Analysis of Distributed Random Grouping for Aggregate Computation on Wireless Sensor Networks with Randomly Changing Graphs

Dynamical connection graph changes are inherent in networks such as peer-to-peer networks, wireless ad hoc networks, and wireless sensor networks. Considering the influence of the frequent graph changes is thus essential for precisely assessing the performance of applications and algorithms on such networks. In this paper, using stochastic hybrid systems (SHSs), we model the dynamics and analyze the performance of an epidemic-like algorithm, distributed random grouping (DRG), for average aggregate computation on a wireless sensor network with dynamical graph changes. Particularly, we derive the convergence criteria and the upper bounds on the running time of the DRG algorithm for a set of graphs that are individually disconnected but jointly connected in time. An effective technique for the computation of a key parameter in the derived bounds is also developed. Numerical results and an application extended from our analytical results to control the graph sequences are presented to exemplify our analysis.