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.

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.

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Tree algorithms are a well known class of random access algorithms with a provable maximum stable throughput under the infinite population model (as opposed to ALOHA or the binary exponential backoff algorithm). In this paper, we propose a tree algorithm for opportunistic spectrum usage in cognitive radio networks. A channel in such a network is shared among so-called primary and secondary users, where the secondary users are only allowed to use the channel if there is no primary user activity. The tree algorithm designed in this paper can be used by the secondary users to share the channel capacity left by the primary users.We analyze the maximum stable throughput and mean packet delay of the secondary users by developing a tree structured Quasi-Birth Death Markov chain under the assumption that the primary user activity can be modeled by means of a finite state Markov chain and that packets lengths follow a discrete phase-type distribution.Numerical experiments provide insight on the effect of various system parameters and indicate that the proposed algorithm is able to make good use of the bandwidth left by the primary users.