Wireless Sensor Networks : Technology, Protocols, and Applications

PERFORMANCE MODELING OF WSNs 293
The one-hop transmission from transmitter i to the receiver j is successful if (1) the
distance between i and j is less than or equal to r: d i; j r; (2) for every other node,
k, which is also receiving at the same time, d i;k > r; and (3) for every other node, l,
which is transmitting at the same time, d l; j > r.
Based on the definition above and the term l n;m , defined as the average transmission
rate between node n and its generic receiver m, Chiasserini and Garetto [11.17]
have constructed an interference model to calculate a successful transmission
probability ðbÞ using l n;m as an input, under the assumption that the WSN employs
a CSMA/CA mechanism with handshaking as in an IEEE 802.11 DCF. Also, if
an IEEE 802.11 DCF or its variants is used as the MAC protocol, one may apply
many existing performance analysis results directly (e.g., [11.19,11.20]) to obtain
performance metrics such as throughput, delay, and collision probability, given the
number of competing nodes.
Routing Model Based on the energy model introduced earlier in the chapter,
energy consumed for a generic route P ½EðPÞŠ can be computed as follows [11.17]:
EðPÞ ¼ X i!P
E i;np ðiÞðl i ; d i Þ ð11:5Þ
where n p ðiÞ is the next hop of node i on path P. E i;np ðiÞðl; dÞ is the energy from node i
to node n p ðiÞ. Assuming that the data size is l i bits and the distance between them is
d i , the total energy consumed can be written using Eq. (11.3).
The advantages of data-centric routing over address-centric routing in supporting
data aggregation were found from analysis [11.21]. These results show that:
1. If the diameter of the set of source nodes ðXÞ is shorter than the minimal
length of the shortest path from any source node to the sink ðD min Þ, the total
number of transmissions under data-centric routing is smaller than with
address-centric routing. Therefore, data-centric routing is more energy
efficient.
2. The larger the distance between X and D min , the more energy is conserved by
the data-centric routing.
System Model Analysis of the overall performance of the sensor network is
presented in [11.17], where a closed-loop model has been constructed to consider
the sensor node model, MAC protocol, and routing policy all at the same time. This
model consists of three submodels, as shown in Figure 11.5. The sensor node model
was shown earlier in the chapter and in Figure 11.4. The interference model was
also described earlier. The network model is used to model routing policy and to
determine the average transmission rate between nodes, which is an input to the
inference model. In [11.17], a simple routing policy is assumed as follows: When
transmitting data to the next hop, a sensor node chooses the neighboring node that
will result in the lowest energy consumption. The solution of the system model in
Figure 11.5 has been obtained through fixed-point approximation [11.17], and