Performance Analysis of Aloha-based MAC
Protocols for Optical WDM Networks
Goran Đambić, Alen Bažant
Abstract—Star and ring are the two most frequent used
topologies for optical networks, due to their superior power
loss compared to bus and hybrid networks. In this work we
will focus our attention to Slotted Aloha-based media access
control protocol designed for star-coupled networks. We will
analyze performance for this protocol, with variations in
number of the nodes, the number of the channels and the size
of buffer in every node.
Index Terms—optics, wavelength division multiplexing, media
access control protocols, aloha, performance, star topology
I. INTRODUCTION
This work uses an analytical model based on Markov
chains introduced in [1], [2], [3], [4], [5], [6], [7], [8], [9]
for performance evaluation of Aloha-derived Media Access
Control protocols in optical networks based on Wavelength
Division Multiplexing (WDM). Wavelength Division
Multiplexing means that there is more than one channel
simultaneously in use, so traditional single-channel Alohabased protocols had to be adapted. Specifically, we analyze
WDM-based, star-coupled, broadcast-and-select single-hop
Metropolitan Area Networks (MAN) based on a
wavelength-insensitive passive star coupler (PSC).
Broadcast-and-select means that PSC will collect all
wavelengths from one node and will broadcast them to all
other nodes, so the destination node will select traffic
headed for him, while the other nodes will discard it.
Single-hop means that every node is able to address and
send packet to any other node directly. That capability is
achieved by having transmitters tunable over all used
wavelengths.
Media Access Protocols designed for optical WDM
networks can be classified as either reservation or preallocation protocols [1], [2]. Reservation protocols mostly
use one control channel (although some don't) to reserve
access on all other channels. Pre-allocation protocols
preassign wavelengths to nodes, where each node has
dedicated home-channel for transmission or reception.
Pre-allocation protocols are generally less complex and
simpler than reservation protocols. Pre-allocation protocols
can be further classified as random or static. Both random
and static pre-allocation protocols have been developed for
nodes with either tunable transmitter and fixed receiver or
fixed transmitter and tunable receiver. In this work we will
consider nodes equipped with one fixed receiver and one
tunable transmitter, which means that every node has
dedicated home-channel for data reception. System cost and
system complexity are reduced since tunable receivers are
not needed.
II. OPTICAL COMPONENTS
Many efforts have been done in research and development
of WDM networks because of two reasons: first, the
bandwidth of current fiber installations can be greatly
enhanced, and second, the speed mismatch between optical
and electronical components can be circumvented because
instead of one very fast channel, there are multiple slower
channels.
Fig. 1: Network architecture
There are two classes of WDM networks – wavelength
routing networks and broadcast-and-select networks, which
is studied in this work. Our network consists of M nodes
equipped with one tunable transmitter and one fixed
receiver. Our network uses C channels, each represented by
one distinct wavelength. This work is not concerned with
physical characteristics of the network – the choice of laser
for the transmitter, the channel spacing between
wavelengths, the channel selectivity of the receiver and
other characteristics are assumed to be sufficiently chosen
for WDM star topology network.
The topology of our network is shown in Fig. 1.
III. INTERLEAVED SLOTTED ALOHA PROTOCOL
Interleaved Slotted Aloha protocol (I-SA) examined in this
work is based on the network where channels are preallocated for data-reception. A source node must first tune
its tunable transmitter to the home channel of the
destination node and then waits for the beginning of the
new slot to transmit a packet. A node receives all traffic on
his home channel. Packets intended for the node are
accepted, and the others are discarded. If there is M = C,
then all packets on node's home channel are sent for the
node.
If a node wants to transmit a packet to another node, it must
first determine the home channel of the other node. That
can be achieved without any global tables, since the
destination node numbers, C and M are known at all times.
Node mi is assigned ci as its home channel for reception
based on
ci = mi mod C
where ci is element of {0, 1, 2, ..., C-1} and 0 ≤ i ≤ M - 1.
In our network, the source node is tuned to his own home
channel, so it cannot find out if the packet successfully
arrived at the destination or the collision has occurred.
There are few ways to assure reception of the sent packet.
In our network, we choose to extend the slot and cut it in
two phases – in phase one, the source node tunes its
transmitter to destination's home channel and transmits the
packet. In phase two, the destination node decodes the
packet header, verifies the CRC, tunes its transmitter to
home channel of the source node and transmits the
acknowledgement.
If
M = C, then the acknowledgement packet is always
received. If M > C, the acknowledgement packet can collide
with another packet on the same channel, so the phase two
must me further subslotted. A source node knows that a
collision has occurred if it does not receive the
acknowledgement packet.
If a collision did occur, the transmitting node goes to
backoff state. In that state, the transmitter decides if it will
retransmit in the next slot based on the backoff probability
Pb. The retransmission can be attempted in the next slot
(Immediate First Retransmission – IFRT) or after a one slot
of pause (Delayed First Retransmission). The protocol used
in this study is based on IFRT approach. If the
retransmission succeeds, it transmits the next packet in the
queue (if there is one). If not, it stays in the backoff state.
IV. MODEL FOR PERFORMANCE ANALYSIS
I-SA protocol described in section III is analyzed through
semi-markov model. This model will be reduced to markov
chain because the sojourn time of every state is 1.
In this work we will consider network throughput and
packet delay. The throughput is expressed as packets per
unit time, where time is normalized to the packet
transmission time, which includes propagation delay and
the processing time of destination node. The packet delay is
defined as the time between generation of the packet and it's
reception by the destination node, and is also normalized to
packet transmission time. There are few assumptions for
this model [2]:
1.
2.
3.
4.
5.
6.
nodes are identical,
in every node, packet generation is a Poisson
process with rate λ,
a packet generated at any node has equal
probability of being directed to any other node,
except for itself,
per slot, only one packet can be generated in every
node,
at most B packets can be queued at the node
(without the one being in process of transmission),
all packets are fixed in length.
The receiver can be in one of the two states: idle – the
receiver is not receiving a packet, and receiving – the node
is receiving a packet. The receiver never initiates activity,
so it will not be included in the model.
The transmitter initiates activity and can be in on of the
states shown in Fig. 2.
Fig. 2: State diagram of I-SA for B = 1
Possible states for transmitter are: idle – there is no
generated packet in the node, transmitting – transmitting
the packet, and backoff – the collision has occurred and the
transmitter will transmit in the next slot with probability of
Pb.
The probability of a transition from state Si to Sj is denoted
as p[i,j]. The τi is average sojourn time of state Si and is
always equal to 1.
The transmitter will leave S0 and go to S1 if a new packet is
generated. States Si, where 1 ≤ i ≤ B+1, are transmit states.
The transition from transmit states depends on whether the
packet was successfully transmitted and whether a new
packet is generated. The probabilities are given in Fig. 2.
The queue is full in state SB+1 and S2(B+1) and packet
generation is blocked.
States S(B+1)+i, where 1 ≤ i ≤ B+1, are backoff states. The
transition from backoff states depends on Pb and on
generation of a new packet.
Limiting probabilities of being in state Si of embedded
markov chain are denoted as Vi and can be calculated from
transition probability matrix shown in Fig. 3.
1-β
Ps(1-β)
0
0
0
P=
β
Ps β
Ps
Pb(1-β)
0
0
0
0
Pbβ
Pb
0
(1-Ps)(1-β)
0
(1-Pb)(1-β)
0
0
(1-Ps)β
1-Ps
(1-Pb)β
1-Pb
Fig. 3: Transition probability matrix for B = 1
Because of sojourn times are equal to 1, the limiting
probabilities of being in state Si of semi-markov process are
Pi = Vi.
The probability of successful transmission Ps depends on
the limiting probabilities of the process being in one of the
transmit states, as shown in [2]:
Ps =
 P1  P2  P3  ...  PB 1 
1 

C


V. ANALYZING MODEL
The model from section IV was used to analyze throughput
and packet delay. The analysis was performed using
Matlab. The purpose of the analysis was to show the
relation of throughput and packet delay to packet generation
rate, number of nodes and number of channels. In every
scenario we assumed the same probability of leaving the
backoff state Pb = 0.05.
A. Network with single channel
Fig. 4 shows a network throughput when there is C = 1,
B = 1 and M is from {4, 8, 16, 32, 64}, and Fig. 5. has the
same C and M, but with B ten times greater,
B = 10.
M 1
Since Ps depends on Pi and Pi depends on Ps, the following
algorithm can be used in calculation:
1.
2.
3.
4.
choose any value for Ps,
compute Pi for that Ps,
compute new Ps with computed Pi,
repeat steps 2 and 3 until Pi converges.
Channel utilization for a node is the percent of the time
node spends transmitting packet. Network throughput is
defined as channel utilization of all C channels. A node
transmits packets when in any of the states Si, where
1 ≤ i ≤ B+1. The number of packets transmitted by node can
be calculated from probabilities of being in one of those
states and probability of successful transmission Ps. The
throughput for the network is
Fig. 4: Throughput of I-SA for system with one channel and
buffer of
size 1
S = M Ps (P1 + ... + PB+1)
The packet delay is defined as a time from a packet creation
until its reception at destination. That time include waiting
for the beginning of the next slot, backoff time (if a
collision occurs), and packet transmission time. The packet
delay can be calculated by applying Little's Law:
D=
E N 
( P1  ...  PB 1 ) Ps
where E[N] is the average number of packets in node,
which is
E[N] = E[N0]P0 + ... + E[N2(B + 1)]P2(B+1)
and E[N0] = 0, E[Ni] = E[N(B+1)+i] = i, for all 1 ≤ i ≤ B+1.
Fig.5: Throughput of I-SA for system with one channel and
buffer of
size 10
As mentioned before, network throughput is defined as
number of packets successfully transmitted per slot over all
data channels. It is primarily dependent on two parameters:
collisions and number of nodes.
Fig. 4 and Fig. 5 clearly show that the size of buffer doesn't
play any significant role in network throughput.
It is also visible that up to a point, the throughput grows
with the growth of packet generation rate and number of
nodes. After that point, if we keep increasing the number of
the nodes, the collisions begin to happen more and more
often and even for small-generated traffic the throughput is
low. For example, for λ = 0.40, if there are M = 16 nodes,
the network throughput is around S = 0.37. But if we
increase the number of nodes to M = 64 the throughput falls
down to only S = 0.13.
following subsection will show how does the number of
channels affect the performance.
B. Networks with multiple channels
Fig. 8 and Fig. 9 show the network throughput when the
number of channel increases from 1 to a value from interval
{M, M/2, M/4}.
Fig. 8: Throughput of I-SA system with varying number of channels and
buffer of size 1
Fig. 6: Packet delay of I-SA for system with one channel
and buffer of
size 1
Fig. 9: Throughput of I-SA system with varying number of channels and
buffer of size 10
Fig. 7: Packet delay of I-SA for system with one channel and buffer of
size 10
Fig. 6 and Fig. 7 show the packet delay for the same
parameters. Again, the size of the buffer doesn't affect the
delay.
It is visible from both pictures that as the number of nodes
increases, the packet delay is greater. The reason for that is
that every node spends more time retransmitting the packet,
because the network is congested and the probability of
successfully transmitted packet is very low.
The above analysis shows that I-SA protocol with one
channel is unacceptable in real-life networks and that even
increase in buffer size doesn't make any difference. The
It is obvious that any increase in number of channels from 1
results in dramatically greater throughput. For example, if
we look in Fig. 4, we will see that the network throughput is
S = 0.13 for M = 64 nodes and λ = 0.40. If we find the same
value in Fig. 8, we will find out that it has increased to
S = 9.1, for C = M = 64, which is a significant increase.
Also, it is visible that the throughput is growing slowly as
we increase the buffer size, which is noticeable only in
networks with 32 or more nodes.
VI. CONCLUSION
Fig. 10: Packet delay of I-SA system with varying number of channels and
buffer of size 1
This works used mathematical model based on semimarkov process to analyze the behavior and performance of
media access control protocol based on Slotted Aloha. It
was shown that the main parameter for the performance is a
ratio of number of the nodes and number of the channels.
The increase in number of nodes creates more traffic and
that means more collisions occur that affects performance.
But if there is also a matching increase in the number of
channels, the traffic distributes to more wavelengths and the
number of collisions falls down, which results in retained
level of performance. That means that I-SA protocol is a
good choice for networks when the traffic is low or
medium. Still, when the traffic is heavy, the performance
will suffer even if ratio M/C = 1.
REFERENCES
[1]
[2]
[3]
[4]
[5]
Fig. 11: Packet delay of I-SA system with varying number of channels and
buffer of size 10
Considering the packet delay shown in Fig. 10 and Fig. 11,
it is noticeable that it decreases as the number of channels
grows, almost insensitive to the number of nodes. From
those figures, we derive a conclusion that as long as the
ratio M/C is maintained, the packet delay will remain
almost the same. That is a very important characteristic of
I-SA protocol. For example, there will be a 65% decrease in
packet delay and a 100% increase in system throughput if
we increase the number of channels from M/4 to M, at
λ = 0.30 and M = 32.
[6]
[7]
[8]
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