Modeling queues using Poisson approximation in IEEE 802.11 ad-hoc networks

In this paper, we demonstrate that probability distribution of service time intervals of MAC queues in 802.11 ad-hoc networks take a simple exponential form when effects of hidden nodes dominate and when neighborhood "menace" increase in the network. We apply Chen-Stein Poisson approximation method to the superposition of several neighborhood service processes. Using the Chen-Stein bounds on distribution distances, we propose a general solution for service interval distribution and prove that the distribution exhibits Poisson properties. Under saturated conditions, the approximation converges to M/M/1/K discipline, thus greatly reducing the complexity of steady-state MAC queueing analysis in 802.11 ad-hoc networks. Further, we show that inter-arrival distribution of next-hop nodes in a multihop network also take an exponential form owing to the reversibility nature of birth-death service process of previous queue. We validate our analytical model using ns2-based simulations of randomly generated topology. Through simulations, we observe that the service intervals are exponentially distributed and the convergence to exponential form occurs as the number of neighbors increase. We believe that our Poisson approximation to service interval distribution is a significant observation established through stochastic superposition of steady-state queues, and it gives a fresh insight into steady-state queueing behavior of 802.11 ad-hoc networks.