Performance Analysis of Collision of Exponential Jitter Mechanism in Wireless Networks

Jittering, a small delay imposed before forwarding a packet, has been used in wireless communication for many purposes. For instance, AODV routing protocol uses jitter mechanism to prevent simultaneous transmission of nodes in route discovery stage, which reduces collisions. Recently, many works have studied possibility of using different random variables with different parameters for jittering rather than a simple uniform random variable. It has been shown that other random variables including Exponential and Pareto distributions can also be beneficial. In this paper, we first propose a discrete time Markov model to capture the behavior of nodes in route discovery stage when they use exponential distribution for their jitter mechanism. With this model, we obtain the number of collisions and route discovery time mathematically, which is proven to be accurate by simulation. We also use our model to find the optimum value of λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document}, exponential distribution parameter, which somehow minimize the probability of collision and route discovery time. We further obtain some equations that give us the relation between parameters of different jitter mechanisms such that their route discovery stage takes almost equal time, which is used for fair comparison. Finally, we show that the exponential jitter mechanism using our optimum λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document} outperform other jitter mechanisms.