Effect of access probabilities on the delay performance of Q-CSMA algorithms

It has been recently shown that queue-based CSMA algorithms can be throughput optimal. In these algorithms, each link of the wireless network has two parameters: a transmission probability and an access probability. The transmission probability of each link is chosen as an appropriate function of its queue-length, however, the access probabilities are simply regarded as some random numbers since they do not play any role in establishing the network stability. In this paper, we show that the access probabilities control the mixing time of the CSMA Markov chain and, as a result, affect the delay performance of the CSMA. In particular, we derive formulas that relate the mixing time to access probabilities and use these to develop the following guideline for choosing access probabilities: each link i should choose its access probability equal to 1/(d_i + 1), where d_i is the number of links which interfere with link i. Simulation results show that this choice of access probabilities results in good delay performance.