Probabilistic Modeling of Leach Protocol and Computing Sensor Energy Consumption Rate in Sensor Networks
Abstract
One important performance index of routing mechanisms in sensor net-
works is sensor lifespan. In our settings, sensors are energy-constrained by batteries and located far away from the access point. A sensor dies once
its battery dies. Since the radio transmission consumes a lot of energy, re-
searchers proposed several routing mechanisms to save energy to prolong
the sensor lifespan. So far, the comparison of di®erent routing mecha-
nisms are based on simulation and little analytical results were available.
In this project, we use graph and stochastic modeling techniques to com-
pare the sensor lifespan among di®erent routing mechanisms including
direct transmission, minimum energy transmission, static clustering, and
dynamic clustering.
1 Introduction
Sensor networks become more and more popular as cost of sensor gets cheaper
and cheaper. The sensor network is a wireless network formed by a group of
sensors deployed in same region, which can be used to measure air pressure,
temperature, acceleration, etc. Sensors transmit signals via radio signal. Since
sensors are now small and cheap, they can be deployed in large scale. They be-
come more and more important for applications like security, tra±c monitoring,
agriculture, war ¯eld, etc.
Most of those sensors are powered by batteries. The lifespan of a energy-
constrained sensor is determined by how fast the sensor consumes energy. Sen-
sors use energy to run circuitry and send radio signals. The later is usually a
function of distance and takes a large potion of the energy. Researchers are now
developing new routing mechanisms for sensor networks to save energy and pro-
long the sensor lifespan. Four primary routing mechanisms are direct transmis-
sion, minimum energy transmission, static clustering, and dynamic clustering.
Sensor lifespan is an important performance index for comparison of di®erent
routing mechanisms. So far, the comparison between routing mechanisms is
based on simulation results. To author's knowledge, little analytical results
have been available. In this project, we will use graph theory and stochastic
modelling techniques to assess the sensor lifespan quantitatively.
2 Related work
In [1], Heinzelman, Chardrakasan, and Balakrishnan propose Low-Energy Adap-
tive Clustering Hierarchy (LEACH), which is an energy-e±cient communication
protocol for wireless microsensor networks. The application scenario is,
² The base station is ¯xed and located far from the sensors.
² All nodes in the network are homogeneous and energy-constrained.
LEACH is a dynamic clustering method. In this method, time is partitioned
into ¯xed intervals with equal length. At the beginning of each interval, each
sensor becomes a cluster head with some prede¯ned probability. The cluster
heads then broadcast messages to their neighbors. Other sensors receive mes-
sages and join a cluster by choosing the cluster head with the strongest signal.
During the interval, cluster members send information to their cluster head.
The cluster heads aggregate the information, compress the information, and
route the information to the remote access point. Once the interval ends, the
whole clustering process restarts. Hence, the clusters and cluster heads are
not ¯xed. Since the cluster heads consume more energy than cluster members
in radio transmission, the rotation of cluster heads makes energy consumption
more evenly across all sensors in the network. Therefore, the sensor network
can last longer. In [1], Heinzelman et al. compare LEACH with direct trans-
mission, minimum energy transmission, and static clustering. The simulation
results show that the LEACH can extend the sensor network life up to eight
times longer than its closest competitors.
In this project, we follow the same assumptions in [1] and use graph theory
and stochastic modelling techniques to explicitly compute the sensor life time
for the four routing mechanisms.

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