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International Journal of Stochastic Analysis
Volume 2016 (2016), Article ID 9152701, 11 pages
Research Article

Analysis of a Priority Queue with Phase-Type Service and Failures

1Department of Applied Mathematics and Cybernetics, Tomsk State University, 36 Lenina Avenue, Tomsk 634050, Russia
2Department of Applied Mathematics and Computer Science, Belarusian State University, 4 Nezavisimosti Avenue, 220030 Minsk, Belarus

Received 30 March 2016; Accepted 17 June 2016

Academic Editor: Lukasz Stettner

Copyright © 2016 Alexander Dudin and Sergei Dudin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a single server queue with two types of customers. We propose a discipline of flexible priority in access that combines the features of randomization and the threshold type control. We introduce a new class of distributions, phase-type with failures () distribution, that generalizes the well-known phase-type () distribution to the case when failures can occur during service of a customer. The arrival flow is described by the marked Markovian arrival process. The service time distribution is of type with the parameters depending on the type of a customer. Customers of both types can be impatient. Behavior of the system is described by the multidimensional Markov chain. Problem of existence and computation of the stationary distribution of this Markov chain is discussed in brief as well as the problem of computation of the key performance measures of the system. Numerical examples are presented that give some insight into behavior of the system performance measures under different values of the parameters defining the strategy of customers access to service.