A new computational algorithm for retrial queues to cellular mobile systems with guard channels

Retrial queueing models have been applied to evaluate the impact of new and handover calls on the call control mechanisms of cellular mobile networks. The fact that the retrial rate depends on the number of retried calls waiting in the system leads to an analytically intractable model. Therefore, approximation procedures should be used to compute the performability of the system. However, there exists a numerical problem concerning a recursive algorithm to compute the stationary probabilities for retrial queues modeling guard channels. Namely, the consideration of guard channels leads to calculations with negative terms in the recursive algorithm. Negative terms and extremely small values involved in the computation are the main causes for a numerical instability in the recursive algorithm. We construct a new numerically stable and efficient algorithm to solve the problem. Moreover, we prove that the distribution of the number of calls in the orbit is the ‘‘mixture” of geometric distributions in the presence of the guard channel concept. In a case study we compare the numerical behavior of the existing methods and the proposed approach with the simulation as well. Numerical results show that our algorithm can tackle the problem of large number of channels, very efficiently.