Mathematical and computer model of multi-server queuing system with preemptive-resume priority in service

The paper presents a mathematical and computer model of multi-server queuing system with preemptive-resume priority in service in terms of point processes and their compensators. The analysis of the complexity of the graph of states in the Markov description of the queuing system is carried out. The advantage of a semimartingale description over a Markovian is demonstrated. In contrast to the Markov description, the model in semimartingale terms allows to model the queuing system for any reasonable number of serving devices, without increasing the complexity of both the mathematical and computer models.