InterJournal Complex Systems, 1110
Status: Accepted
Manuscript Number: [1110]
Submission Date: 2004
Whisperers and Shouters: Random Wireless Sensor Networks with Asymmetric Two-Tier Connectivity
Author(s): Nagendra Marupaka ,Ali A. Minai

Subject(s): CX.6



There has recently been great interest in networks with small-world and power-law connectivity. Such networks have been shown to possess several characteristics that are very desirable for communication networks, e.g., short path lengths, high robustness, etc. However, most of the work has focused on networks in abstract spaces where the geographical constraints of two or three dimensional space are not a concern. This is an appropriate model for networks such as the internet and the World Wide Web, but in wireless networks (such as networks of randomly deployed sensors), the use of only short-range communication results in connectivity patterns with a strong geographical constraint. Recently, many researchers have applied methods from percolation theory and critical systems to these networks, and have demonstrated the presence of typical phase-transition phenomena. In particular, some studies have looked at the effect of communication range (hop length) on connectivity, path length, and other network properties. However, there has been no explicit analog of the small world approach involving the introduction of a few long-range connections --- presumably because of the fundamentally local nature of connectivity in wireless networks. In this work, we look at wireless networks comprising two types of nodes: "Shouters", which have a large transmission range (implying higher energy usage per transmission); and "whisperers", which have a smaller transmission radius. This creates a two-tier network architecture somewhat reminiscent of clustered networks, but we do not explicitly consider clustering. Rather, we focus on the resulting random network which, unlike most of those studied in the literature, has asymmetric connectivity due to the two-tier structure: The whisperers can hear shouters that cannot hear them. Like long-range connections in small world networks, shouters create shortcuts in the wireless network, but are much more constrained by the fundamentally local nature of wireless transmission and the directionality of the short-cuts. We investigate whether, and to what degree, the benefits of small world networks still obtain in this case. We present three types of results: 1. Phase transition phenomena in connectivity as a function of node population densities and the ratio of whisperer-shouter transmission radii. 2. Trade-offs in message latency, hop count (path length), energy efficiency, network lifetime and robustness as network parameters are varied. 3. Possible approaches for the self-organized configuration of whisperers and shouters in initially homogeneous random networks, with the goal of optimizing efficiency, reliability, robustness, and network lifetime. Simulation results are presented to demonstrate the phenomena and the utility of random two-tier networks, and the benefits of self-organized configuration.

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