Spatial fairness in multi-channel CSMA line networks

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.