Wireless Sensor Networks : Technology, Protocols, and Applications

294 PERFORMANCE AND TRAFFIC MANAGEMENT
Figure 11.5 Closed-loop model for the system [11.17].
system performance metrics such as average energy consumption and average delay
have also been calculated in the following manner:
1. Construct a DTMC sensor node model, represented by the leftmost box for
each sensor node i to get the stationary distribution p i and the probability that
data are received in a time slot ða i Þ in node i.
2. Solve the network model using queuing network analysis to calculate the
average data transmission rate between any pair of sensor nodes n and m in
the network ðl n;m Þ as well as the average throughput for each sensor node.
3. Given l n;m as input to the interference model, compute the value of the
probability that data are transmitted successfully in a time slot in node iðb i Þ.
4. b i is used as input to the sensor node model, iterating through steps 1 to 3.
The worst relative error for two successive estimates of the sensor throughput
is used as the stopping criterion. It is stated in [11.17] that 10 iterations result
in an error below 0.0001.
11.5 CASE STUDY: SIMPLE COMPUTATION
OF THE SYSTEM LIFE SPAN
In this section we present a simple model to compute the system life span. The
following assumptions are made:
1. All sensor nodes ðNÞ in the network organize a two-tiered topology. The
sensor nodes in the lower layer are called leaf nodes. The sensor nodes in the
high layer are called leader nodes. At the high layer, there are N 1 leader nodes
forming a k-tree topology with h þ 1 levels (or h hops) from the sink, where
each leader node in level i connects k child nodes in level i þ 1 to its parent
node at layer i 1 (see Figure 11.6). Each leader node in the higher layer that