IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 11, NOVEMBER 2010
3391
E-PULRP: Energy Optimized
Path Unaware Layered Routing Protocol for
Underwater Sensor Networks
Sarath Gopi, Kannan Govindan, Deepthi Chander, U. B. Desai, and S. N. Merchant
Abstract—Energy optimized Path Unaware Layered Routing
Protocol (E-PULRP) for dense 3D Underwater Sensor Network
(UWSN) is proposed and analysed in this paper. In the proposed
E-PULRP, sensor nodes report events to a stationary sink node
using 𝑜𝑛 𝑡ℎ𝑒 𝑓 𝑙𝑦 routing. E-PULRP consists of a layering phase
and communication phase. In the layering phase, a layering
structure is presented wherein nodes occupy different layers in
the form of concentric shells, around a sink node. The layer
widths and transmission energy of nodes in each layer are chosen
taking into consideration the probability of successful packet
transmission and minimization of overall energy expenditure
in packet transmission. During the communication phase, we
propose a method to select intermediate relay nodes 𝑜𝑛 𝑡ℎ𝑒 𝑓 𝑙𝑦,
for delivering packets from the source node to sink node.
We develop a mathematical framework to analyse the energy
optimization achieved by E-PULRP. We further obtain expressions for throughput, delay and derive performance bounds for
node densities and packet forwarding probabilities, for given
traffic conditions. A comparison is made between the results
obtained based on simulations and analytical expressions. The
energy efficiency is also demonstrated in comparison with existing
routing protocol for underwater sensor networks.
Index Terms—Under sensor networks, energy aware routing,
end-to-end throughput.
I. I NTRODUCTION
U
NDERWATER Sensor Networks (UWSN) enable realtime monitoring of selected ocean areas with the provision of remote real-time wireless data access. A number
of issues need to be addressed while using sensor networks
as an effective technology for underwater systems [2]. In
this paper, we consider the design of a routing protocol
for underwater sensor networks. Unlike in terrestrial adhoc
networks, the underwater scenario poses challenges of high
propagation delay, uncontrollable variations in node locations,
varying network topology and frequent loss of connectivity
due to underwater currents [3]. Therefore, conventional routing protocols are not appropriate for UWSN, and it calls
for customized routing algorithms. A Path Unaware Layered
Routing Protocol (PULRP) was proposed for a 3D UWSN
Manuscript received April 24, 2009; revised December 2, 2009; accepted
July 6, 2010. The associate editor coordinating the review of this paper and
approving it for publication was T. Hou.
A preliminary version of this work has been published at IEEE Globecom2008, New Orleans, USA [1].
The authors are with the Spann Laboratory, Department of Electrical Engineering, IIT Bombay, Powai, Mumbai-400076 (e-mail: {sarathgopi, gkannan,
deepthi.chander, merchant, ubdesai}@iith.ac.in; [email protected]).
Digital Object Identifier 10.1109/TWC.2010.091510.090452
with a uniform distribution of sensor nodes in [4] and 2D
non-uniform distribution of underwater sensor nodes in [5].
One of the primary concerns in designing a routing protocol
for UWSN, is the limited battery power of underwater sensor
nodes. In order to maximize the lifetime of networks, the
routing protocol must ensure that traffic is relayed through
nodes which have sufficient battery power. Moreover, the
transmission range of each node must be optimized in order to
avoid early node failures due to energy depletions. Access to
the deployed underwater sensor nodes are highly impractical
for battery replacements. Both [4] and [5] do not incorporate
energy in the design of the routing protocol. A novel Energy
optimized Path Unaware Layered Routing Protocol, E-PULRP
has been proposed for a densely deployed 3D UWSN in [1]
where a uniform distribution of underwater sensor nodes was
considered. A stationary sink node was assumed to be located
at the center of the deployment volume. In such a setup, each
node monitors the volume of interest and reports events to the
sink node using the proposed E-PULRP routing algorithm.
The sink node in turn communicates the aggregated data to
the surface station as shown in Fig. 1. The schematic shown
in Fig. 1 represents a typical system architecture used in
underwater surveillance or data collection applications, where
the sink node is an array connected to a ship, and expendable
sonobuoys are deployed around the sink node.
The proposed E-PULRP algorithm has two phases:
1) Layering Phase: A layered architecture is constructed
with the sink node at the center and sensor nodes occupying different layers around it. Nodes within a layer
have the same hop count to the sink node. Essentially,
the layering structure is a set of concentric shells, around
the sink node. Moreover, the transmit energy levels
of nodes in a particular layer are chosen such that
communication occurs only with nodes in the immediate
lower layer in the direction of the sink.
2) Communication Phase: In this phase, the multihop
routing path is determined 𝑜𝑛 𝑡ℎ𝑒 𝑓 𝑙𝑦. Starting from
the nearest lower layer to the source, a relay node is
identified in each layer, such that the distance between
consecutive relay nodes (hop size) is maximum and the
residual energy of the chosen node is also sufficiently
high. The identified relay nodes are termed as potential
relay nodes, which relay data from the source node to
the sink node, and form the routing path.
In order to achieve energy efficiency in the proposed E-
c 2010 IEEE
1536-1276/10$25.00 ⃝
3392
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 11, NOVEMBER 2010
Immoveable
surface station
Sea
surface
Floating
nodes
Water
column
x
x
x
Sea floor
x
Fig. 1.
x
x
Proposed system model.
PULRP algorithm [1], transmission energy of the nodes is
selected in such a way that the overall energy consumption in
the network is minimized. The primary contributions of this
paper are: (a) Development of an 𝑜𝑛 𝑡ℎ𝑒 𝑓 𝑙𝑦, energy efficient
protocol E-PULRP, for 3-D UWSN. (b) Analysis of E-PULRP
in terms of throughput and end-to end delay. (c) Performance
bounds on node densities and packet forwarding probabilities
for given traffic conditions. (d) Extension of simulation results
in [1] for normalised energy expenditures, throughput and
delay for varying node densities as well as for various number
of layers and varying path forwarding probabilities, for a
more realistic underwater channel model. (e) Comparison of
numerical results with analytical results.
The approach in E-PULRP can certainly be adopted to terrestrial networks as well. However, the terrestrial environment
is not as dynamic as the underwater scenario and additional
advantages like availability of localization techniques and
alternate sources of energy (solar) to empower sensor nodes
can motivate the use of light weight routing protocols for
terrestrial networks.
II. R ELATED W ORK
Over the last few years, extensive research has been carried
out in routing protocol design for terrestrial wireless networks. However, due to the peculiar nature of the underwater
environment and applications, there are several drawbacks
with respect to the suitability of existing routing solutions
for underwater networks. In [6], AODV protocol has been
modified for suitability to UWSN, where most nodes are
assumed to be static. Some recent papers propose network
layer protocols specifically tailored for underwater acoustic
networks. In [7], the authors provide a simple design example
of a shallow water network, where routes are established by
a central manager based on neighborhood information. In [8],
a routing protocol is proposed based on centralized network
manager (surface station) that autonomously establishes the
underwater network topology, controls network resources, and
establishes network flows. Both [7] and [8] use periodic
flooding and depends heavily on the central manager. In [9],
a vector-based forwarding (VBF) routing is developed, which
does not require state information on the sensors and involves
only a small fraction of the nodes in routing. However, it
requires location information of all the nodes. Similarly, [10]
has suggested a location aware focused beam routing scheme.
Beam focusing with single sensor node may not be practically feasible. An integer-linear programming approach to
jointly optimize routing, link-scheduling and node placement
in UWSN is proposed in [11]. However, this is a fixed routing
protocol and does not consider the mobility of nodes in the
underwater environment. A resilient routing protocol is suggested in [12]. A similar approach is available in [13] for delay
sensitive and delay insensitive networks. However, both [12]
and [13] are based on a graph theoretic approach and rely on
complete network information. Therefore, they are relatively
complex and demand more computational resources and may
not be practically suitable for dynamic underwater networks.
An optimal transmission distance for routing in underwater
sensor networks is reported in [14], which also emphasises
on a need for an energy efficient algorithm. However, [14]
considers a static node deployment and requires geographical information. An Underwater Diffusion (UWD) routing
protocol based on community to community forwarding [15]
is proposed in [16]. Even though [16] uses only controlled
flooding, it does not ensure energy efficiency and waits for
the complete path to be established to start the data transfer.
A geographical random forwarding routing scheme is reported
in [17] and its energy and latency analysis is presented in[18].
Even though [17] seems to be quite promising for practical
implementation, it requires localization for identifying the
relay nodes and synchronization for collision avoidance, which
may not be easily achievable in underwater sensor networks.
E-PULRP considerably differs from all the above stated works
in terms of its unique layering structure, on the fly routing and
most importantly, it uses energy optimization for estimating
the optimal transmission ranges. It is designed for a mobile
3D deployment and does not require localization and/or synchronization techniques.
III. D ETAILS OF E-PULRP
E-PULRP consists of two phases: Layering phase and
Communication phase. In the layering phase, a layer structure
is formed around the sink node and in the communication
phase one relay node is identified from each layer to forward
the packet. The method of determining the path from source
node 𝐴 in layer 𝑙 + 1, to the sink node 𝑆 in E-PULRP is
described below.
1) Node 𝐴 broadcasts a control packet, which contains
the source ID, the destination ID, packet ID and the
spreading code which will be used for data packet transmission. This is transmitted using a common spreading
code for broadcast. E-PULRP uses CDMA MAC with
orthogonal spreading sequences [19] for minimizing
GOPI et al.: E-PULRP: ENERGY OPTIMIZED PATH UNAWARE LAYERED ROUTING PROTOCOL FOR UNDERWATER SENSOR NETWORKS
collisions during data forwarding. If this control packet
is received properly (i.e. no other nodes in the neighborhood, tries to send a control packet simultaneously),
a collision free transmission will be ensured.
2) On
receiving
the
control
packet,
the
𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑟𝑒𝑙𝑎𝑦 𝑛𝑜𝑑𝑒, 𝐵 in the lower layer 𝑙, will
respond with an ACK. Once the 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑟𝑒𝑙𝑎𝑦 𝑛𝑜𝑑𝑒
is identified, all other nodes can go back to sleep.
3) A particular interval (𝜏 ) after the control packet is transmitted, the source node sends the data packet without
waiting for the acknowledgement. The interval, 𝜏 is
fixed as slightly greater than the round-trip delay time
of layer 𝑙, given by 2𝑎𝑙 /𝑣 for proper reception and to
avoid collisions, where 𝑎𝑙 and 𝑣 are the layer width
of layer 𝑙 and speed of sound, respectively. If node 𝐵
successfully receives the packet, then 𝐵 will broadcast
a control packet to find its next 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑟𝑒𝑙𝑎𝑦 𝑛𝑜𝑑𝑒
(towards the destination), as in Step 1. The broadcast
control packet from 𝐵 acts as an acknowledgment for
𝐴. If node 𝐴 does not receive 𝐵 ′ s broadcast control
packet message, then it will broadcast the control packet
as in Step 1 and the process will be repeated, until the
packet reaches the destination.
Network Model: To derive the design parameters, we consider
the network model followed in [16] i.e. the total volume
occupied by the UWSN in the region of interest is divided
into a large number of small virtual cubes with a Binomial
probability distribution for the occupancy of a node in a cube.
If we assume that the number of such cubes is large and
Poisson approximation to the Binomial distribution [20], the
probability of 𝑘 nodes occupying a volume V is given by:
)𝑘
(∫
∫
V 𝜌𝑑v
exp− V 𝜌𝑑v
(1)
𝑃 𝑟[𝑥 = 𝑘] =
𝑘!
∫
where 𝜌 is the volume density of the nodes, 𝑉 indicates
integral over the volume 𝑉 .
Path Loss Model: Underwater communication is severely
affected by physical properties like temperature and chemical
properties of water, as well as on the depth of transceivers.
The basic propagation paths between a source and a receiver
are illustrated in Fig. 2. The channels shown in Fig. 2 are
surface reflection (A), surface duct (B), bottom bounce (C),
convergence zone (D), deep sound channel (E) and reliable
acoustic path (F). In shallow water, the path can be worse
as seen in (G). However, in all of the above scenarios (other
than in cases (B) and (E)), the path loss can be modeled as
follows: For a transmitted energy of 𝐸𝑇 , the received energy
𝐸𝑅 at distance 𝑅 is given by:
𝐸𝑅 =
𝐸𝑇
𝐵/10
𝑅
10(𝛼𝑅+𝛽)/10
(2)
where 𝐵 takes values 10, 15 or 20 depending on the type
of propagation, 𝛽 is a constant independent of range and 𝛼
is a range-independent absorption coefficient, which maybe
a constant or a random variable, depending on multipath
characteristics. An overview of channel models is available
in [21]. Eq. (2) shows that, except for scenarios in Fig. 2 (B)
and Fig. 2 (E), the received energy is a decreasing function
of range. Therefore, for a dense deployment and short range
3393
Fig. 2. Signal propagation between transmitter and receiver in a deep oceanic
environment.
transmission model with the range of a few meters sound can
be assumed to have near straight line propagation. For the case
of non-straight line propagation, we assume the transmission
angle to be the same as the reception angle at any node.
This will ensure channel reciprocity for short duration of time.
Since we consider omni-directional antennas, this assumption
of the angle of transmission being the same as the angle of
reception, holds true. Therefore, the channel can be assumed
to be reciprocal for short durations over which the channel
conditions do not vary significantly [22].
IV. L AYERING P HASE
In this phase, a set of concentric shells (layers) are formed
around the central sink node. The layering structure ensures
that the packet is forwarded towards the sink node. Layer
formation is explained as follows: A probe of energy 𝐸𝑝1 is
initiated at the sink node (layer 0) and all nodes that receive
the probe with energy at least equal to 𝐸𝐷 (the detection
threshold) will assign themselves as layer 1 nodes. Layer 1
nodes can communicate with the sink node in single hop. Now,
after waiting for a time 𝜅 (derived in Section V) a node in
layer 1 transmits a probe with energy 𝐸𝑝2 to create layer 2,
constituted by nodes which receive packets with energy at least
equal to 𝐸𝐷 from layer 1 nodes. The waiting time 𝜅 given by
(5) is independent of any global time and it solely depends on
received energy. Since no localization or synchronization of
nodes is assumed, we adopt the waiting time based approach in
order to minimize collisions between probing packets initiated
by nodes in consecutive layers. The probe gets propagated as
described above throughout the network thus forming 𝐿 layers.
All nodes in a particular layer can forward data to the sink
node over an equal number of hops. The design parameters
in this phase are the probing energy 𝐸𝑝𝑙 , the transmission
energies of control/data packets and the layer widths. The
probing energy for nodes in layer 𝑙 − 1 is related to layer
3394
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 11, NOVEMBER 2010
width 𝑎𝑙 of layer 𝑙 as follows:
𝐸𝐷 =
x
𝐸𝑝𝑙
𝐵/10
𝑎𝑙
10(𝛼𝑎𝑙 +𝛽)/10
Therefore, the determination of layer width automatically fixes
the probing energy value assuming that 𝐸𝐷 is a known
system specification. Hence, the parameters to be estimated are
layer widths and transmission energies (or the corresponding
transmission ranges). The estimation procedure is explained
below.
x
x
x
x
V. C OMMUNICATION P HASE
The communication phase involves selection of intermediate
relay nodes for forwarding packets from source to sink. An
intermediate relay node is identified from each lower layer.
The identified relay nodes in each layer are termed as potential
relay nodes. The selection of potential relay node is based on
the following theorem.
Theorem 1: Let us assume that a source node 𝑇 in layer 𝑙
sends a control packet. As in [1], some node 𝐴 in layer 𝑙 − 1
x
x
x
x
Layer 5 (L=5)
Layer 4
x
x
x
x
x
Layer 1 S
x
x
x
Sink node
Layer 2
x
x
x
x
x
x
x
x
Layer
3
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
RL
x
Range
circle
(4)
∑𝐿
ˆ
such that 𝑃1 (𝑅𝑙 , 𝑎𝑙 ) > 𝑃𝑡ℎ , 𝑅𝑙 < 𝑅𝑚𝑎𝑥 ,
𝑙=1 𝑅𝑙 = 𝑅.
In (4) 𝐸𝑇 𝑜𝑡𝑎𝑙 is the total energy consumption in the network, which is a function of the layer width (𝑎𝑙 ), maximum
attainable range (𝑅𝑙 ) corresponding to transmission energy
(𝐸𝑇 𝑙 ) of a node in layer 𝑙, and the number of layers (𝐿).
The first constraint ensures that the probability of a packet
being forwarded from a layer (i.e. probability 𝑃1 that at
least one node is present in the intersection region) is greater
than a minimum value 𝑃𝑡ℎ . The maximum value of 𝑃𝑡ℎ is
in turn limited by network traffic, as will be discussed in
Section VI-C. The other two conditions in (4) are boundary
conditions. 𝑅𝑚𝑎𝑥 is the transmission range corresponding to
ˆ is the
the maximum possible transmission energy of a node. 𝑅
distance of the farthest node from the sink which is effectively
the radius of the deployment region. The derivation of each of
the expressions in (4) and the expressions of different terms
are detailed in Appendix. A.
Equation (4) is a conventional non-linear constrained optimization problem and the solution of which will give a set of
values for 𝑅𝑙 . For each 𝑅𝑙 , it further gives an upper bound
on the value of the corresponding 𝑎𝑙 [1]. It is advisable to
choose the value of 𝑎𝑙 slightly less than the upper bound
obtained from (4), since the probability of packet delivery
failure as well as the latency will increase with decrease in
value of 𝑎𝑙 [4]. Even though the scheme has been designed
with spherical region assumption, it can be used with any
geometry of node deployment by dividing the region between
the sink and the farthest node into spherical elements.
x
x
x
x
The transmission energy of nodes and layer widths are
determined based on the minimization of the total energy
expenditure in packet transmission, while keeping the packet
failure rate less than a threshold. Mathematically, the problem
can be formulated as:
𝑅𝑙 ,𝑎𝑙 ,𝐿
x
x
A. Estimation of Node Transmission Energy 𝐸𝑇 𝑙 and Layer
Width 𝑎𝑙
min 𝐸𝑇 𝑜𝑡𝑎𝑙
x
x
(3)
Fig. 3.
x
aL
x
T
x
x
x
x
x --nodes’ location
Layer radius estimation.
declares itself as potential relay node, if it does not overhear
any other potential relay node declaration for a time interval
𝜅 = 𝜆𝑚𝑖𝑛 (𝐸𝑅 − 𝐸𝐷 )/𝛾,
(5)
where 𝐸𝑅 is the received power of the control packet and 𝐸𝐷
is the detection threshold. 𝛾 is an energy dependent factor
which is the ratio of the energy remaining in the node to the
total initial energy and 𝜆𝑚𝑖𝑛 is a constant given by [4]
𝜆𝑚𝑖𝑛 =
2𝑎𝑙−1
)]
[
(
𝑅𝑙
𝑣 𝛼𝑎𝑙−1 + 𝐵 log 𝑅𝑙 −𝑎
𝑙−1
(6)
Since the waiting time of each node receiving the control
packet, solely depends on the received signal strength and the
energy factor 𝛾, it can be determined independently at each
node. This avoids the need for time synchronization among
nodes. With this particular waiting time the scheme tries to
select the relay node, which is maximally away from the
source, and is closer to the sink, within the shell structure
of the deployment region. Such a choice would support fewer
number of hops, and consequently reduce the packet delivery
delay.
The proposed collision avoidance scheme will work well,
when all receiving nodes are in a vertical line with the source
node (e.g A and B in Fig. 4) and if the transmission time
between control and data packet is greater than 2𝑎𝑙 /𝑣, i.e.
the interval after which A overhears B’s potential relay node
declaration. Consider a case, where two nodes are almost at
the same distance from the transmitter 𝑇 , but are horizontally
separated (such as C and D in Fig. 4). In this scenario both
C and D receive the request from 𝑇 almost at the same time
and after the same interval, they send the potential relay node
declaration. This may lead to collision at 𝑇 . This problem
can be avoided by embedding the value of the received signal
strength (RSSI) from the source on the potential relay node
declaration packet. Therefore, once each node receives the
GOPI et al.: E-PULRP: ENERGY OPTIMIZED PATH UNAWARE LAYERED ROUTING PROTOCOL FOR UNDERWATER SENSOR NETWORKS
VI. A NALYSIS OF E-PULRP A LGORITHM
x
A. Throughput
Consider a node located in layer 𝑙 + 1 at distance 𝑥 from
the boundary of layer 𝑙 as shown in Fig. 5. All nodes generate
packets according to a Poisson process with average rate 𝜆
packets per second. The packet will be received successfully
by a node in layer 𝑙, if at least one node is present in the
intersection region (shaded region in Fig. 3), which does not
have any other packet to forward.
Assuming uniform node distribution the probability that at
least one node will be present in the intersection region (𝑃1 )
of volume 𝑉 (which is a function of 𝑥 and 𝑎𝑙 ) can be obtained
from (33) as
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
xS
x
x
x
x
x
x
x
x
x
x
x
x
x
x
𝑃1 (𝑥, 𝑎𝑙 ) = 1 − 𝑒−𝜌𝑉 (𝑥,𝑎𝑙 )
x
B
x
x
x
C
x
Rl
al-1
Ax
x
x
D
Rl- al-1
x
T
x --nodes’ location
Fig. 4. Pictorial representation of layout of nodes and the layering structure.
x
x S
x
Layer l
Layer l+1
x
ql
x
x
l
x
x
x
x
x
y
R
x
x
x
x
The probability that a node in layer 𝑙 has no packet to transmit
other than a relay packet from layer 𝑙 + 1 can be obtained by
using Poisson probability distribution for 0 event with 𝜆′𝑙 − 1
replacing 𝜆𝑙 and is given by
x
x
T
Illustration of average delay.
potential relay node declaration packet of another node, it can
compare its own RSSI with that of the other node. If its RSSI
is less than that of all other nodes, it can forward the data
packet, otherwise it will enter into silent mode. This strategy
will also fail if two nodes receive exactly the same power,
however, the probability of such an event is zero.
The layer number may have to be updated frequently (relayering) in order to cater to the mobility of nodes. It is
assumed that the network does not vary at a rate faster than
a round trip time. In E-PULRP, rather than using separate
transmissions, flooding or repeating the layering process, an
implicit re-layering scheme, exploiting the transmission of various control packets in the communication phase, is used [1].
Such a scheme would reduce latency and communication
overhead which are generally due to explicit acknowledgement
mechanisms.
(7)
Let the number of nodes in layer 𝑙 be 𝑛𝑙 . Average number of
packets generated in the last layer 𝐿 is 𝑛𝐿 𝜆. Each of these
packets has to be serviced by a 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑟𝑒𝑙𝑎𝑦 𝑛𝑜𝑑𝑒 in layer
𝐿 − 1. Therefore, the average number of packets of layer 𝐿
𝐿𝜆
serviced by a single node in layer 𝐿 − 1 is 𝑛𝑛𝐿−1
. Therefore,
the total average
its own traffic) per node in
( traffic (including
)
𝐿
layer 𝐿 − 1 is 1 + 𝑛𝑛𝐿−1
𝜆. If we generalize this argument,
the total traffic load in layer 𝑙 due to all other higher layers
and its own traffic is
(
)
∑𝐿
𝑖=𝑙+1 𝑛𝑖
′
𝜆𝑙 = 1 +
𝜆
(8)
𝑛𝑙
′
𝑝𝑙 = 𝑒−(𝜆𝑙 −1)
(9)
Since the events in (7) and (9) are independent, the probability
that a packet in layer 𝑙 + 1 will be successfully received by a
node in layer 𝑙 is given by
𝑃𝑙+1,𝑙 = 𝑃1 (𝑥, 𝑎𝑙 )𝑝𝑙
Fig. 5.
3395
(10)
As can be seen, this probability is function of distance 𝑥.
But the node can be present anywhere in the layer. Now, if
we assume that the node distribution is symmetric around the
sink node, the average probability that the packet from layer
𝑙 + 1 is successfully received by a node in 𝑙 is
𝑃ˆ𝑙+1,𝑙 = 𝐸𝑥 (𝑃𝑙+1,𝑙 )
(11)
where 𝐸𝑥 is the statistical expectation operator with respect to
random variable 𝑥. Therefore, probability of successful packet
delivery from source node in layer 𝑙 + 1 to the sink node is
𝑃𝑙+1,𝑠 = 𝑃1,𝑠 Π2𝑖=𝑙+1 𝑃ˆ𝑖,𝑖−1
(12)
where 𝑃1,𝑠 is the probability that the packet is successfully
transmitted from layer 1 node to sink node. If we assume that
the sink node is super node and can process any number of
packets simultaneously then 𝑃10 will become 1. Now the total
throughput 𝜂 is given by
𝜂=
∑
𝑃 (𝑠𝑢𝑐𝑐𝑒𝑠𝑠𝑓 𝑢𝑙 𝑝𝑎𝑐𝑘𝑒𝑡 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦/𝑠𝑜𝑢𝑟𝑐𝑒 𝑖𝑠 𝑖𝑛 𝑙𝑎𝑦𝑒𝑟 𝑙) .
𝑙
.𝑃 (𝑠𝑜𝑢𝑟𝑐𝑒 𝑖𝑠 𝑖𝑛 𝑙𝑎𝑦𝑒𝑟 𝑙)
(13)
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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 11, NOVEMBER 2010
From (12), (13) and by using the uniform distribution
assumption for nodes, we can get
𝜂
=
1
∑
𝑛𝑙
𝑙=𝐿
𝑁
𝑃𝑙,𝑠
(14)
(14) is an approximate value of the throughput with the assumption that packet transmission in each layer is independent
of other layers. In addition, we assume that every node treats
the packet which is to be forwarded as same priority as the
packet generated by itself.
B. Average Delay
Let us assume that a node 𝑇 in layer 𝑙 + 1, at a distance
𝑥 from the boundary of layer 𝑙 (as shown in Fig. 5), wants
to transmit a packet and the 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑟𝑒𝑙𝑎𝑦 𝑛𝑜𝑑𝑒 for this
packet is at a distance 𝑦 from the source as shown in Fig. 5.
The packet reaches the 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑟𝑒𝑙𝑎𝑦 𝑛𝑜𝑑𝑒 after a delay of
𝜏𝑦 = 𝑦𝑣 + 𝜏 + 𝑇𝑜𝑡ℎ where, 𝜏 is the constant waiting time at
the transmitting node between the request packet and the data
packet (see Section V) and 𝑇𝑜𝑡ℎ consists of all other delays,
such as transmission delay, processing delay, etc. According to
E-PULRP, the node which is farthest from the source (assume
same energy levels in all nodes) has the highest precedence
to receive the packet and become 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑟𝑒𝑙𝑎𝑦 𝑛𝑜𝑑𝑒.
Hence, a node at a distance 𝑦 from the source will become
𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑟𝑒𝑙𝑎𝑦 𝑛𝑜𝑑𝑒, if no other eligible relay node is present
at a distance greater than 𝑦 in the intersection region i.e. in the
shaded region of layer 𝑙 as shown in Fig. 5. The probability
of no eligible relay node being present at a distance greater
than 𝑦, (say, 𝐺𝑦 ) in the intersection region, can be obtained
as follows: The absence of eligible relay nodes can be either
due to the absence of nodes or due to the load on nodes to
transmit other packets.
Since nodes are uniformly distributed, the probability that
no node is present farther than 𝑦 (𝐺𝑦0 ) in the intersection
region shown as the shaded region in Fig. 5 can be obtained
using (33) as,
𝐺𝑦0 = 𝑒−𝜌𝑉𝐼
(15)
where 𝑉𝐼 is the volume of the intersection region. Let 𝐺𝑦𝑏 be
the probability that the eligible node in the shaded region of
layer 𝑙 is not free then
′
𝐺𝑦𝑏 = 1 − 𝑒−𝜆𝑙
(16)
Since the two events are independent, 𝐺𝑦 is given as
𝐺𝑦 = 1 − (1 − 𝐺𝑦0 )(1 − 𝐺𝑦𝑏 ) ≈
𝐺𝑦0 + 𝐺𝑦𝑏
3
3 𝑦𝜃𝐺𝑦
4𝜋𝑞𝐿
The factor ‘𝑦𝜃’ in (18) gives the length of the arc, corresponding to nodes which are at a distance 𝑦 from the source. It is
3
known that for a uniform node distribution 4𝜋𝑞
3 is the node
𝐿
density corresponding to a sphere of radius 𝑞𝐿 . Therefore, the
3
factor 4𝜋𝑞
3 𝑦𝜃 in (18) denotes the probability of finding a node
𝐿
at a distance 𝑦 from the source. Hence we obtain 𝑓𝑦 as in (18).
It should be noted that the delay will be added to the
computation of average delay, only if the packet is successfully transmitted. Therefore, the probability that the packet is
subjected to a delay 𝜏𝑦 , given that the packet is successfully
delivered is given as follows:
𝑓𝑦
𝑓𝑠𝑦 = ∫ 𝑅𝑙
𝑓𝑦 𝑑𝑦
𝑥
(17)
(18)
∑𝑙
where 𝑞𝑙 = 𝑖=1 𝑎𝑖 is the distance of the boundary of the
𝑙𝑡ℎ layer from the sink and 𝑞𝐿 is the radius of the region of
(20)
∫𝑅
where 𝑥 𝑙 𝑓𝑦 𝑑𝑦 is the normalization factor. Therefore, the
average delay in successfully delivering a packet from a node
at a distance 𝑥 in layer 𝑙 + 1 to layer 𝑙 is given by
∫ 𝑅𝑙
𝐷(𝑥) = 𝐸𝑦 (𝜏𝑦 ) =
𝜏𝑦 𝑓𝑠𝑦 𝑑𝑦
(21)
𝑥
However, we further observe that the 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑟𝑒𝑙𝑎𝑦 𝑛𝑜𝑑𝑒
can be placed anywhere in the intersection region, i.e. from
distance 𝑥 to 𝑅𝑙 . Now the total average delay in delivering a
packet from layer 𝑙 + 1 to layer 𝑙 is given as
𝐷𝑙 = 𝐸𝑥 (𝐷(𝑥))
(22)
Therefore, the total delay in a packet transmission from layer
𝑙 + 1 to sink node is given by
𝐷𝑇 𝑙 =
1
∑
𝐷𝑖 + 𝐷0
(23)
𝑖=𝑙
where 𝐷0 is the average delay in delivering a packet from
layer 1 to the sink node and it is equal to 𝐸𝑥0 ( 𝑥𝑣0 ) and 𝑥0 is
the distance between the forwarding node in layer 1 to the sink
node. Since 𝑣 is a constant we can obtain 𝐷0 = 𝑎2𝑣1 . Therefore,
the average delay in a packet transmission in E-PULRP can
be obtained as,
𝐷 = 𝐸𝑛 (𝐷𝑙 ) =
1
∑
𝑙=𝐿−1
In (17) we considered 𝐺𝑦0 𝐺𝑦𝑏 is negligible. Now a packet
will incur a delay of 𝜏𝑦 if a relay node is present at a distance
𝑦 and no other eligible relay nodes are located farther than 𝑦.
The probability for this event to occur can be obtained as
𝑓𝑦 =
interest. Now 𝜃 as shown in Fig. 5 can be obtained by using
the cosine formula as
( 2
)
𝑞𝑙 − 𝑦 2 + (𝑞𝑙 + 𝑥)2
(19)
𝜃 = 2 cos−1
2𝑦(𝑞𝑙 + 𝑥)
𝐷𝑇 𝑙
𝑛𝑙
𝑁
(24)
where 𝐸𝑛 is the statistical expectation operator with respect
to number of nodes in layer 𝑙. The underlying assumptions in
deriving (24) are same as that of (14).
C. Relation Between Traffic and Number of Nodes in Each
Layer
An important requirement of the proposed E-PULRP algorithm is that probability of at least one node lying in the
intersection volume (𝑃𝑙 ) should be greater than the threshold
value (𝑃𝑡ℎ ) as given in (34). Here, we obtain the relationship
GOPI et al.: E-PULRP: ENERGY OPTIMIZED PATH UNAWARE LAYERED ROUTING PROTOCOL FOR UNDERWATER SENSOR NETWORKS
Traffic Vs P for different no of layers
th
0.045
0.035
0.02
0.015
0.005
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
P
(27)
th
Fig. 6.
Average traffic vs 𝑃𝑡ℎ for various number of layers.
0.02
Pth=0.59
Pth=0.79
0.018
P =0.99
th
Average Traffic(pkts/sec)
If the number of nodes in the 𝐿𝑡ℎ layer is 𝑛𝐿 , we can get a
lower limit on the number of nodes in any lower layer using
back calculations in (29). Therefore, the minimum number of
nodes required for successful packet forwarding in 𝑖𝑡ℎ (for
𝑖 = 1, 2, ...𝐿 − 1) layer is
( 𝛿 )𝐿−𝑖−1
0.016
0.014
0.012
0.01
0.008
0
0.002
0.004
0.006
0.008
0.01
Node Density (nodes/m3)
Fig. 7.
Average traffic vs Node density for various 𝑃𝑡ℎ .
(30)
Equation (30) gives the minimum number of nodes required
in each layer to meet a specific average traffic 𝜆. It also
determines the maximum value of 𝑃𝑡ℎ that can be used for
a specific system design in a given traffic condition. Based
on Equations (30) and (34), we therefore infer that (30)
gives a performance bound on the protocol for a given traffic
condition.
VII. S IMULATION R ESULTS
Extensive simulations have been carried out to evaluate
the performance of the E-PULRP algorithm. An underwater
spherical region of radius 500 𝑚 is considered, where the
nodes are uniformly deployed. The sink node is located at the
center of the sphere, i.e. (0, 0, 0). Nodes move according to the
Random Waypoint (RWP) [23] mobility model with velocity
uniformly chosen from [0 0.5] 𝑚/𝑠. The pause time of RWP
model is also uniformly chosen from the interval [0 60] 𝑠𝑒𝑐.
We have used the energy propagation model as suggested
in (2) with reliable acoustic path parameters (Fig. 2 (F)). A
CDMA based scheme with eight orthogonal spreading codes
is used at the MAC layer. Simulations have been conducted
for 150 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 with the following parameters:
𝑅𝑚𝑎𝑥 = 100 𝑚, 𝐵 = 20, 𝛼 = 0.7, 𝛽 = 0,
𝑁𝑡 = 5 𝑘𝑏𝑖𝑡𝑠, 𝑁𝑐 = 64 𝑏𝑖𝑡𝑠, 𝑁𝑓 = 32 𝑏𝑖𝑡𝑠
0.025
0
0.1
Now, by substituting 𝑝𝑙 from (9) and 𝜆′1 from (8) we get
)
(
∑𝐿
𝑖=𝑙+1 𝑛𝑖
𝜆<𝛿
(28)
1+
𝑛𝑙
( )
where 𝛿 = 1 + log 𝑃1𝑡ℎ . Rearranging (28), we can get the
relationship between the number of nodes in a particular layer
and the sum of total nodes in all the higher layers as
∑𝐿
𝑛𝑖
(29)
𝑛𝑙 > 𝑖=𝑙+1
𝛿
𝜆 −1
𝑛𝑖 > ( 𝜆
)𝐿−𝑖 𝑛𝐿
𝛿
𝜆 −1
0.03
0.01
From (25) and (26) we get
𝑃𝑡ℎ ≤ 𝑝𝑙
L=5
L=6
L=7
L=8
0.04
Average Traffic(pkts/sec)
between number of nodes and traffic using (34). By substituting (10) and (11) in (34), we can get
𝑃𝑡ℎ
𝐸𝑥 (𝑃1 (𝑥, 𝑎𝑙 )) =
(25)
𝑝𝑙
where the left hand side of (25) is the average value of
𝑃1 (𝑥) and hence should lie in the interval [0, 1], since
0 ≤ 𝑃1 (𝑥) ≤ 1.
∫
𝐸𝑥 (𝑃1 (𝑥, 𝑎𝑙 )) = 𝑃1 (𝑥, 𝑎𝑙 )𝑓𝑥 (𝑥)𝑑𝑥
∫
(26)
≤ 𝑓𝑥 (𝑥)𝑑𝑥 ≤ 1
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The values of 𝑅𝑚𝑎𝑥 and 𝑁𝑡 corresponds to a safe operating
range and data rate of UWM1000 acoustic modem [24]. The
bound on the network traffics are plotted against probability
of packet forwarding (𝑃𝑡ℎ ) and node density (𝜌) in Fig. 6
and Fig. 7 respectively. It can be seen that as 𝑃𝑡ℎ increases,
the traffic that the network can handle decreases. This is
evident from (30) and it means that for a low traffic network,
the probability that the packet is forwarded will be high.
In addition, the average traffic that the network can handle
decreases as the number of layers increases (various curves
in Fig. 6 are plotted for number of layers from 𝐿 = 5 to
𝐿 = 8). This is because, the lower layers get overloaded with
relay demands as the number of layers increases. Similarly,
the average traffic that the network can handle decreases with
increase in the node density. This is due to the fact that
the total packets generated by the nodes will be high, which
will produce more traffic on nodes in the lower layers. For
the simulation studies, the packet generation is considered
as a Poisson point process with mean inter arrival time of
5 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 (corresponding to 𝜆 = 0.0033).
Energy expenditure is compared between the theoretically
obtained value, the value obtained empirically by simulations
and also the energy expenditure of the previously proposed
PULRP protocol in [4]. Energy required to receive/process the
packet (𝐸𝑅𝑃 ) is taken as 0.06𝐸𝑚𝑎𝑥 . These specific values are
3398
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 11, NOVEMBER 2010
−2
1
0.8
0.8
Throughput
Normalized Energy
Node Density = 10
1
0.6
Empirical (10−2)
Theoretical (5x10−3)
0.4
0.4
0.2
5
Theoretical (10−2)
0.6
6
7
8
9
10
11
−3
Empirical (5x10 )
5
6
5
6
7
8
7
8
12
0.24
Normalized Energy
1
E−PULRP (Thoeretical)
E−PULRP(Empirical)
PULRP
0.8
0.6
Average Delay
−3
Node Density = 5x10
0.235
0.23
0.225
0.4
0.22
0.2
0
5
No of Layers
6
7
8
9
Number of Layers
10
11
12
Fig. 9.
layers.
Fig. 8. Normalized energy expenditure (where the legend is common for
both of the above plots).
Throughput
0.9
0.85
0.8
0.75
0
0.002
0.004
0.006
0.008
0.01
0.24
Average Delay
chosen after considering WHOI micro modem for which the
receive power and the maximum transmission powers are 3W
and 50 W respectively [25]. Two different node densities (𝜌 =
5 × 10−4 and 𝜌 = 10−2 ) are considered in our simulations.
Fig. 8 shows the normalized energy expenditure per node
(normalized with respect to the energy expenditure corresponding to the case of equal layer widths where node transmit
at their maximum transmission range). The minimum value
of 𝐿 required to span the entire region of interest is 5
(≈ 500/𝑅𝑚𝑎𝑥). The expected (mathematically computed) as
well as the actual energy expenditure (obtained from simulation) are shown. In addition, the energy expenditure in the
previously proposed PULRP [4] is also shown for comparison.
It is to be noted that in PULRP algorithm, equal layer widths
were assumed and nodes transmitted with maximum range
without considering optimum utilization of energy. In the case
of proposed E-PULRP algorithm for 𝜌 = 10−3 , the total
energy expenditure decreases with increase in 𝐿 until 𝐿 = 13,
after which it starts increasing. This is because, when 𝐿 is
small the interference term (third term in (33)) dominates the
other two terms. Therefore, when 𝐿 increases (which in turn
reduces the transmission range), the number of overhearing
nodes is reduced, and therefore the overall energy expenditure
decreases. However, when 𝐿 increases beyond a certain point,
there will be more transmissions and receptions. Therefore,
the first-two terms in (33) dominate over the third interference
term and eventually energy expenditure will start increase. For
𝜌 = 5×10−4, the number of layers corresponding to minimum
energy expenditure is 11. The number of layers, corresponding
to minimum energy expenditure will decrease with decrease
in node density. This is because, the effect of interference
will be less for low node densities. However, in the case
of PULRP the number of layers corresponding to minimum
energy expenditure is always 8 for both the densities.
The other performance parameters considered for evaluation
are the network layer throughput and average delay. Throughput is defined as the ratio of total packet delivered to the sink
Throughput and Average delay comparison for different number of
0.23
0.22
E−PULRP (Theoretical)
E−PULRP (Empirical)
UWD
0.21
0.2
0.19
0
0.002
0.004
0.006
Node Density
0.008
0.01
Fig. 10. Throughput and Average delay comparison for various node densities
for fixed 𝑃𝑡ℎ = 0.8.
to the total packet generated. The average delay is the average
end to end delay for each packet delivered to the sink.
Fig. 9 shows the throughput and the average delay performance for various choices of 𝐿. It can be observed that
the throughput decreases as 𝐿 increases. This phenomenon
can be explained as follows: In (12) we can see that as
𝐿 increases, 𝑃𝑙,𝑠 will decrease exponentially. However, in
(14) as 𝑙 increases the total sum increases linearly only,
resulting in decreasing 𝜂 with increasing 𝑙. This can also be
understood intuitively, since as the number of hops increase,
the throughput will drop. From Fig. 9 we can further observe
that the average delay increases with 𝐿. This is due to the fact
that when the number of layers increases, the average traveling
distance of the packets remain more or less the same, on the
other hand the contribution of overhead terms, i.e. the constant
waiting time between the control and data packet (𝜏 ) and other
delays (𝑇𝑜𝑡ℎ ) in (24) increases.
Fig. 10 and Fig. 11 show the performance comparison of the
E-PULRP algorithm with the Underwater Diffusion (UWD)
algorithm proposed in [16]. Throughput as well as average
delay are estimated mathematically using (14), (24) and also
determined empirically through simulations. The throughput
GOPI et al.: E-PULRP: ENERGY OPTIMIZED PATH UNAWARE LAYERED ROUTING PROTOCOL FOR UNDERWATER SENSOR NETWORKS
Throughput
0.95
0.9
0.85
0.8
0.75
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Average Delay
0.24
0.22
E−PULRP (Theoretical)
E−PULRP (Empirical)
UWD
0.2
0.18
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
P
th
Fig. 11. Throughput and average delay comparison for various probability
of packet forwarding (𝑃𝑡ℎ ) for fixed 𝜌 of 5 × 10−3 .
and average delay are plotted against 𝜌 in Fig. 10. It can be
seen that theoretical and empirical values of the throughput of
the proposed algorithm are almost the same or better than that
of UWD. The theoretical value of average delay of E-PULRP
and UWD are found to be comparable. But the average
delay of E-PULRP obtained through simulation has better
performance compared to that of UWD. The slight difference
between the theoretical and empirical values can be due to the
various assumption, we have made in the derivation and also
due to the mobility of the nodes. The throughput and average
delay increase as node density, 𝜌 increases. The increase in
the throughput with 𝜌 is due to the increased number of nodes
available for forwarding the packets. However, as 𝜌 increases,
the volume of intersection region in Fig. 3, will decrease for
a given 𝑃𝑡ℎ . This will cause the ring radius to increase, thus
increasing the delay.
Similar plots are shown in Fig. 11 for various values of 𝑃𝑡ℎ .
For all 𝑃𝑡ℎ values, the throughput of the proposed E-PULRP
algorithm is better than that of UWD. The average delay also
shows a marginally better performance compared to UWD.
It can be observed that the average delay decreases as 𝑃𝑡ℎ
increases. This is due to the fact that when 𝑃𝑡ℎ increases,
the layer width decreases (for fixed 𝜌) so that the intersection
region in Fig. 3 should increase. This reduces the average
delay.
VIII. C ONCLUSION
We have proposed an energy efficient 𝑜𝑛 𝑡ℎ𝑒 𝑓 𝑙𝑦 routing
protocol, E-PULRP for underwater sensor networks (UWSN),
where the communication parameters are chosen in order to
achieve energy optimization. The 𝑜𝑛 𝑡ℎ𝑒 𝑓 𝑙𝑦 nature of the
protocol, its re-layering mechanism as well as its energy efficiency enable E-PULRP to combat connectivity losses due to
mobility, multipath or energy depletion. Note that the increase
in Bit Error Rates due to multipath is beyond the scope of
this paper and is assumed to be handled in the physical layer.
This paper specifically describes the detailed mathematical
framework of E-PULRP and obtains analytical expressions
for its performance metrics. This paper also provides a bound
for the average traffic that the network can withstand with
3399
successful packet transmission. The principle can be extended
to arrive at an optimal node distribution to handle a prescribed
traffic condition. Extensive simulations have been performed,
to compare the simulation based results with the analytical
results. E-PULRP is simple, efficient and hence can be implemented without much difficulty for UWSN, even in the
absence of routing tables, localization and synchronization
techniques. In our protocol, we assume only one relay in
each layer, in order to avoid flooding. On the other hand,
if we had assumed more than one relay node in each layer,
the relaying redundancy would have increased the throughput.
However, increasing the number of relays would have to
resolve issues related to channel contention. In such a case,
a more complicated design would have to be used to avoid
collisions, in order to ensure that throughput does not reduce.
This algorithm can further be extended to terrestrial sensor
networks with appropriate modifications in the system models
and parameters. Terrestrial networks can however leverage
on available localization, time synchronization techniques and
will not suffer from large propagation delays. Protocols with
better efficiency can therefore be designed for terrestrial
networks which exploit these features.
A PPENDIX A
D ERIVATION OF E QUATION . (4)
The expression for the total energy expenditure in the
network can be computed as follows. Assume the following
network parameters:
∙
∙
∙
∙
∙
𝑁𝑐 - Control packet length, 𝑁𝑓 - Potential node declaration packet length, 𝑁𝑡 - Data packet length
𝐸𝑅𝑃 - Energy required to receive/process one bit of data,
𝐸𝑇 𝑙 - Energy required for a node in 𝑙𝑡ℎ layer to transmit
one bit of data, 𝐸𝑚𝑎𝑥 - Maximum transmission energy
per bit
𝑓 (𝑟) - Probability density of node occurrence at a distance 𝑟 from the sink, 𝐿 - Number of layers
𝑡ℎ
𝜌 - Node
∑𝐿 Density, 𝑛𝑙 - Number of nodes in 𝑙 layer, such
that 𝑙=1 𝑛𝑙 = 𝑁
𝜆𝑙 - Average number of packets generated by a node in
𝑙𝑡ℎ layer, 𝑀𝑙 - Number of nodes overhearing the control
packets and 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑟𝑒𝑙𝑎𝑦 𝑛𝑜𝑑𝑒 declaration packet in
the 𝑙𝑡ℎ layer
Energy consumption in transporting a packet from 𝑙𝑡ℎ layer
to (𝑙 − 1)𝑡ℎ layer is given by
𝐸𝑙,𝑙−1 = (𝑁𝑐 + 𝑁𝑡 + 𝑁𝑓 )(𝐸𝑇 𝑙 + 𝐸𝑅𝑃 ) + (𝑁𝑐 + 𝑁𝑓 )𝑀𝑙 𝐸𝑅𝑃
(31)
where the first term corresponds to the energy consumption
due to transmission and reception of data packets and second
term indicates the energy consumption in receiving packets,
when the nodes overhear the control and 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑟𝑒𝑙𝑎𝑦 𝑛𝑜𝑑𝑒
declaration packets of other nodes, and
𝐸𝑇 𝑙 (𝑑𝑏) =
𝐵 log(𝑅𝑙 ) + 𝛼𝑅𝑙 + 𝛽
(32)
Now if we follow the procedure adopted in [1], we can get
the 𝐸𝑇 𝑜𝑡𝑎𝑙 in terms of transmission radii 𝑅𝑙 and ring width
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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 11, NOVEMBER 2010
𝑎𝑙 as follows
𝐸𝑇 𝑜𝑡𝑎𝑙 =
𝐿
∑
(
𝜆 𝑙 𝑘1
𝑙=1
+ 𝑘3
𝑙 ∫
∑
𝑖=1
𝑙(𝑙 + 1)
+ 𝑘2
2
)∫
𝑉𝑖𝑛𝑡
𝑓 (𝑟)𝑑𝑟
𝑙 (
∑
𝛼𝑅𝑙 + 𝐵 log(𝑅𝑙 ) + 𝛽
)
𝑖=1
𝑎𝑙
𝑎𝑙−1
𝑓 (𝑟)𝑑𝑟
where 𝑘1 = (𝑁𝑐 +𝑁𝑡 +𝑁𝑓 )𝐸𝑅𝑃 , 𝑘2 = (𝑁𝑐 +𝑁𝑡 +𝑁𝑓 ), 𝑘3 =
(𝑁𝑐 + 𝑁𝑓 )𝐸𝑅𝑃 and 𝑉𝑖𝑛𝑡 is the volume over which nodes face
interference due to transmissions made by other nodes.
To ensure reliable packet delivery, the probability of successful packet forwarding is also considered in the design. The
expression for this probability can be found by considering
the layering structure with some width 𝑎𝑙 as shown in Fig. 3.
Assume a node 𝑇 in layer 𝑙 transmits a packet to sink node
with maximum attainable range 𝑅𝑙 corresponding to receive
energy 𝐸𝐷 (detection threshold). Now consider a range circle
with center 𝑇 and radius 𝑅𝑙 as shown in Fig. 3. The packet
from 𝑇 will be forwarded to the layer 𝑙 − 1, only if at least
one node is located in the intersection of the range circle and
boundary of layer 𝑙 − 1 (shaded region in Fig. 3). Probability
of at least one node lying in the intersection volume (𝑃1 ) can
be determined from (1), as follows
𝑃1 (𝑅𝑙 , 𝑎𝑙 ) = 1 − 𝑒−
∫
V
𝜌𝑑v
(33)
where V is the volume of the intersecting region, which is
derived as a function of 𝑅𝑙 and 𝑎𝑙 in [5]. Let us assume 𝑃𝑡ℎ
is the lower bound on 𝑃1 (𝑅𝑙 , 𝑎𝑙 ) then
𝑃1 (𝑅𝑙 , 𝑎𝑙 ) > 𝑃𝑡ℎ
(34)
(34) gives bounds on values of 𝑎𝑙 and 𝑅𝑙 and (33) gives
the total energy expenditure in packet transmissions. Now the
problem is to minimize 𝐸𝑇 𝑜𝑡𝑎𝑙 , while ensuring the probability
of packet forwarding is above a certain threshold value.
However, the minimization of 𝐸𝑇 𝑜𝑡𝑎𝑙 should ensure that the
transmission energy in any layer is less than or equal to the
maximum transmission energy and the summation of layer
widths should be able to cover the total region of deployment.
Therefore, the minimization criterion subject to the three
constraints leads to a mathematical formulation given by (4).
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Sarath Gopi received the BE in electronics and
communication engineering from the National Institute of Technology, Calicut, India in 2002, and the
MTech in electrical engineering from IIT Bombay,
India in 2008. He is currently working as a Scientist
for the Indian Defence Research and Development
Organization (DRDO), Cochin, India.
GOPI et al.: E-PULRP: ENERGY OPTIMIZED PATH UNAWARE LAYERED ROUTING PROTOCOL FOR UNDERWATER SENSOR NETWORKS
Kannan Govindan received the BE in electronics
and communication engineering from the National
Institute of Technology Trichy, India in 2002, and
the PhD in electrical engineering from IIT Bombay,
India in 2009. He is currently working as a postdoctoral researcher in the Department of Computer
Science at the University of California Davis. For
more details see www.cs.ucdavis.edu/∼gkannan.
Deepthi Chander received the B.Tech in electrical engineering from the Cochin University of
Science and Technology in 2002, and the M.E in
communication systems from Anna University in
2005. Deepthi is currently a Ph.D student at the
SPANN Lab, Department of Electrical Engineering,
IIT Bombay.
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U. B. Desai received the B. Tech. degree from
the Indian Institute of Technology, Kanpur, India,
in 1974, and the Ph.D. degree from The Johns
Hopkins University, Baltimore, U.S.A., in 1979, in
electrical engineering. Since 2009, Prof. Desai has
taken charge as the first Director of IIT Hyderabad.
For more details see www.iith.ac.in/∼ubdesai.
S. N. Merchant is a Professor in the Department of
Electrical Engineering, IIT Bombay. He received his
B. Tech, M. Tech, and Ph.D. degrees all in electrical
engineering from IIT Bombay, India. He is a Fellow
of IETE. He is a recipient of the 10th IETE Prof.
S. V. C. Aiya Memorial Award for his contribution
in the field of detection and tracking. He is also
a recipient of the 9th IETE SVC Aiya Memorial
Award for “Excellence in Telcom Educationâ.”