If the standard deviation of cluster sizes in a network is
small enough, the load will be distributed evenly among clusterheads. This
will help to reduce the load disparity and prolong the overall system lifetime.
In our simulation, we run LEACH, Max-Min and Forest schemes for 100
rounds and the average results are shown in Figure 1.
As shown in Figure 1(a) and Figure 1(b), the average number of clusters
is inversely proportional to the average cluster size.
In LEACH simulation, the percentage of clusterheads P is set to 0.05. The
simulation shows that the average number of clusters in LEACH is exactly
0.05 times the number of nodes. When the number of nodes increases, the
average cluster size slightly decreases in Max-Min D Cluster. As the network
density increases, there are more nodes in a node??™s d neighborhood (d is set
to 3 in our simulation), thus Max-Min has fewer clusters and larger cluster
sizes. In Forest, we set the desired cluster size equal to the square root of the
number of nodes. It shows from the simulation that Forest??™s average cluster
357
Yadi Ma and Maggie Cheng
(a) number of clusters
(b) average cluster size
(c) standard deviation of cluster size
Fig. 1. Cluster sizes under various node density.
size is close to the square root of node sizes in all settings. Forest has a
size control mechanism, preventing each cluster from getting too large, the
simulation results having confirmed that it is indeed e?®ective.
Pages:
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572