Analytical and simulation modeling of a multi-server queue with Markovian arrivals and priority services

We consider a multi-server queueing system in which two types of customers arrive according to a Markovian arrival process. Type 1 customers have preemptive priority over Type 2 customers. A Type 2 arrival finding all servers busy will be lost. However, a Type 1 customer finding all servers busy with at least one Type 2 in service will get into service by pre-empting one of the Type 2 customers in service. Pre-empted Type 2 customers enter into a buffer of finite capacity. These (preempted) customers eventually leave the system after completing a service. In the case of exponential services, this model is studied analytically in steady-state by exploiting the special nature of the queueing model. A number of useful performance measures along with some illustrative examples are reported. In the case of non-exponential services, we simulate the model and discuss the effect of the variatio the services on some selected performance measures.