Asymptotic and Numerical Analysis of Multiserver Retrial Queue with Guard Channel for Cellular Networks

Abstract: This paper considers a retrial queueing model for a base station in cellular networks where fresh calls and handover calls are available. Fresh calls are initiated from the cell of the base station. On the other hand, a handover call has been connecting to a base station and moves to another one. In order to keep the continuation of the communication, it is desired that an available channel in the new base station is immediately assigned to the handover call. To this end, a channel is reserved as the guard channel for handover calls in base stations. Blocked fresh and handover calls join a virtual orbit and repeat their attempts in a later time. We assume that a base station can recognize retrial calls and give them the same priority as that of handover calls. We model a base station by a multiserver retrial queue with priority customers for which a level-dependent QBD process is formulated. We obtain Taylor series expansion for the nonzero elements of the rate matrices of the level-dependent QBD. Using the expansion results, we obtain an asymptotic upper bound for the joint stationary distribution of the number of busy channels and that of customers in the orbit. Furthermore, we derive an efficient numerical algorithm to calculate the joint stationary distribution.