Priority Multi-Server Queueing System with Heterogeneous Customers

Valentina Klimenok, Alexander Dudin and Vladimir Vishnevsky
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Valentina Klimenok: Department of Applied Mathematics and Computer Science, Belarusian State University, 220030 Minsk, Belarus
Alexander Dudin: Department of Applied Mathematics and Computer Science, Belarusian State University, 220030 Minsk, Belarus
Vladimir Vishnevsky: Sciences and Closed Corporation Information and Networking Technologies, Institute of Control Sciences of Russian Academy, 119991 Moscow, Russia

Mathematics, 2020, vol. 8, issue 9, 1-16

Abstract: In this paper, we analyze a multi-server queueing system with heterogeneous customers that arrive according to a marked Markovian arrival process. Customers of two types differ in priorities and parameters of phase type distribution of their service time. The queue under consideration can be used to model the processes of information transmission in telecommunication networks in which often the flow of information is the superposition of several types of flows with correlation of inter-arrival times within each flow and cross-correlation. We define the process of information transmission as the multi-dimensional Markov chain, derive the generator of this chain and compute its stationary distribution. Expressions for computation of various performance measures of the system, including the probabilities of loss of customers of different types, are presented. Output flow from the system is characterized. The presented numerical results confirm the high importance of account of correlation in the arrival process. The values of important performance measures for the systems with the correlated arrival process are essentially different from the corresponding values for the systems with the stationary Poisson arrival process. Measurements in many real world systems show poor approximation of real flows by such an arrival process. However, this process is still popular among the telecommunication engineers due to the evident existing gap between the needs of adequately modeling the real life systems and the current state of the theory of algorithmic methods of queueing theory.

Keywords: multi-server queueing system; heterogeneous customers; marked Markovian arrival process; priorities; loss probabilities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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