On two parallel queues with one-way overflow

This paper deals with a system consisting of two parallel multiserver queues with waiting places, which receive demands from two types of customers respectively. Customers for the first queue are allowed to overflow to the second queue, if they are blocked at the first queue. The first sections of the paper are devoted to the numerical solution of the linear system of equilibrium equations in order to be able to compute loss probabilities and average system times. The algebraic structure of the linear system leads naturally to the use of a block iterative method. An iteration procedure based on the Accelerated Overrelaxation (AOR) method is described. Then the behaviour of systems with two parallel queues is discussed. Remarks are made with respect to some general notions on how to find queueing systems that satisfy certain requirements.