Numerical-Analytic Model of Multi-Class, Multi-Server Queue with Nonpreemptive Priorities

We consider a multi-class, multi-server queuing system with preemptive priorities. We distinguish three groups of priority classes that consist of multiple customer types, each having their own arrival and service rate. We assume Poisson arrival processes and exponentially distributed service times. The performance of the system is described in event language. The created software automatically constructs and solves system of equilibrium equations to find steady state probabilities. We suggest a numerical-analytic method to estimate the probabilities. Based on these probabilities, we can compute a wide range of relevant performance characteristics, such as average number of customers of a certain type in the system and expected postponement time for each customer class.