Network Lifetime of Application-Specific Randomly Deployed Wireless Sensor Networks in Arbitrary Sensor Density

In many cases, sensors are randomly deployed in wireless sensor networks (WSN), called sensor- randomly-deployed WSN (SRD WSN). Several cluster-based routing protocols are provided to maximize network lifetime of SRD WSN in different sensor densities. LEACH performs better than direct routing in the density of 0.01. BCDCP excels LEACH in the density of 0.05. DMSTRP outperforms LEACH and BCDCP in the density of. However, simulation results under one or two kinds of sensor densities are not strong enough to prove the optimum of the routing protocols. In this paper, we give the general formulas to compute the network lifetimes of the above three routing protocols, discuss their optimal number of clusters, and compare their optimal network lifetime in arbitrary sensor densities. These formulas can provide more general design guidelines applicable to SRD WSN than simulation results under only one or two kinds of sensor densities.