This work presents an analysis of a cluster of finite population of low cost sensor nodes operating in a ppersistent S-Aloha framework with multipacket messages. Using this analytical framework, we consider the issue of partitioning the nodes and available frequencies into groups so as to maximize the system throughput. Assigning the nodes and frequencies into "groups" is important because the size of the group impacts the tradeoff between the benefits of frequency diversity and the cost of collision on the shared medium imposed by the nodes in a group. We study this tradeoff through analytical and numerical results and show how the correct choice of group sizes can vary depending on various factors like the ratio of nodes to frequencies and the overall system load.

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Abstract-In this paper, we consider the problem of placing, with course-grained control, a large number of wireless networked sensor nodes employing a clustering network architecture. The goal of the deployment strategy is to maximize the lifetime while ensuring connectivity between cluster-heads so that samples from the monitored area may be forwarded to a fusion center. A model is derived to approximate the lifetime of a differentially deployed random network using both the density of cluster-heads and non-clusterheads as variables. Through optimization of the lifetime expression over both variables and through simulation results, it is shown that 1) a differential node deployment with a uniform cluster-head density increases the lifetime of the network over a uniform deployment and 2) the addition of a suitable differential cluster-head density further increases lifetime over the differential node deployment with uniform cluster-head density.

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