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Two-Server Queueing System with Unreliable Servers and Markovian Arrival Process

  • Valentina KlimenokEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 800)

Abstract

In this paper, we investigate a queueing system consisting of an infinite buffer and two unreliable heterogeneous servers which fail alternately. If both servers are able to provide the service, they serve a customer in parallel, independently of each other. The service of a customer is completed when his/her service by any of two servers ends. The service times at the servers have PH-type (Phase-type) distributions. The input flow and the flow of breakdowns are described by the MAP (Markovian Arrival Process). An arriving breakdown is directed to the first server with some probability and to the second server with complementary probability. After a breakdown occurrence a server fails and the repair period starts immediately. A customer, whose service is interrupted by the breakdown, goes to another server if it is idle, or enters the queue otherwise We derive a condition for the stable operation of the system, calculate its stationary distribution and base performance measures. Illustrative numerical examples are presented.

Keywords

Unreliable queueing system Markovian Arrival Process Phase-type service time distribution Stationary distribution Performance measures 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Computer ScienceBelarusian State UniversityMinskBelarus

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