A hierarchical cellular system with reneging and dropping for waiting new and handoff calls

We analyze a hierarchical cellular system with an overflow scheme and finite queues for new and handoff calls. The effect of the guard channel scheme and the effects due to reneging of waiting new calls because of the caller´s impatience and dropping of queued handoff call as the callers move out of the handoff area are considered. We successfully solve the system by adopting the multi-dimensional Markovian chain and use the transition-probability matrix and the signal-flow graph to obtain the average new-call blocking probability, the forced termination probability, and the average waiting time of queued new and handoff calls. We further investigate how the guard channel scheme and buffer provision scheme affect the hierarchical cellular system. The results show that it seems unnecessary to provide a guard channel and waiting buffer for microcells in the hierarchical cellular system with an overflow mechanism