Performance Evaluation of the Priority Multi-Server System MMAP/PH/M/N Using Machine Learning Methods

Vladimir Vishnevsky, Valentina Klimenok, Alexander Sokolov and Andrey Larionov
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Vladimir Vishnevsky: Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia
Valentina Klimenok: Department of Applied Mathematics and Computer Science, Belarusian State University, 220030 Minsk, Belarus
Alexander Sokolov: Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia
Andrey Larionov: Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia

Mathematics, 2021, vol. 9, issue 24, 1-27

Abstract: In this paper, we present the results of a study of a priority multi-server queuing system with heterogeneous customers arriving according to a marked Markovian arrival process ( MMAP ), phase-type service times ( PH ), and a queue with finite capacity. Priority traffic classes differ in PH distributions of the service time and the probability of joining the queue, which depends on the current length of the queue. If the queue is full, the customer does not enter 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 with K priority classes, a new method for assessing the performance characteristics of complex priority systems has been developed, based on a combination of machine learning and simulation methods. We demonstrate the high efficiency of the new method by providing numerical examples.

Keywords: multi-server queueing system; heterogeneous customers; marked Markovian arrival process; priorities; loss probabilities; machine learning; artificial neural networks; simulation modeling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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