Insensitivity of multiclass systems with general dynamic preemptive resume queueing disciplines

Abstract

We are concerned with the insensitivity of the stationary distributions of the system states inM/G/s/m queues with multiclass customers and with LIFO preemptive resume service disciplines. We introduce general entrance and exit rules into and from waiting positions, respectively, for the behaviour of waiting customers whose service is interrupted. These rules may, roughly speaking, depend on the number of customers in the system. It is shown that the stationary distribution of the system state is insensitive not only with respect to the service time distributions but also with respect to the general entrance and exit rules. As well as the insensitivity of the service scheme, our results are obtained for a special form of state and customer type dependent arrival and service rates. Some further results are concluded related to insensitivity like the formula for the conditional mean sojourn time and the property of transformation of a Poisson input into a Poisson output by the systems.