Analysis of a multi-server queueing model with MAP arrivals of regular customers and phase type arrivals of special customers

• Arrivals of two types with one needing a server and other all on a preemptive basis.
• Versatile process to model one type and a phase type process for the other type.
• Applications in practice notably in military and healthcare systems.
• An example of queues with interruptions.
• Model not studied before to make this as a particular/generalization of existing one.

We consider a multi-server queueing model in which two types of arrivals occur. Regular customers arrive according to a Markovian arrival process and special customers arrive according to a phase type renewal process. The service times are exponentially distributed with parameter depending on the type served. While a regular customer requires the attention of only one server, a special customer needs the attention of all servers. An arriving special customer finding the servers busy with a special customer is lost; otherwise, the special customer will enter into service immediately by possibly pre-empting existing services of regular customers. The displaced customers will enter into service once the special customer leaves. The model is analyzed in steady state and some illustrative numerical examples are discussed to bring out the key effect of the special customers on selected system performance measures.