An approximation method for a non-preemptive multiserver queue with quasi-Poisson arrivals

We consider a non-preemptive multiserver queue with multiple priority classes. We assume distinct exponentially distributed service times and separate quasi-Poisson arrival processes with a predefined maximum number of requests that can be present in the system for each class. We present an approximation method to obtain the steady-state probabilities for the number of requests of each class in our system. In our method, the priority levels (classes) are solved “nearly separately”, linked only by certain conditional probabilities determined approximately from the solution of other priority levels. Several numerical examples illustrate the accuracy of our approximate solution. The proposed approach significantly reduces the complexity of the problem while featuring generally good accuracy.