Adaptive multistage queues with two operating conditions

This paper analyzes a queueing model where the service time distribution is regulated in two ways: first according to the arrival process, as a correlated queue, and second according to the system state at the time when service starts. The second regulation mechanism acts by distinguishing between two operating conditions, called normal-load and overload respectively. Conditionally on such operating conditions, the service time distribution is hyperexponential. The stability conditions of the system are discussed and the stationary distribution is found explicitly. Then the existence and determination of an optimal system is discussed, with respect to a preference structure which represents typical customer objectives.