index, allowing the application of a gradient-based algorithm, in order to optimize the system
performance. Such optimization approaches are known in the literature as on-line surrogate
optimization methodologies, because they act in real time, with a gradient-based algorithm,
by applying a “surrogate” relaxation of the discrete functional cost [44].
We briefly summarize the control structure of an on-line surrogate optimization methodology,
suitable for the network problem under investigation, adopted in [45, 46]. Let L(C (i ) ) be the
performance metric of interest (for example the loss volume at the packet or at the call level).
Our aim is to apply an estimator for the derivative of such performance index. To do this, it is
firstly necessary to “relax” the discrete constraint set, denoted by  d :

 d  C d (t )   N : C d (t )  hi (t )  MAU , hi (t )  ,


C
(i )
d (t )
i 1
into a continuous one, denoted by  c . Then, the gradient

 C ; MAU  Minimum Allocation Unit

L(C c(i ) )
C c(i )
is used to optimize a
continuous bandwidth allocation C c with the following surrogate constraints:
N


C c   c ,  c  C c(i )    ; i  1,..., N ; C c(i )  C 
i 1



If L () is the loss volume of a traffic buffer, the computation of such a gradient is detailed in
[47]. If L () is the blocking probability of the connection requests, details about the gradient
estimation can be found in [48]. In both cases, a PA technique is studied to compute the
gradient estimation only as function of the sample paths of the stochastic processes involved
in the system. No further knowledge about the statistical properties of the traffic sources is
necessary.
The following scheme illustrates each step of the on-line surrogate optimization algorithm, in
relation to the minimization of the overall packet loss probability of N traffic buffers (located in
different earth stations). Let tˆ be the delay latency of the system (around 1.0 second for a
satellite network). Initially, the bandwidth resources are equally distributed among the stations
and, during the system evolution, for every t  tˆ,   1,2,..., each station i must:
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1. observe the buffer temporal evolution during the time interval [(  1)tˆ, tˆ] according to the current sample
path i and bandwidth allocation C d(i ) [(  1)tˆ], C d [(  1)tˆ]   d ;
2. compute the derivative estimation
L(Cc(i ) [(  1)tˆ])
Cc(i )
through Perturbation Analysis [51];

3. adjust the value of its “bandwidth allocation need“ using the gradient method:

L(Cc(i) [( 1)tö]) 
 (   () being a projection operator);
Cc(i) [tö]    Cc(i) [( 1) tö]  


Cc(i)


4. communicate such Cc(i ) [tˆ] to each master station;


5. (for each station that has the role of master station),
by looking at the information received by the other stations (i.e., Cc( ) [(  1)tˆ],   1,..., N ;   i ), and, on
the basis of the local bandwidth need Cc(i ) [(  1)tˆ] ,
convert Cc [(  1)tˆ] to the nearest discrete feasible neighbor Cd [tˆ] in such a way that Cd [tˆ]   d ;
such conversion defines the bandwidth allocation for the satellite system in the time interval
[tˆ; (  1)tˆ] .
The nearest feasible neighbor Cd [tö]  d of C c [(  1)tˆ] can be determined, at step 5, by
using a O(N+1) algorithm, based on the N+1 discrete neighbors of C c [(  1)tˆ] , not
necessarily all feasible, and on the selection of one of them, which satisfies the discrete
constraint set  d . 
The gradient-descent algorithm of step 3 allows a decentralization of the optimization
procedure. We suppose that a personal processor is assigned to each station i; in this way,
the optimization procedure runs in parallel on each independent processor located in each

station. Such distributed computation is a very attractive property, as it enables each station
to compute its “optimized bandwidth need” locally on the basis of the current behaviour of the
stochastic processes.
The temporal evolution of the optimization procedure is depicted in Fig. 2. We denote by
I i [tˆ] the information available for the (currently active) master station i, at the reallocation
time instant tˆ (i.e.: Cc( ) [(  1)tˆ],   1,..., N ). I i [tˆ] is necessary to perform the
aforementioned “surrogate to discrete” mapping C c [(  1)tˆ] => Cd [tˆ] and to deploy the
bandwidth allocation for the next time interval [tˆ; (  1)tˆ] .
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Fig. 2. Bandwidth allocation timing at each step of the optimization procedure.
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BANDWIDTH ALLOCATION FOR TCP FLOWS
In [27], the application of adaptive FEC (Forward Error Correction) techniques was
investigated, to optimize the efficiency of TCP connections when transmitted over rain-faded
geostationary satellite channels, with fixed user antennas, as in the environment that we
consider now. We have adopted the same philosophy in [23, 29, 49], by trading the
bandwidth of the satellite link for the packet loss rate due to data corruption. In fact, over
wireless links, any gain in the bit error rate (BER) (thus, in the packet loss) is generally
obtained at the expenses of the information bit rate (IBR), and the goodput increases with the
IBR and decreases with the BER. The FEC techniques adopted do not interfere in any way
with the normal behaviour of the TCP stack, as they are applied just before the transmission
over the satellite link. It has been shown in [27] that, given an available radio spectrum,
antenna size, and transmission power, the selection of an appropriate modulation scheme
and a FEC type allows choosing the BER and the IBR of the link that maximize the goodput
of a TCP connection. This optimization can be done for different channel quality conditions
caused, for example, by atmospheric events. The optimal transmission parameters, for each
channel condition, can be reported in look-up tables and then applied in an adaptive fashion.
Connections take place within different source-destination (SD) pairs over satellite links,
which may be generally subject to diverse fading conditions, according to the atmospheric
effects at the source and destination stations (i.e., on the up- and down-links). We refer to
connections on the same SD pair, which experience a specific channel condition, as
belonging to the same “class”; they feed a common buffer at the IP packet level in the traffic
station, which “sees” a transmission channel with specific characteristics (that may differ, in
general, from those of other SD pairs originating either from the same station or from other
stations). The bandwidth allocated to serve such buffers is shared by all TCP connections in
that class, and, once fixed, it determines the “best” combination of bit and coding rates for the
given channel conditions. The goal of the allocation is to satisfy some global optimality
criterion, which may involve goodput, fairness among the connections, or a combination
thereof. Therefore, in correspondence of a specific channel situation, determined by the
various up- and down-link fading patterns, and a given traffic load, we face a possible twocriteria optimization problem, whose decision variables are the service rates of the above
mentioned IP buffers for each SD pair, and the corresponding transmission parameters. We
will refer to these allocation strategies as TCP-CLARA (Cross Layer Approach for Resource
Allocation), and we will analyze a few different criteria. In all cases, the indexes chosen for
the performance evaluation of the system are the TCP connections’ goodput and the fairness
of the allocations. The optimal allocations are derived numerically on the basis of an
analytical model, under different fade patterns. A possible pricing scheme has been also
derived in this context [23], based on the fact that each class of TCP connections “sees” a net
bandwidth that is generally obtained at the expense of diverse channel redundancy. The
different strategies have been compared first in a static fading scenario [29] and then in a
dynamically varying one [49], with fading traces taken from real-life samples. In this case, the
allocation is applied adaptively, following the fading and traffic variations, similarly to the
dynamic situation considered in the previous section.
3.1. Goodput-fairness tradeoff.
The problem we address in the following is thus the assignment of bandwidth, bit and coding
rates to the IP buffers that serve each specific link, given the rain fading conditions and the
traffic load of the satellite network. We make the following assumptions.
1. The end-to-end delay of the TCP connections is the same for each station.
2. In each station, there is an IP buffer for each SD pair, and we say that the TCP
connections that share it belong to the same class; obviously, they experience the same uplink and destinations’ down-link conditions.
3. In defining and solving the optimal bandwidth-redundancy assignment problems, we
consider the system in static conditions. In other words, given a certain number of ongoing
connections, distributed among a subset F of SD pairs, characterized by a certain fading
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attenuation, we find the optimal assignment as if the situation would last forever. Clearly, in a
dynamic environment, under variable fading conditions and with starting/ending TCP
sessions, a possibility is to perform our calculations at each change of parameters. It is worth
noting that this simple form of adaptation, though involving some cross-layer interaction, does
indeed maintain a flavor of separation principle, as is common in adaptive control and, as
such, represents a “cautious” approach, in the sense of [12], not violating any basic layering
concept. However, care has to be taken with respect to possible fast fading variations, which
might cause oscillations in TCP behavior.
Since there is no more need to distinguish between station and fade class, we will use the
single index f in the following to indicate the fading class. We assume that, if the fading
(f )
conditions of an active class f (f = 1,2,…, F ) are such that a minimum goodput Tg, thr cannot
be reached by its connections, the specific SD pair is considered in outage, and no bandwidth
is assigned to it.
 
Let Bf  0,W (where W is thetotal bandwidth to be allocated, expressed
in segments/s),



rf  R (1),...,R (P ) , and nc( f ) , f 1,...,F , be the bandwidth, the redundancy factor, chosen


in the set of available ones (each value R , k  1,...,P , corresponds to a pair of bit and
coding rates), and the number of connections, respectively, of the i-th SD pair. In case
different bit and 
coding rates yield the same redundancy factor, the pair will be selected that
gives rise to the minimum BER.
(k )

The bandwidth assignment consists in the setting of the parameters of each scheduler (which
serves the buffers that use a given station’s up-link), together with the correspondent optimal
channel bit and coding rates. There are two essentially complementary goals that the
bandwidth and transmission parameters assignment may want to achieve.
G1) To maximize the global goodput, i.e.,
F
max
 (1)

B f  0,W , r f Ź
R ,..., R (P) , f 1,..., F


 
 nc( j)Tög( j) ,
j1
(15)
F

subject to
 Bj W ,
Bf  0, f  1,...,F
j1
(16)
G2) To reach global fairness, i.e., to divide the bandwidth in such a way that all TCP
connections achieve the same goodput.

Note that, even though the goodput expressions derived in Section 2.3 are applied in both
cases, the two goals are different and generally yield different results in the respective
parameters: maximizing the global goodput may turn out in an unfair allocation (in the sense
that some SD pairs may receive a relatively poor service), whereas, in general, a fair
allocation in the above sense does not achieve globally optimal goodput.
As far as the single goals are concerned, the relative calculations may be effected as follows.
The maximization in (15) is over a sum of separable nonlinear functions (each term in the
sum depending only on its specific decision variables, coupled only by the linear equality
constraint in (16)). As such, it can be efficiently computed by means of Dynamic
Programming [11, 41], if the bandwidth allocations are expressed in discrete steps of a
minimum bandwidth unit (mbu), which is the minimum granularity achievable.
The goodput-equalizing fair allocation can be reached by starting from an allocation
proportional to the number of TCP connections per SD pair, computing the average of the
corresponding optimal (in the choice of transmission parameters) goodputs, then changing
the mbu allocations (under constraints (16)) by discrete steps, aiming to decrease the
absolute deviation of each SD pair’s goodput from the average, and repeating the operation
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with the new allocations. The convergence, within a reasonable tolerance interval, can be
obtained in few steps.
In order to achieve a reasonable combination of goodput and fairness, we have proposed [29,
49] the following two strategies, which are termed Tradeoff and Range, respectively.
Tradeoff Strategy. The following steps are performed:
B , r ,
*
f
Compute the pairs
*
f
f  1,...,F , maximizing the global goodput, under constraints
(16);


Compute the pairs Bf , rf , f  1,...,F , corresponding to the goodput-equalizing fair choice;

*
Calculate the final allocation as B÷f  Bf   Bf (1  ), f  1,...,F , where 0    1 is a
tradeoff parameter, along with the corresponding bit and coding rates.

Range Strategy. The following steps are performed:




Compute the pairs Bf , rf , f  1,...,F , corresponding to the goodput-equalizing fair choice;
Choose a “range coefficient”   0 ;
Compute the global allocation, by effecting the constrained maximization in (23), with B f

 



 
varying in the range max Bf (1  ), 0 , min Bf (1  ),W , instead of 0,W , f  1,...,F .

As terms of comparison, we have also considered two other possible strategies, termed BER
Threshold and Generalized Proportionally Fair (GPF), respectively. The first one
only assigns
the transmission parameters (bit and coding rates) to each SDpair, in order to keep the BER

on the corresponding channel below a given threshold. The bandwidth assignment is then
done proportionally to the number of connections per link, multiplied by the corresponding
redundancy. The second one is derived from the concept of Generalized Proportional
Fairness (GPF) [50]. Without going into details, which can be found in [23, 49], the GPF
assignment stems from the concept of Nash Bargaining Problem [50, 51], and is found by
solving the maximization problem
F
 
max
 nc( j) ln Tö( j) Bj
F
B f 0,W  :  B j W j1
j1
(17)
where

 
Tö( j) Bj 
max


r j R (1),..., R (P ) 



Tög( j) rj , Bj

(18)
In order to evaluate the different options, we define the following indexes for comparison:
F

Goodput Factor:
g 
n
i 1
F
n
(i ) ˆ (i )
c Tg
Bi , ri 
(i ) ˆ (i )
c Tg
B , r 
*
i
*
i
i 1


(19)
where Bi , ri  is a generic choice and Bi* , ri* is the global goodput-maximizing one.
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L
 Tˆ
( j)
g
 fr  1 
Fairness Factor:
 Tg
j 1
2Tg ( L  1)
(20)
F
where L   n (i) is the total number of ongoing TCP connections, and Tg 
i1
1
L
L
 Tˆ
(k )
g
is the
k 1
average goodput. Note that  fr 1 when all goodputs are equal, and  fr  0 when the
imbalance among the connections’ goodputs is maximized, i.e., the goodput is Tg  L for one
 connection and 0 for the others (yielding a deviation from
Tg  L  Tg  0  Tg 
 L 1  2Tg  L  2Tg , which is the denominator
 of (20)).


 
the
average


4. RESULTS IN BANDWIDTH ALLOCATION POLICIES
In this part we summarize some of the numerous numerical results obtained in the analysis of
the above-mentioned techniques. In most cases, great attention has been paid in using
realistic models of the satellite link budget and of the fading levels, deriving them from real
data. In particular, where real fading data have been used, they have been taken from a reallife data set chosen from the results of the propagation experiment, in Ka band, carried out on
the Olympus satellite by the CSTS (Centro Studi sulle Telecomunicazioni Spaziali) Institute,
on behalf of the Italian Space Agency (ASI). The up-link (30 GHz) and down-link (20 GHz)
samples considered were 1-second averages, expressed in dB, of the signal power
attenuation with respect to clear sky conditions. The attenuation samples were recorded at
the Spino d’Adda (Northen Italy) station, in September 1992. The adoption of real fading
traces has been favored, rather than relying upon a model for rain fade generation, as no
thoroughly satisfactory model has been devised so far. In all cases, we have considered a
satellite network that uses bent-pipe geostationary satellite channels. This means that the
satellite is only a repeater and it does not perform any demodulation of data.
4.1. Numerical results for mixed traffic
We consider first the case of mixed Guaranteed Performance and Best-Effort traffic. Results
on the static cases described in subsection 3.2 can be found in [38], as regards the model
based on self-similar traffic aggregation only, and in [31], as regards the model that takes into
account the separation of TCP and UDP traffic. We report here some results pertaining to the
dynamic cases, which are taken from [41] and [45].
TABLE I. MOST SIGNIFICANT VALUES OF THE MF-TDMA SYSTEM CONSIDERING THE ITALSAT
PAYLOAD.
Stations’ antenna diameter
1.8 m
Stations’ power
13 dBW
Satellite G/T
5.9 dB/˚K
Satellite E.I.R.P. (effective isotropic radiation power)
48 dB W
Number of carriers
3
Capacity of each carrier (QPSK modulation)
8.192 [Mbit/s]
Up-link power control range
5 [dB]
Min. net Eb / N0 in clear sky conditions for non-real-time traffic (real-time
7 (5) [dB]
traffic)
BER guaranteed for non-real-time traffic (real-time traffic)
10-7 (10-4)
Possible data coding rates
4/5 (clear sky), 2/3, 1/2
Total information bit rate in clear sky conditions
19.66 [Mbit/s]
Information bit rate in clear sky conditions after system overhead
18 [Mbit/s]
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We consider a Multi-Frequency Time Division Multiple Access (MF-TDMA) system, i.e., a
network where the total capacity of the satellite transponder is divided into carriers at different
frequencies, each one accessed in TDMA. We also assume that a traffic station cannot
transmit at different frequencies in the same temporal slot. The most significant parameters of
the real satellite system adopted are reported in Table I. In order to compute the link budget,
we took data from [52], relevant to the transponder #1 of the Italsat national coverage payload
(20/30 GHz band), which is currently no longer operating, but still represents a reasonably upto-date situation. The information rate of 6.554 Mbit/s for each carrier is obtained with a 4/5
punctured convolutional encoder. The net values of 7 and 5 dB of channel Eb / N0 (bit energy
to one-sided noise spectral density ratio) are assumed as the thresholds of the clear sky
conditions for best-effort traffic and real-time connections, respectively. At the conditions of
the thresholds, after the Viterbi decoder, the bit error rates are 10-7 and 10-4, respectively.
In order to compute the resulting net values of Eb / N0 at the earth station’s receiver input,
relation (21) below has been used. No automatic gain control feature operates on the
transponder. For this reason the attenuation on the up-link affects both the up- and down-link
C / N 0 (carrier-to-noise) values.
Eb / N 0  C
(res)
10Log1 0br  m i
(21)
where:
C
(res)
(up )
 Cr
(dn)
 (C r(up) Au p )/10
(C r A u p Ad )/10 
 Au p  Ad  10Log10 10
10



(carrier power to one-sided noise spectral density ratio) at the
(dn )
 Au p  C r
is the resulting C / N 0
earth station receiver,
(u p)
C r is the reference (in clear sky) up-link C / N 0 = 80.7 [dBs-1],
(d n)
Cr is the reference (in clear sky) down-link C / N 0 = 81.6 [dBs-1],
A d is the dB down-link attenuation of the receiving station,
Au p is the dB up-link attenuation of the transmitting station, after up-link power control
intervention:
Au p  0 , if the up-link attenuation Au  pr ( pr is the up-link power control range =
5 dB); Au p  Au  p r , if Au  pr ,
b r is the data bit rate in bit/s,
mi is the modem implementation margin (assumed equal to 1 dB).
Table II contains the fade classes of the traffic stations as a function of the C / N 0 values.
TABLE II. REDUNDANCY FACTORS AND SIGNAL-TO-NOISE RATIOS VERSUS FADE CLASSES.
Fade
classes
1
rf ,rt
Coding rate, bit rate
[Mbit/s]
Coding rate, bit
rate [Mbit/s]
(non-real-time traffic)
(real-time traffic)
C / N 0 [dB]
1
1
4/5, 8.192
4/5, 8.192
1.2
1
2/3, 8.192
4/5, 8.192
77.13 – 75.13
3
1.2
1.2
2/3, 8.192
2/3, 8.192
75.13 –74.63
4
1.6
1.2
1/2, 8.192
2/3, 8.192
74.63 – 72.63
5
3.2
1.6
1/2, 4.096
1/2, 8.192
72.63 – 70.63
7
3.2
3.2
1/2, 4.096
1/2, 4.096
70.63 – 69.63
8
6.4
3.2
1/2, 2.048
1/2, 4.096
69.63 – 67.63
9
6.4
6.4
1/2, 2.048
1/2, 2.048
67.63 – 66.63
10
outage
6.4
-------------
1/2, 2.048
66.63 – 64.63
11
outage
outage
-------------
-------------
<64.63

2

rf ,nrt

>77.13

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Each fade class imposes the adoption of the indicated transmission parameters (and then rf
values) to limit the BER below the chosen thresholds. The system configuration used consists
of ten active stations, five of which are in clear sky, whereas the other five experience up-link
fading.
According to (21) and Table II, the attenuation level determines the attribution
 of each
station's traffic type to a certain fade class. In order to avoid too many oscillations in the
“instantaneous” bandwidth assignment of a station, a sort of hysteresis mechanism has been
introduced, whereby a station's traffic type remains in the same fading class, unless the
corresponding attenuation value exhibits a change above a given threshold (1 dB, in our case)
for more than 3 seconds. On the other hand, as far as the station’s outage is concerned, the
definition of “unavailable time”, given in ITU-T Recommendation G.821 [53] for connections,
has been adopted.
The data reported in Table III have been used for the generation of the traffic. The minimum
bandwidth unit that can be allocated has been taken as equal to 8 kbit/s. Each simulation run
covers a 10,000 s time span. The final values are obtained by averaging the results on a
number of simulation runs sufficient to produce a 5% confidence interval at 99% level.
In the graphs produced, a “SP (Simple Proportional) policy” also appears, where the master
acts passively, only making assignments proportional to the bandwidth requests received;
moreover, the requests do not take into consideration any specific prediction and cross-layer
interaction, but they are simply based on measurements of the traffic intensity. The SP policy
has been presented in the graphs as a comparison with a very simple and straightforward
method for satellite resource allocation.
TABLE III. DATA USED IN THE SIMULATION.
 s = 0.2 [request/s]
1   60 [s]
  1.5
Station connection generation rate for real-time traffic
Average real-time connection duration
Shape parameter of the Pareto distribution
Number of cells generated in one slot time (see Appendix B)
Cell payload (see Appendix B)
Non-real-time traffic sources’ peak rate

Slot time duration (see Appendix B)
Average non-real-time traffic burst duration
T=15 [ms]
[slot]
or 29.175 [ms]
burst = 16.67 [burts/s]
  1.945
Non-real-time traffic burst generation intensity (equal for all
stations)
Buffer dimension

Pblock threshold (equal for all stations)
Ploss threshold (equal for all stations)
R = 10
L = 384 [bit]
Bng = 256 [kbit/s]

8000 [cell]
 = 5%

= 1%
The results are divided into two sets. The first one (Figs. 3-4)
 shows the call blocking, call
dropping and cell loss probabilities, averaged over all stations
in the system, and over a time
window of 1000 s. The second set (Figs. 5-7) shows the same quantities for each station,
averaged over the entire simulation time (10,000 s).
As regards the blocking probability, it can be seen that all methods keep the average overall
system blocking probability below the 5% threshold. However, the individual (per station)
blocking probability is highly unbalanced for the SP, whereas both OC and OP tend to
essentially equalize this value: as their goal is to respect the constraint, they do not waste
bandwidth in favor of the more privileged stations (the ones that are not in fade); this saving
can be dedicated to keeping the number of packets dropped at the faded stations at a lower
value.
A more evident difference is shown by the probability of call dropping, both in the overall
system average and in the individual cases. We recall that a call is dropped at a station
whenever the applied redundancy (needed in response to a change in fading class) is such
that the sum of the bandwidths of the calls in progress overcomes the maximum amount of
bandwidth temporarily allocated to the station. This is a quantity over which we have no direct
control, as we have assumed that the stream traffic does not tolerate a reduction in the
transmission speed.
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0.044
0.052
P block
0.032
SP
0.028
0.024
SP
0.02
OP
0.016
0.012
OC
0.044
System's Cell Loss Probability
OP
0.036
System's Probabilities
0.048
OC
0.04
P drop
SP
0.04
0.036
0.032
0.028
System P loss OP
0.024
0.02
System P loss OC
0.016
System P loss SP
0.012
0.008
OP
0.004
OC
0
0.008
1
2
3
4
5
6
7
8
9
1
10
2
Simulation time [1000 s per unit]
5
6
7
8
9
10
Fig. 4. Average system’s cell loss
Probability [y axix] vs simulation time.
0.044
0.045
0.04
0.04
0.035
0.03
Pblock OP
0.025
Pblock OC
0.02
Pblock SP
0.015
0.01
0.036
Call Dropping Probability
Call Blocking Probability
4
Simulation time [1000 s per unit]
Fig. 3. Average system’s call blocking and
dropping probabilities [y axis] vs simulation time.
0.032
Pdrop OP
0.028
Pdrop OC
0.024
Pdrop SP
0.02
0.016
0.012
0.008
0.005
0.004
0
0
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
Number of stations
Number of stations
Fig. 5. Average call blocking probability [y axis]
station.
Fig. 6. Average call dropping probability [y axis] per
station. Stations 6-10 do not experience fade.
Windows XP, CPU AMD, 1800 MHz
0.084
10
0.078
max=10000 mbu
Ploss OP
0.066
Ploss OC
0.06
0.054
Ploss SP
0.048
0.042
0.036
0.03
0.024
0.018
0.012
1
Computational Times [s]
0.072
Cell Loss Probability
3
100 stations
max=3333
0.1
max=1000 mbu
0.01
max=333 mbu
10 s tatio ns
0.001
0.0001
1E-05
0.006
0
1
2
3
4
5
6
7
8
9
10
Number of stations
Fig. 7. Average cell loss probability [y axis] per
station.
1E-06
0
10
20
30
40
50
60
70
80
90 100
Minimum assignment [mbu]
Fig. 8. Computational times [y axis] for the dynamic
programming algorithm, depending on constrains
A different scenario could be envisaged, in the presence of a certain degree of elasticity in the
stream service, or in the presence of Variable Bit Rate (VBR) coding (see, e.g., [1, 54]). In
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this scenario, the dropping rates experienced by OP and OC could be further reduced by the
adoption of suitable rate adaptation techniques. Anyway, the call blocking and dropping
probabilities are loosely related, as a more cautious acceptance behavior implies a smaller
likelihood of dropping in severe fading conditions. In this sense, the OC shows slightly more
robustness than the OP (see Fig. 3).
A remarkable gain is obtained by the cross-layer adaptive policies as regards the cell loss
probability. Both the system’s averages (Fig. 4) and the per-station ones (Fig. 7), are kept
under the 1% threshold. However, the difference with respect to the OP policy is less
remarkable than what one might expect, owing to the more decentralized nature of the latter.
In this respect, it must be noted that both criteria are based on the same traffic models and
essentially operate the bandwidth assignment in a centralized way. The main difference lies
in the amount of signaling and in the computational times required to implement them.
The calculations needed to compute the bandwidth allocations in the OP strategy (which are
essentially the same that yield the cost-per-station components in the OC) can be performed
in advance for all possible values of the fading coefficients and of the discrete capacity
allocations, and stored in look-up tables. Therefore, the main computational burden that is left
for on-line execution to the master station is the actual calculation of the bandwidth partitions.
In the OP case, the computational time is practically negligible; on the other hand, it may rise
to significant values in the OC, where the constrained dynamic programming algorithm
outlined in [41] must be implemented. Figure 8 shows that, in the case of 10 stations
considered here, even the highest values are still quite manageable; at any rate, the presence
of constraints on the minimum and maximum numbers of mbu that can be allocated per
station may greatly help in reducing them. Figure 8 also presents the computational times in
the case of 100 stations, with a total capacity of 10000 mbu, and 3333 mbu per carrier. Both
computational times refer to the execution on a computer running Windows XP, with AMD
CPU and a clock of 1800 MHz.
4.2. Numerical results on TCP bandwidth allocation.
In the case of the optimal assignment of TCP bandwidth and redundancy, we summarize the
results presented originally in [23], [29] and [49]. The fully meshed satellite network
considered uses bent-pipe geo-stationary satellite channels and operates in TDMA (Time
Division Multiple Access) mode. The master station maintains the system synchronization,
other than performing capacity allocation to the traffic stations. The master station
performance is the same as that of the others; thus, any station in the system can assume the
role of master, because when the current master’s attenuation exceeds a given threshold, its
role is assumed by another station that is in better conditions. To counteract the signal
attenuation the system operates bit and coding rates changing. Traffic stations transmit in
temporal slots assigned by the master. Table IV reports the most significant system
parameters. In order to compute the link budget, a portion of the Ka band (20/30 GHz)
transponder of the Eutelsat satellite Hot Bird 6 was considered, and data taken from the file
"Hot Bird 6 data sheet.fm", which is downloadable from [55]. Net values of Ec / N 0 at the earth
station’s receiver input result from the relation
Ec / N 0  C / N 0 10Log10br  mi ,
(30)
We have assumed b=1 (no Delayed ACKs option) and To =1.5 s,when using relation (3). We

also considered ls = 4608 bits (576 bytes), which is the default segment length assumed by
sender and receiver TCP agents, when no other agreement has been possible.
Actually, not all combinations of bit and coding rates must be probed to find the maximum
 (i.e., they yield higher BER with the same
goodput, because some of them result inefficient
redundancy).
The possible cases are then limited to the following 7 ones: 10 Mbits/s, with

code rates 7/8, 3/4, and 1/2; 5 Mbits/s, with code rates 3/4, and 1/2; 2.5 Mbits/s, with code
rates 3/4 and 1/2.
Table V and Figure 9 show the configurations and the results of two static tests carried on,
denoting the link status ( C / N 0 [dB]), which is supposed to hold forever, and the number of
TCP connections in each class. A more complete set of results, though limited to the Range
and Tradeoff strategies, can be found in [29].
We used the 
TEAM (TCP Elephant bandwidth Allocation Method) software, which was
specifically developed to implement the mechanisms proposed in Section 4. The source code
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is freely available at the web address http://www.isti.cnr.it/ResearchUnits/Labs/wnlab/software-tools.html. We validated the results by means of ns-2 simulations, by running the
TCP connections under the bandwidth partitions provided by the TEAM software. The
simulations, which fall within a 99% confidence interval of width less than 1% of the
corresponding values, totally agree with the analytical calculations, and confirm the accuracy
of the analytical model of the TCP goodput adopted.
TABLE IV. MOST SIGNIFICANT VALUES OF THE TDMA SYSTEM CONSIDERING THE HOT BIRD 6 KA
PAYLOAD.
Stations’ antenna diameter
Stations’ maximum transmission power
Satellite G/T
Satellite transponder E.I.R.P. (effective isotropic radiation power)
Share of the satellite transponder power
Maximum/minimum capacity of the carrier (QPSK modulation)
Net Ec / N0 in clear sky conditions ( C / N 0 =77.5 dBs-1)(10Mbit/s)
Possible data coding rates
BER in clear sky after Viterbi decoder (7/8)
mbu (min. bandwidth unit) in clear sky
 sky (10Mbit/s at 7/8 coding rate)
Information bit rate in clear
Information bit rate in clear sky after system overhead
1.2 m
7 dBW
13 dB/˚K
52 dBW
1/4
10/2.5 [Mbit/s]
7.5 [dB]
7/8 (clear sky), 3/4, 1/2
10-7
5 Kbit
8.75 [Mbit/s]
8[Mbit/s] = 1600 mbus
TABLE III. CONFIGURATION OF THE 2 TESTS (nc is the number of TCP connections in the relevant class).
Record#
Class 1
Class 2
Class 3
Class 4
Class 5
Class 6
Class 7
Class 8
Class 9
Class 10
C/N0;nc
C/N0;nc
C/N0;nc
C/N0;nc
C/N0;nc
C/N0;nc
C/N0;nc
C/N0;nc
C/N0;nc
C/N0;nc
1
78.0;2
77.0;3
76.1;2
68.9;4
74.0;2
75.0;3
76.5;1
71.8;4
76.3;3
76.6;6
2
78.0;2
68.0;3
76.1;2
68.9;4
73.0;2
73.0;3
75.0;1
72.0;4
76.3;3
76.6;6
10 TCP classes; 30 total connections (record #2)
TRADEOFF-goodp ut factor
1
TRADEOFF-fairness factor
RANGE-goodput factor
0.9
RANGE-fairness factor
0.8
BER 10**-6-goodp ut factor
0.7
BER 10**-6-fairness factor
0.6
BER 10**-7-goodp ut factor
BER 10**-7-fairness factor
0.5
Fairness & Goodput Factors
Fairness & Goodput Factors
10 TCP classes; 30 total connections (record #1)
1.1
1.1
T
1
T
R
0.9
R
0.8
B
0.7
B
0.6
B
B
0.5
P
Proportionally Fair-goodput factor
0.4
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Proportionally Fair-fairness factor
0.4
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
 values
values
Fig. 9. Goodput and fairness indexes for the data in records #1 and #2.
For each record of values in Table V, the figure depicts the behavior of the goodput and
fairness factors, respectively, for the Tradeoff, Range, Generalized Proportionally Fair (NBS)
and BER Threshold strategies that have been defined in Section 4, for values of the
parameters  and  between 0 and 1. It can be noted that constantly keeping the BER
below a given threshold lowers the goodput and does not always maximize the fairness. The
Proportionally Fair strategy aims at maximizing the goodput and keeps an optimal value of
fairness, but it does not allow changing the fairness value, trading it with the goodput, as is
 possible
 by the Tradeoff and Range strategies. The expected value of fairness can
made
change due to fading conditions. This effect is more evident in the results of the dynamic
case.
The Tradeoff and Range strategies have a similar behavior, though they span different values
of goodput and fairness factors, depending on the system parameters. In all cases, as
expected, the goodput factor increases and the fairness factor decreases with increasing 
and  . In general, the span of the Tradeoff strategy’s goodput and fairness index values is


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wider in the interval [0, 1] than that of the Range strategy, but it must be noted that the
parameter  could be increased beyond 1, within the limits imposed by the total bandwidth
available. From the results obtained, it derives that both strategies allow a sufficient flexibility
in choosing a compromise between the two goals of overall goodput maximization and
fairness.

C/No [dB]
The results regarding the dynamic case under real fading patterns (Fig. 10) have been
obtained by means of the TEAM software and the ns-2 simulator. The TEAM software
calculates both the bandwidth allocations for each class, according to the chosen strategy,
and the relative segment loss rates, according to the C / N 0 values of the SD pairs. Ns-2
performs a dynamic simulation, according both to the input trace files, provided by the TEAM
software, and the attenuation patterns. The situation investigated in Fig. 11 shows a faded
class and a clear-sky class out of ten active ones. Five of the classes are in clear sky
condition, while the other five experience different
 patterns of fading. The total number of TCP
connections is 30 and the number of connections per class is the following: 2 for classes 1, 4,
5, and 9; 3 for classes 2, 3, 7, and 8; 4 for class 10; 5 for class 6. Three different allocation
strategies are considered: “Merge”, Proportionally Fair (GPF) and BER Threshold, with the
threshold set to 10-6. The Merge strategy is simply a merge between the Range and the
Tradeoff ones: for each record of the input file the two strategies are run in parallel, for a
certain fairness factor threshold (0.85 in the simulation runs); for each record, the allocation
values that yield the best performance in terms of goodput factor are passed to ns-2. Each
simulation run gives an observation window of 600 s. In each chart, we trace the behavior of
the goodput and of the segment loss rate, respectively, as functions of time.
78
77
76
75
74
73
72
71
70
69
68
67
66
65
64
63
62
Class #8
Class #4
0
50 100 150 200 250 300 350 400 450 500 550 600
Time [s]
Fig. 10. C/N0 values vs. time, represented for the 10 classes.
The allocations of the Merge strategy present many oscillations, as is highlighted in Fig. 11
(a), in the range 400-600 s. This tendency is due to the optimal choice in a range in which the
cost function is quite flat, and variations in the bandwidth allocation do not produce a sensible
change in the cost value in terms of goodput. However, it must be remarked that the TCP
congestion window filters these oscillations, reducing them, as shown in Fig. 12.
Table VI shows the percentage gain in total goodput, normalized with respect to the worst
case, namely, the BER Threshold strategy, with the threshold set to 10 -7. In the Range and
Tradeoff strategies, the fairness factor is targeted to 0.85. The absolute goodput value per
strategy is given by the sum of the goodputs of all classes, obtained by averaging the values
of the dynamic simulation over 600 s. All allocation strategies are based on an optimization
technique, so we do not reasonably expect large differences in performance. Anyway, the
merging between Range and Tradeoff gives a further gain over both the threshold policies,
and over the GPF one, in the range of 10% with respect to the latter and of 25%-30% with
respect to the former ones.
Fig. 13 reports the goodput per connection in the three most significant cases considered, for
all classes, with the selected fairness factor of 0.85. The Merge strategy privileges the faded
classes, i.e., classes 6, 7, 8, 9, 10, reducing the allocations and therefore the goodputs of the
classes in clear-sky; the allocations and the goodputs are equalized all over the classes also
June 2005
33
Progetto IS-MANET
ISTI
Deliverable WP6D5
in the presence of hard fading conditions. The goodput gain of the Merge strategy for the
faded classes is furthermore evident if compared to that of the threshold policy. As a final
comparison, Fig. 14 shows that the Merge strategy gives a further gain in terms of fairness, in
comparison with the GPF one, over a simulation window. The Merge strategy does not
experience fading effects, in terms of fairness, as GPF instead does, and the fairness factor is
kept to the target value.
June 2005
34
2.20E+06
2.00E+06
1.80E+06
1.60E+06
1.40E+06
1.20E+06
1.00E+06
8.00E+05
6.00E+05
4.00E+05
2.00E+05
0.00E+00
Time [s]
Time [s]
2.40E+06
Goodput
Segment Loss Rate
2.20E+06
2.00E+06
Goodput - [Bit/s]
1.80E+06
1.60E+06
1.40E+06
1.20E+06
1.00E+06
8.00E+05
6.00E+05
4.00E+05
2.00E+05
0.00E+00
Time [s]
Time [s]
Time [s]
(a) – BER Threshold
(b) – Proportionally Fair
2.40E+06
2.20E+06
2.00E+06
1.80E+06
Goodput - [Bit/s]
1.00E+00
Goodput
1.00E-01
Segment Loss Rate
1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
1.00E-07
1.00E-08
1.00E-09
1.00E-10
1.00E-11
1.00E-12
1.00E-13
0 50 100 150 200 250 300 350 400 450 500 550 600
Segment loss rate
Goodput [Bit/s]
(a) – Proportionally Fair
2.40E+06
2.20E+06
2.00E+06
1.80E+06
1.60E+06
1.40E+06
1.20E+06
1.00E+06
8.00E+05
6.00E+05
4.00E+05
2.00E+05
0.00E+00
1.00E+00
1.00E-01
1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
1.00E-07
1.00E-08
1.00E-09
1.00E-10
1.00E-11
1.00E-12
1.00E-13
0 50 100 150 200 250 300 350 400 450 500 550 600
Goodput
Segment Loss Rate
1.60E+06
1.40E+06
1.20E+06
1.00E+06
8.00E+05
6.00E+05
4.00E+05
2.00E+05
0.00E+00
1.00E+00
1.00E-01
1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
1.00E-07
1.00E-08
1.00E-09
1.00E-10
1.00E-11
1.00E-12
1.00E-13
0 50 100 150 200 250 300 350 400 450 500 550 600
Goodput
Segment Loss Rate
Time [s]
(b) – BER Threshold
Fig 11. Merge, Proportionally Fair and BER Threshold (thr=10-6) strategies for class #8 in
fading (a) and for class #4 in clear sky (b)
TABLE VI. TOTAL GOODPUT AVERAGED OVER ALL CLASSES IN THE DIFFERENT STRATEGIES.
Strategy
Merge
Range
Tradeoff
GPF
BERthr0 BERthr0
Goodput
5.921
5.858
5.437
5.412
4.791
4.526
6
7
Gain %
30.8
29.4
20.1
19.6
5.8
0
[Mbit/s]
June 2005
Segment loss rate
1.00E+00
1.00E-01
1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
1.00E-07
1.00E-08
1.00E-09
1.00E-10
1.00E-11
1.00E-12
1.00E-13
0 50 100 150 200 250 300 350 400 450 500 550 600
(b) – Merge
Segment loss rate
Goodput [Bit/s]
(a) – Merge
2.40E+06
2.20E+06
2.00E+06
1.80E+06
1.60E+06
1.40E+06
1.20E+06
1.00E+06
8.00E+05
6.00E+05
4.00E+05
2.00E+05
0.00E+00
1.00E+00
1.00E-01
1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
1.00E-07
1.00E-08
1.00E-09
1.00E-10
1.00E-11
1.00E-12
1.00E-13
0 50 100 150 200 250 300 350 400 450 500 550 600
Goodput
Segment Loss Rate
Segment loss rate
2.40E+06
Goodput
Segment Loss Rate
35
Segment loss rate
1.00E+00
1.00E-01
1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
1.00E-07
1.00E-08
1.00E-09
1.00E-10
1.00E-11
1.00E-12
1.00E-13
0 50 100 150 200 250 300 350 400 450 500 550 600
Deliverable WP6D5
Goodput - [Bit/s]
2.40E+06
2.20E+06
2.00E+06
1.80E+06
1.60E+06
1.40E+06
1.20E+06
1.00E+06
8.00E+05
6.00E+05
4.00E+05
2.00E+05
0.00E+00
ISTI
Segment loss rate
Goodput [Bit/s]
Progetto IS-MANET
Progetto IS-MANET
ISTI
Deliverable WP6D5
180
160
140
Packets
120
100
80
60
40
20
0
0
50 100 150 200 250 300 350 400 450 500 550 600
Time [s]
Fig. 12. TCP congestion window [in packets]of class #8 vs. time
Fig. 13. Goodput per TCP class per connection for the most significant strategies.
1.05
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
80
C/No
78
76
74
72
C/No [dB]
Fairness Factor
1.2
1.15
1.1
70
Merge
68
Proportionally fair
66
64
62
60
0 50 100 150 200 250 300 350 400 450 500 550 600
Time [s]
Fig. 14. Fairness factor of Merge and Proportionally Fair strategies vs. time, with an indicative
value of C/N0, averaged over classes.
APPENDIX. Cell Loss Probability Evaluation for BE Traffic.
We consider the following formula [15], which gives an asymptotic (in the buffer length Q (i) )
upper bound to the cell loss probability in a buffer loaded with the self-similar traffic
introduced in paragraph 1.2 of Section C:

June 2005
36
Progetto IS-MANET
 


c  (i)

ng R
min 
 (Q (i) )  1,
(i)
X (t)     ( 1)  X (i) (t)  (i) R
ng
 

1


(i)
Ploss
ISTI



Deliverable WP6D5


1 if X (i)  (i)
ng R


otherwise
(A1)

Some of the parameters appearing in (A1) have been previously defined; the others are
explained as follows. Let T be a reference time interval (slot), to which we will refer all the
relevant parameters of the cell queue. The slot also represents the minimum duration of a
burst, and the burst length  is expressed as an integer number of slots. Let Bng be the peak
generation rate of each asynchronous source [bits/s], and L the number of bits in a cell. Then,
R  T (L /Bng) TBng L is the number of cells generated by an active burst in a slot ( x 
being the smallest integer greater than or equal to x). The number of new sources becoming
(i)
active in each slot is i.i.d. Poissonian, with parameter (i)
ng  burst T . If H is the cell’s header


 represents the
(i)
r
(t)D


 level, ng

length in bits, and we define D = (L+H)/T, then X (i) (t)  
(i)
Cnrt
(i)
bandwidth Cnrt
(t) expressed in [cells/slot] ( x being the largest integer less than or equal to
x), taking into account the redundancy coefficient of BE.
(i)
 from 0 to N (i) , as a consequence, C (i) (t)
Since n (t) can assume only discrete values
max
nrt
only
 takes on discrete values withcertain probabilities, depending on the probability of having
(i )
(i)
n (t) connections in progress at time t at station i. If we indicate by X j the realization of the
(i)
(i)
variable X (t) , corresponding to n (t)  j , we have:
C (i)  jB(i) r (i) (t) 
level, rt

,
X (i)

j
(i)

 D  rlevel, nrt (t) 


and


(i)
j  0,1,...,N max
 
(A2)

Pr X (i) (t)  X (i)
 Pr n(i) (t)  j
j


where Pr n(i)(t)  j
(A3)
 is given by the stationary distribution of a
(i)
(i)
M / M / Nmax / N max queueing
system.
 assume as an indication of the cell loss rate at station i the quantity defined in (A1),
We
averaged over the number of guaranteed bandwidth connections; thus we have:
(i)
Ploss
C
(i )
N max
(i)
(i)
, rlevel,
nrt
  P

n
(i)
(i)
loss( X j )  Pr
(i)

(t)  j
(A4)
j0


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