On the Stochastic Modeling of the Holding Time of SUs to PU Channels in Cognitive Radio Networks

To efficiently utilize the idle periods on primary channels in cognitive radio networks; unlicensed secondary users (SUs) should have prior knowledge of the periods of time over which they can use the channel(s). Therefore, we focus on the problem concerned with the amount of time with which a SU holds a primary channel or more as well as the average amount of data that can be transmitted during this time. We start by deriving closed-form probabilistic expressions for the distribution of that time for different cases that model realistic scenarios. This is done based on the activity levels of primary users (PUs) for cases that include identical and non-identical primary channels for different numbers of SUs. To reduce the computational complexity, we derive closed-form expressions to approximate the obtained expressions for all considered scenarios. Numerical investigations and simulations are carried out to study the correctness of the exact expressions as well as the approximations. The obtained results demonstrate full agreement with the derived expressions and highlight the fact that the gamma distribution is a better approximation than the normal distribution. Finally, two simple channel allocation strategies are implemented to demonstrate the simplicity with which the obtained expressions can be used.