Perforamnce evaluation of the priority multi-service system MMAP/PH/M/N using the Monte Carlo method

In this paper, we present the results of a study of a priority multiline queuing system with a marked Markov arrival process (MMAP), phase-type service time (PH), and a buffer with finite capacity. Priority traffic classes differ in the probability of joining the queue, which depends on the number of customers in buffer, and in the service time PH distribution. If the buffer is full, customers don't join the system. An analytical model has been developed and studied for a particular case of a queueing system with two priority classes. We present an algorithm for calculating stationary probabilities of the system state, loss probabilities, the average number of customers in the queue, and other performance characteristics for this particular case. For the general case of a system with K-classes, a simulation model is constructed, with the help of which various characteristics of the system are studied.