A priority tandem queue with no intermediate buffer

Priority queues are important in modelling and analysis of manufacturing systems, and computer and communication networks. In this paper, a priority tandem queueing system with two stations in series is studied. There is no intermediate buffer between the two stations, and the lack of buffers may cause blocking at the first station. K types of customers arrive at the system according to Poisson processes. The expected delay in the system for each type of customer is obtained when all the customers have the same service time distribution at the second station. Two cases are studied in detail when service times are either all exponentially distributed or all deterministic.