Spatial Fairness in Multi-Channel CSMA Line Networks

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 one 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. We consider both standard CSMA networks and CSMA networks with so-called channel repacking. 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 and low traffic, but no such simple formula seems to exist in general. On the other hand, numerical experiments show that the fairness index when using the simple single channel formula in the multi-channel setting is very close to one, meaning this simple formula also eliminates most of the spatial unfairness in a multi-channel network.