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

Vladimir Vishnevsky,Alexander Sokolov,Andrey Larionov,Valentina Klimenok

doi:10.3390/math9243236

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.

Highlights

Priority queuing systems, which are an essential part of the queuing theory, are effectively used in the analysis of real technical and social systems [1,2,3,4,5,6,7]
This paper presents for the first time the results of a study of a multi-server queueing system with a marked Markovian arrival process (MMAP), a queue with finite capacity, and an arbitrary number of customers types
We generated a synthetic dataset for training and testing machine learning (ML) models

Summary

Introduction

Priority queuing systems, which are an essential part of the queuing theory, are effectively used in the analysis of real technical and social systems [1,2,3,4,5,6,7]. Information services with different categories of users [5], as well as any social systems with different types of clients, such as hospitals, are other examples of the systems with priority traffic. Priority systems are used to provide users with priority login when working with various services. The paper [5] provides an analysis of the impact of priorities on the workload, transaction time, and other characteristics, investigating the performance of various databases for users with different access priorities

Objectives

Methods

Results

Conclusion