Multi-server Queueing Model with Many Types of Priority Customers

Priority queuing systems can be used to solve problems of designing and optimizing various real systems, in particular, telecommunication and emergency medical systems. Various prioritization schemes have been supplemented in recent years by dynamic priorities that can change while a customer waits for service. In this paper, we analyze multiserver queuing system providing service to heterogeneous requests arriving in the Marked Markov Arrival Process and having different priorities. These priorities are randomized preemptive at the moments of request admission to a finite buffer and are non-preemptive during the service. Requests of each type form own queue in the common buffer space. During the stay in the queue, request can transit to a queue for requests of higher priority and may depart from the system due to impatience. Stationary distribution of the system states is computed via the construction and analysis of the multi-dimensional Markov chain with a special generator structure. Performance measures of the system are computed. Numerical results, including solution of optimization problem, are presented.