2 FINITE QUEUES WITH RELATIVE PRIORITY IN A SINGLE-SERVER SYSTEM WITH PHASE-TYPE DISTRIBUTIONS

A queueing system with one server serving two recurrent inputs with phase type distribution functions is studied. Service times also have phase type distribution functions is studied. Customers of each input wait in separate waiting rooms of finite capacity. Customers of the first input have relative priority over those of the second input. Our main result is a matrix recurrent algorithm for solving a system of equilibrium equations. It perceptibly reduces the order of the initial system of equations and yields a stationary distribution of queues at arbitrary times or at the time of arrival or end of service of customers.