We consider a carrier sense multiple access (CSMA) in an unslotted cognitive radio network with random residence time. In this system, if an arriving secondary user (SU) does not find any idle channels, then the SU either enters the back-off group or gives up its service and leaves the system. SUs in the back-off group have random mobility, so may re-access the channel after random time or go to the other network after random residence time. We model the system by 3-demensional Continuous Time Markov Chain (CTMC) and obtain the steady state probability of the system by matrix analytic method. In numerical results, we compare the performance of two systems with and without residence time of SUs. It is shown that the random mobility of SUs has an impact on the performance of SUs in cognitive radio networks.
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