Analysis of Energy Conservation in Sensor Networks

Abstract

In this paper we use the Erlang theory to quantitatively analyse the trade offs between energy conservation and quality of
service in an ad-hoc wireless sensor network. Nodes can be either sleeping, where no transmission or reception can occur,
or awake where traffic is processed. Increasing the proportion of time spent in the sleeping state will decrease throughput
and increase packet loss and delivery delay. However there is a complex relationship between sleeping time and energy consumption.
Increasing the sleeping time does not always lead to an increase in the energy saved. We identify the energy consumption profile
for various levels of sensor network activity and derive an optimum energy saving curve that provides a basis for the design
of extended-life ad hoc wireless sensor networks.

Full text

Page 1

Analysis of Energy Conservation in Sensor Networks
Q.Gao1, K.J.Blow1, D.J.Holding1, Ian Marshall2
1Aston University, Aston Triangle, Birmingham, UK, B4 7ET, Tel: +44 121 359
3611, Fax: +44 121 359 0156
(qianggao@aston.ac.uk, k.j.blow@aston.ac.uk, d.j.holding@aston.ac.uk)
2University of Kent, Canterbury, Kent, UK, CT2 7NF, Tel: +44 1227 827753, Fax:
+44 1227 762811
(i.w.marshall@kent.ac.uk)
Abstract
In this paper we use the Erlang theory to quantitatively analyse the trade offs
between energy conservation and quality of service in an ad-hoc wireless sensor
network. Nodes can be either sleeping, where no transmission or reception can occur,
or awake where traffic is processed. Increasing the proportion of time spent in the
sleeping state will decrease throughput and increase packet loss and delivery delay.
However there is a complex relationship between sleeping time and energy
consumption. Increasing the sleeping time does not always lead to an increase in the
energy saved. We identify the energy consumption profile for various levels of sensor
network activity and derive an optimum energy saving curve that provides a basis for
the design of extended-life ad hoc wireless sensor networks.
Keywords: Sensor networks, Ad hoc networks, Energy efficient design, QoS, Erlang
formula

Page 2

1 Introduction
Recent advances in micro-electro-mechanical systems (MEMS) technology,
wireless communications and digital electronics have enabled the development of
low-cost, low-power, multifunctional smart sensor nodes [1]. Smart sensor nodes are
autonomous devices equipped with heavily integrated sensing, processing, and
wireless communication capabilities [2][3]. When these nodes are networked together
in an ad-hoc fashion, they form a sensor network. The nodes gather data via their
sensors, process it locally or coordinate amongst neighbors and forward the
information to the user or, in general, a data sink. Due to the node’s limited
transmission range, this forwarding mostly involves using multi-hop paths through
other nodes [3]. A node in the network has essentially two different tasks: (1) sensing
its environment and processing the information for onward transmission, and (2)
forwarding traffic from other sensors as an intermediate relay in the multi-hop path.
The major design challenge for this type of network is to increase the operational
lifetime of the sensors as much as possible [1][4]. Indeed, sensor nodes are miniature
devices and operate on a tiny, non-replaceable battery. Energy efficiency is therefore
the critical design constraint. Research can address two different perspectives of the
energy problem: (1) an increase in battery capacity and (2) a decrease in the amount of
energy consumed at the wireless terminal. The focus of battery technology research
has been to increase battery power capacity while restricting the weight of the battery.
However, unlike other areas of computer technology such as microchip design, battery
technology has not experienced significant (compared to Moore’s Law) advancement
in the past 30 years. Therefore, unless a breakthrough occurs in battery technology, a
goal of research should be to decrease the energy consumed in the wireless terminal
[5].
In terms of energy consumption, the wireless exchange of data between nodes
strongly dominates other node functions such as sensing and processing [6][7].
Moreover, actual radios consume power not only when sending and receiving data,
but also when listening. Energy models have been developed [7][8] which show that
the energy consumption ratio of listen:receive:send is about 1:1:1.5. With this model,
node listening time dominates energy consumption in light or moderate traffic
scenarios. Significant energy savings are only obtainable by putting the node into a
sleep mode when there is no traffic [4][9][10].
Given the importance of energy conservation in sensor networks we now describe a
simple model that allows us to investigate a) the relationship between energy
consumption and network traffic and b) the trade off between energy consumption and
network performance. Our asynchronous queuing model looks rather like pure
ALOHA with random periods of sleep although the local connectivity of nodes in a
sensor network is quite different to the global connectivity of nodes in a simple
ALOHA network. Recently, there has been some research on slotted ALOHA medium
access control protocols for sensor networks [18][19][20]. The performance analysis
of pure ALOHA algorithm provides a base level of performance for judging the
effectiveness of the slotted ALOHA algorithm. Similarly, our simple model also
provides a benchmark against which the performance of more complex sleep
synchronisation protocols can be judged.
2 Description of sensor node
We consider a network of wireless sensor nodes where each node consists of a
transmitter and receiver together with some sensing device. For our purposes the
sensing device is a source of information flow local to the sensor node. We will
assume that the sensor node is kept as simple as possible in order to enable mass
deployment. Thus, we assume that a single antenna is available and that the node can

Page 3

transmit or receive but not both simultaneously. Each sensor node will accept
information from other nodes for onward transmission. There will also be special
'sink' nodes in the network where information terminates, these will not be explicitly
modelled here as we are only interested in the relationships between local and transit
traffic and how these affect the performance of the network. Since nodes will have
limited computational and memory resources we will explicitly model the queuing of
packets in the node.
The four possible states of the nodes are shown in Figure 1. A node is said to be
'active' when it is transmitting or receiving information and 'idle' when it is listening
(i.e. listening but not actually receiving data) or asleep (i.e. not listening to the outside
world). These four states have different levels of energy consumption, as we will
discuss in the next section. Transitions between these states can occur naturally, such
as the change from listening to receiving when data arrives from a neighbouring node,
or as a result of some internal decision, such as the scheduling algorithm used to
decide when to change from listening to sleeping and vice versa.
3 Energy-conserving algorithm
To reach our low energy target, we can let radios sleep most of the time and yet let
them awaken precisely when they need to transmit or receive data. Unfortunately,
current radio technology does not easily allow a radio to be awakened upon request.
Hence, a radio must wake up periodically, see if anyone wants to talk to it, and, if not,
go back to sleep. The simple energy-conserving algorithm that we will analyse will
now be described.
Nodes are in one of the following states: sleeping, listening, sending or receiving.
The state transition diagram is shown in Figure 1. We use the term idle to describe the
sleeping and listening states and the term active to describe the sending or receiving
states.
Initially nodes start out in the sleeping state. When sleeping, the radio is off and
therefore not consuming power. (Although the radio is off, sensors or other low power
parts of the node may be on.) In this state the radio remains turned off for time Ts and
then undergoes a transition to listening. If, however, while a node is sleeping data to
be transmitted is generated then it changes to the active transmit state and starts
sending the data. During the listening state if neighboring nodes try to transfer packets
via the node, or if data needs to be sent, the node changes to the appropriate active
state. Otherwise it returns to the sleeping state after time Tl. When in an active state a
node either sends or receives data. After all data transmission has finished, the node
changes to an idle state and begins alternately sleeping and listening according to
some pre-defined pattern.
The algorithm that turns off the radio is targeted to improve power consumption.
However turning off the radio has implications for network performance such as
reduced throughput, added latency and possibly more packet loss compared to the
communication protocols without sleeping patterns. Here our objective is to
characterize the trade-off and enable optimal control of the sleep/listen pattern in
future networks.
We must point out that here we do not consider the synchronization of sleep
schedule among the nodes as discussed in [14] where they listen at the same time and
go to sleep at the same time. Though synchronization might reduce the additional
latency it will increase the chance of overhearing traffic when a node picks up packets
that are destined to other nodes and it will also increase the control packet overhead
(synchronization packets). These are two additional sources of energy consumption
and also increase the complexity of the algorithm. It should be noticed that the
randomly occurring sensor information traffic is a potential interruption to the

Page 4

synchronization and to avoid this would require storage of information in the queue
until the next waking period. This might well increase the required queue lengths in
the nodes. So we consider the simplest algorithm in which each node chooses its own
sleep schedule independently. This asynchronous algorithm may in some cases
increase the probability of network connection. This is because long-range
synchronisation involves some network overhead. Methods based on local
synchronisation can lead to islands of synchronisation where nodes within an island
are synchronised but different islands are not [16][17]. This is illustrated in Figure 2
where a node in island 1 wants to transmit data to a node in island 5. Recall that in a
sensor network the radio range will generally be smaller than the network size and so
global synchronization to a central clock is difficult to guarantee. In this simple
example the nodes in island 1 and island 5 cannot communicate directly. The
probability of connection from the node in island 1 to the node in island 5 in an
asynchronous sleep schedule is larger than in a synchronous sleep schedule because
there are more opportunities to find one of the nodes in islands 2, 3 or 4 awake. In the
extreme case where the islands wake-up periods do not overlap then no
communication will be possible. This problem can be avoided if the sensor nodes
move or there is some level of noise. However, when the network is sufficiently large
the finite propagation speed of the information will limit the achievable global
synchronization or at best lead to synchronization on extremely long timescales. Also,
the performance analysis of a simple asynchronous algorithm provides a base level of
performance for judging the effectiveness of synchronous or other more complex
algorithms in the future.
4 Theoretical analysis
Here we use a similar method to the Erlang formula in telephone systems [25] to
calculate the effects of throughput, packet loss and delay induced by turning off the
radio. Let us consider that node 1 needs to transfer data to node 2. Suppose that A is
the traffic in Erlang that needs to be transferred by node1. It may be local data or data
needing to be forwarded from neighboring nodes. The number of packets waiting in
the queue is x and the number of packets in onward transmission is s. Let [x,s] denote
the state of the sending node 1 when x packets are in the waiting queue and s packets
are in onward transmission; u(x,s) the probability that a packet begins to be
transmitted after a packet arrives at state [x,s]; v(x,s) the probability that, after a packet
finishes transmission, another packet begins to be transmitted. They are expressed as
the following respectively
u x,s={
T , s=0
0, s=1
vx,s={
T , x≥1, s=1
0, x=0 or s=0
(1)
where s∈{0,1}; 0≤x≤K and K is the length of waiting queue. T is the connection
probability from node 1 to node 2 and is determined by the sleeping time, listening
time of receiving node 2 and the traffic between node 1 and node 2 which we will
discuss in detail later.
Assuming that the traffic can be described by Poisson distributed arrival times and
negative exponential holding times (the holding time corresponds to the packet
length) we can obtain general equations of statistical equilibrium [13]. The
assumption of Poisson statistics is questionable given the nature of the anticipated
applications of sensor networks. We might expect more bursty traffic described by
fractal statistics to occur. However, at present there is no experimental evidence
available to resolve this issue. The use of Poisson statistics allows us a) to build an

Page 5

analytic model of traffic dependent energy consumption and b) to provide a base
model against which future numerical simulations can be judged.
Let p(x,s) be the probability of the state [x,s]. Consider a very short interval time dt.
By the assumption that packets occur individually, i.e. in accordance with the Poisson
distribution, the probability of a packet arrival is Adt (terms in higher powers of dt are
neglected). By the assumption that the traffic packets have a negative-exponential
holding-time distribution, the probability that a packet finishes transmission is sdt. For
the statistical equilibrium assumption that p(x,s) is independent of the time, this
implies that the state p(x,s) is created as often as it is destroyed otherwise p(x,s) would
change with time. Therefore the general equations of statistical equilibrium are as
follows:
 As p x,s=A[1−u x−1,s] p x−1,sAu x ,s−1 p x,s−1
s1[1−vx ,s1] p x,s1svx1,s p x1,s
The left-hand side of the equation represents the rate at which the system leaves the
state [x,s] due to the packet arrival rate Ap(x,s) and packet finishing transit rate sp(x,s).
The first term of the right represents the rate at which the system leaves the state [x-
1,s] and enters [x,s], the second term represents the rate at which it leaves [x,s-1] and
enters [x,s], the third and the forth terms represent the rate at which it leaves [x,s+1]
or [x+1,s] and enters [x,s] respectively.
To give the solution we have the further standard assumption [14]: transition
probabilities from state [x-1,s] to state [x,s] and from [x,s-1] to [x-1,s] are the same as
those from [x,s] to [x-1,s] and from [x,s] to [x,s-1], respectively. The following
expressions are then obtained for the probability of the state [x,s] that x packets are in
the queue and s packets are in transit.

p x ,0=Ax1−T x
T
x
(2)
x
p 0,0
p x ,1=Ax1Tp 0,0∑
Using the fact that p K 1,s=0 we have
If T 1
2 and 0≤A
1
p 0,0
1−[A1−T 
T
1−A1−T 
T
AK21−T [1−1−T
T
1−A1−1−T
T
If T 1
2 and A=
1−T
i=1
Ax11−T i
T
i−1
p 0,0
(3)
(4)
T
1−T
or
T
1−T
A1
=
]K1
TA1−AK1
1−A

A21−T {1−[A1−T 
T
]K}
1−A[1−A1−T 
T
]
−
K]

(5)
T

Page 6

1
p 0,0
=K 1TA1−AK1
1−A
KA21−T 
1−A
−
AK21−T [1−1−T
T
K]
1−A1−1−T
T

(6)
If T =1
2 and 0≤A1
1
p 0,0
1−[A1−T 
T
1−A1−T 
T
If T 1
2 and 0≤A1
1
p 0,0
1−[A1−T 
T
1−A1−T 
T
The probability of packet loss is
L = p K ,1 p K ,0
The carried traffic is
A'=A[1− p K ,1− p K ,0]
The average delay time, that is the waiting time averaged over the carried traffic, is
q
A'
where the average number of waiting packets is
K
xp x,1∑
x=1
=
]K1
TA1−AK1
1−A

A21−T {1−[A1−T 
T
]K}
1−A[1−A1−T 
T
]
−KAK21−T 
1−A
(7)
=
]K1
TA1−AK1
1−A

A21−T {1−[A1−T 
T
]K}
1−A[1−A1−T 
T
]
−
AK21−T [1−1−T
T
K]
1−A1−1−T
T

(8)
(9)
(10)
D =
(11)
q =∑
x=1
K
xp x,0
(12)
5 Connection Probability T
In an ad-hoc network each node is, in general, surrounded by a dynamic collection
of other nodes. Each node also performs a dual function of sending out data collected
locally and relaying data sent from other nodes as shown in Figure 3. While
transmission of local data will only involve the use of the transmitter, relaying
network traffic will involve the use of both the receiver and the transmitter. Since our
simple nodes cannot perform transmit and receive simultaneously we need to account
for the mutual blocking of these two processes. When a node has some data needing
to be sent out, it should try to establish a connection first. We denote the connection
probability by T. We assume that the sending operation has a higher priority than the
receiving operation. Then the sending node can connect to the receiving node when
there is no packet in the waiting queue of the receiving node and the receiving node is
also in the listening state. If we also assume that every node is equivalent, from a

Page 7

traffic carrying perspective, in the whole network then we have the following formula
for the connection probability
T =T
T
l
T
l
and Ts are the listening time and sleeping time respectively. When there is heavy
traffic in the network there will always be some packets in the waiting queue of the
receiving node, which will keep trying to send the packets out. Under these
conditions, the probability of the receiver being available is very low. Our calculations
based on this assumption, that transmission has a higher priority than receiving,
confirm that the throughput in the network is very low under heavy traffic conditions.
Here we consider the alternative prioritisation, that the receiving operation has
higher priority than the sending operation. The sending node can successfully connect
to the receiving node when there is no packet in the waiting queue of the receiving
node and it is in listening state or when there are some packets in the waiting queue
but the receiving node is not actually in the process of sending packets. In this case the
formula for the connection probability becomes
T =T
where the first term is the contribution due to being in the listening state and the
second term is the contribution when there are some packets in the queue but the
receiving node is not actually sending information. Note that A’ is the traffic that is
actually carried by the node and that the connection probability given by equation (14)
is always larger than (13). From equations (5-8), (10) and (14) we can self-
consistently calculate the connection probability T and the other variables.
6 Trade-off between Energy Conserving and QoS
0p 0,0
(13)
where T
0=
sT
represents the sleeping time factor of the receiving node, Tl
0p 0,01− p 0,0−A'
(14)
Quality of Service (QoS) is an important consideration in any communications
network. It can be measured in many ways depending on the nature of the applications
deployed. In our case, we will use packet delay or packet loss as measures of QoS.
In order to save the energy in sensor networks we turn off the radio when there is no
data to transfer. However it will reduce the network throughput and increase packet
loss and delay. This technique trades off energy savings versus QoS of sensor
networks. We can deduce the relationships, which are shown in the following figures
from the formulas above.
In Figure 4, the packet loss rate L is plotted versus the offered traffic, A, on one
node. The length of its waiting queue is K=5. We observe that for higher values of the
sleeping time Ts, that is the smaller T0, the higher the packet loss becomes. Indeed, as
A approaches 1 these curves will diverge in the normal way as the offered traffic is
close to the maximum capacity.
Figure 5 shows the carried traffic A’ as a function of the offered traffic A. The peak
of each curve corresponds to the maximum throughput. We observe that for higher
values of the sleeping time Ts, that is the smaller T0 , the throughput in the network is
lower, as we would expect. The carried traffic curve in the absence of the blocking
effect (i.e. if two radio cards are used, one for sending and one for receiving) is also
shown in this figure.
In Figure 6, the packet delay D is plotted versus the amount of traffic A. We
observe that the packet delay increases with increased sleeping time. In other words,
conserving energy leads to a reduction in network QoS. We have also observed that
longer queues lead to longer packet delays with an associated reduction in packet loss
in the normal way, which is not shown in the figures.

Page 8

We now take the energy consumption ratios to be (note that energy consumption is
zero in the sleeping state) listen:receive:send = 1:1:b . The total energy consumption
of one node can then be expressed as
E =A
The first term A’ is the energy consumption for data receiving. The second term
1−A' p 0,0T
listening when the node is idle, that is when it is neither sending nor receiving traffic.
The last term b 1−A'[1− p 0,0] is the energy consumption when the node is
in sending state. There are two parts in this term: one is the energy consumption for
the actual process of sending packets bA’, which we call the sending consumption; the
other is the energy consumption for establishing a connection before the sending
operation b 1−A'[1− p 0,0]−b A', which is called the connecting
consumption.
Figure 7 shows the energy consumption of one node for data receiving, data
sending, connection establishing, listening and the total energy consumption when
T=0.3, K=5, b=1.5 and T=0.5, K=5, b=1.5. We can see that the difference in energy
consumption, for establishing connections, between T=0.3 and T=0.5 is much bigger
than the differences in energy consumption for other contributions such as listening,
sending and receiving data. This is the main reason for the complex relationship
between energy saved and sleeping time. A longer sleeping time does not always lead
to an increase in energy saving. In some cases we cannot even save energy by adding a
sleeping schedule into the communication protocol.
Figure 8 shows the surface of energy consumption E (K=5, b=1.5) versus the
amount of traffic A and the sleeping time factor variable T0. We can save the energy
from the area of the energy consumption surface under the energy consumption plane
(T=1.0) when there is no sleeping schedule in the radio. The maximum energy saving
curve (i.e. minimum energy consumption curve) is shown in Figure 8 as well.
In Figure 9, the energy consumption normalized to the maximum energy consumption
is plotted versus the amount of traffic A when, T0=0.1 and T0=0.5 for the energy
consumption ratio 1:1.05:1.4 [21]. For comparison, simulation results from recent
work [22] based on numerical simulations are shown as point values. The agreement
is excellent given that the only fitting parameter required was the scaling between
traffic levels in the numerics and the analytic model. Our model clearly captures the
essential elements of the network properties which allow the overall network
performance to be predicted. Indeed, the numerical model also allowed for non-
Poissonian statistics and the level of agreement might well suggest that this plays a
small part in determining the overall network performance.
Suppose the sensor network had a perfectly synchronised sleep schedule. Here we
don't consider how this happens or how much network traffic would be necessary to
make it happen. We can calculate the performance of such a network by setting
T
time under synchronized conditions. The packet delivery delay for any amount of
sleeping time is given by the curve corresponding to T0=1.0 in figure 6. This is a result
of the receiver model assumption that the transition to the sleeping state can occur
when the node is idle. Thus the node is active for a much larger fraction of time than
the sleeping schedule would predict. If we keep the connection probability factor T0 =
1.0 in equation (14) but use T0 = 0.5 in equation (15) we can calculate the energy
consumption when the node spends half of the time in the sleeping state under
synchronized conditions. Figure 10 shows the comparison between the energy
consumption under synchronized and unsynchronized conditions when T0 = 0.5. The
relatively modest energy saving that is achieved through synchronisation would be
'1−A
' p 0,0T0b 1−A
'[1− p 0,0]
(15)
0 is the energy consumption of periodically waking up for
0=1 in equation (14). The connection probability is independent of the sleeping

Page 9

reduced by the network traffic needed to maintain synchronisation. Further detailed
study of synchronization algorithms is therefore required in order to demonstrate
useful energy savings from their application.
The radio transceiver TR1000 from RF Monolithics, Inc is widely used in developing
sensor nodes. When using OOK modulation at a transmission rate of 19.2 kbps the
power consumption is 13.5mW, 24.75mW and 0.015mW in receiving, transmitting
and sleep respectively. There is no difference between listening and receiving in this
radio transceiver model [23]. When it provides a transmission rate of 2.4 kbps the
power consumption in receiving, listening, transmitting and sleep is 12.5mW,
12.36mW, 14.88mW and 0.016mW respectively [24]. There is no significant change
of our results for these representative power numbers.

7 Conclusions
In wireless sensor networks, where energy efficiency is the key design challenge,
the energy consumption is typically dominated by the node’s communication
subsystem. It can only be reduced significantly by transitioning the radio to a sleep
state when there is no traffic needing to be transferred. However increasing the
sleeping time will reduce throughput and increase packet loss and delivery delay. We
have quantitatively analysed the relationship between energy consumption and
sleeping time and the relationship between QoS and sleeping time. Increasing the
proportion of time spent in the sleeping state will decrease the QoS but does not
always lead to an increase in the energy saved. We have also shown that, where use of
the transmitter and use of the receiver are mutually exclusive then network
performance is improved by giving higher priority to the receiver.
Our analysis shows that the relationship between sleeping time, energy consumption
and QoS is complex and subtle and that detailed analysis and design is therefore
required to achieve good energy saving and an acceptable QoS in ad hoc sensor
networks. We have identified the energy consumption profile for various levels of
sensor network activity and also derived an optimum energy saving curve that
provides a basis for the design of extended-life ad hoc wireless sensor networks.
References
[1] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “Wireless Sensor
Networks: A Survey”, Computer Networks, 38 393-422, 2002
[2] K. Sohrabi, J. Gao, V. Ailawadhi and G. Pottie, “Protocols for self-organization of
a wireless sensor network,” IEEE Personal Communications Magazine, 7 16-27, 2000
[3] L. Clare, G. Pottie and J. Agre, “Self-organizing distributed sensor networks,”
SPIE - The International Society for Optical Engineering, Orlando, FL, 229-237, April
1999
[4] C. E. Jones, K. M. Sivalingam, P. Agrawal, and J. C. Chen, “A survey of energy
efficient network protocols for wireless networks”, Wireless Networks, 7 343-358,
2001
[5] Lettieri, P. and M. srivastava, “Advances in wireless terminals”, IEEE Personal
communications, 6 6-18, 1999
[6] D. Estrin and R. Govindan, “Next century challenges: scalable coordination in
sensor networks,” MobiCom 1999, Seattle, USA, 263-270, 1999
[7] A. Savvides, C. C. Han and M. Srivastava, “Dynamic fine-grained localization in
ad-hoc networks of sensors,” MobiCom 2001, Rome, Italy, 166–179, 2001
[8] M. Stemm and R. H. Katz, “Measuring and reducing energy consumption of
network interfaces in hand-held devices”, IEICE Transactions on Communications,
E80-B 1125-1131, 1997

Page 10

[9] J. M. Rabaey, M. J. Ammer, J. L. da Silva Jr., D. Patel and S. Roundy, “PicoRadio
Supports Ad Hoc Ultra Low-Power Wireless Networking,” IEEE Computer, 33 42-8,
2000
[10] C. Schurgers, V. Tsiatsis and M.B. Srivastava, “STEM: Topology management
for energy efficient sensor networks”, IEEE Aerospace Conference, 2001
[11] Y. Xu, J. Heidemann, and D. Estrin, “Adaptive energy-conserving routing for
multihop ad-hoc networks”, USC/ISI Research Report 527, 2000
[12] C. S. Raghavendra, S. Singh, “PAMAS--Power Aware Multi-Access Protocol
with signaling for Adhoc Networks”, Computer Communications Review, July 1998
[13] D. Bear, “Principles of Telecommunication. Traffic Engineering”, Peter
Peregrinus Ltd. 1988
[14] M. H. Thierer, “Delay systems wich limited accessibility”, preprints of technical
papers, 5th International Teletraffic Congress, New York, 203-213, 1967
[15] W. Ye, J. Heidemann and Deborah Estrin, “An Energy-Efficient MAC Protocol
for Wireless Sensor Networks”, the Proceedings of the 21st International Annual Joint
Conference of the IEEE Computer and Communications Societies (INFOCOM 2002),
New York, NY, USA, 2002
[16] I. Wokoma, I. Liabotis, O. Prnjat, L. Sacks, I. Marshall, “A Weakly Coupled
Adaptive Gossip Protocol for Application Level Active Networks”, IEEE 3rd
International Workshop on Policies for Distributed Systems and Networks - Policy
2002, Monterey, CA, USA, 2002
[17] R. E. Mirollo, S. H. Strogatz, “Synchronization of pulse coupled biological
oscillators”, SIAM J. Applied Mathematics, 1990
[18] R. Simon and E. Farrugia, Topology-transparent support for sensor networks,in:
Proc. of 1st European Workshop on Wireless Sensor Networks (LCNS 2920), Berlin,
Germany, 122-137, 2004
[19] P. Venkitasubramaniam, S. Adireddy and L. Tong, Opportunistic ALOHA and
Cross-Layer Design for Sensor Networks, in: Proc. of IEEE Military Comm. Conf.,
Boston, USA, 123-128, 2003
[20] R. Zheng, J. Hou and L. Sha, Asynchronous Wakeup for Ad Hoc Networks, in:
Proc. of MobiHoc 2003, Annapolis, Maryland, USA, 35-35, 2003
[21] Q. Gao, D.J. Holding, Y. Peng and K.J. Blow, Energy Efficiency Design
Challenge in Sensor Networks, in: Proc. of LCS 2002, London, UK, 69-72, 2002
[22] S. Raghumanshi and A. Mishra, An Approach Towards Improved Energy-
efficiency in Wireless Sensor Nets, in: Proc. of IEEE RAWCON 2003, Boston USA,
225-228, 2003
[23] C. Schurgers, V. Tsiatsis, S. Ganeriwal and M. B. Srivastava, Optimizing Sensor
Networks in the Energy-Latency-Density Design Space, IEEE Transactions on Mobile
Computing, 1(1) 70-80, 2002
[24] W. Ye, J. Heidemann and D. Estrin, Medium Access Control with Coordinated,
Adaptive Sleeping for Wireless Sensor Networks, Technical Report ISI-TR-567,
USC/Information Sciences Institute, 2003
[25] J.E. Flood, Telecommunications, Switching, Traffic and Networks, Longman
1994

Page 11

Idle Active
Sleeping
Listening
Sending
Receiving
Traffic arrives or
local data occurs
Transmission
finishes
After Ts
After Tl
Figure 1: State diagram of the model sensor node.

Page 12

Figure 2: Illustration of a partially synchronised network. Each island, labeled 1-5,
consists of a set of nodes that have achieved local synchronisation. Since the islands
are unsynchronised with each other, this leads to a lower probability of a network path
between island 1 and island 5 compared to the asynchronous case.

Page 13

Figure 3: Diagram illustrating the traffic flows in the node, note that the sending
operation and the receiving operation may block each other.

Page 14

0
0.1
0.2
0.3
A
0.4
0.5
0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
L
T0=0.3
T0=0.5
T0=0.7
T0=1.0
T0=0.1
Figure 4: Packet loss ratio as a function of traffic for the energy-conserving algorithm.

Page 15

0
0.1
0.2
0.3
A
0.4
0.5
0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
A'
T0=0.1
T0=0.3
T0=0.5 T0=0.5
T0=0.7
T0=1.0
T0=0.5, no-blocking
Figure 5: Carried traffic as a function of offered traffic for the energy-conserving
algorithm.