Preemptive Resume Priority Retrial Queue with Two Classes of MAP Arrivals

Abstract: Generally in call centers, voice calls (say Type 1 calls) are given higher priority over e-mails (say Type 2 calls). An arriving Type 1 call has a preemptive priority over a Type 2 call in service, if any, and the preempted Type 2 call enters into a retrial buffer (of finite capacity). Any arriving call not able to get into service immediately will enter into the pool of repeated calls provided the buffer is not full; otherwise, the call is considered lost. The calls in the retrial pool are treated alike (like Type 1) and compete for service after a random amount of time, and can preempt a Type 2 call in service. We assume that the two types of calls arrive according to a Markovian arrival process (MAP) and the services are offered with preemptive priority rule. Under the assumption that the service times are exponentially distributed with possibly different rates, we analyze the model using matrix-analytic methods. Illustrative numerical examples to bring out the qualitative aspects of the model under study are presented.