Spatial fairness in multi-channel CSMA line networks

Abstract

In this paper we consider a multi-channel random-access carrier-sense multiple access (CSMA) line network with n saturated links, where each link can be active on at most k of the C available channels at any time. Using the product form solution of such a network, we develop fast algorithms to compute the per-link throughputs and use these to study the spatial fairness in such a network.Recently it was shown that fairness in a single channel CSMA line network can be achieved by means of a simple formula for the activation rates, which depends solely on the number of interfering neighbors. In this paper we show that this formula still achieves fairness in the multi-channel setting under heavy traffic, but no such simple formula seems to exist in general, unless k equals C. On the other hand, numerical experiments show that the fairness index when using the simple single channel formula in the multi-channel setting is close to one and tends to improve as k increases. In other words this simple formula eliminates most of the spatial unfairness in a multi-channel network, especially when k is close to C.