A class of multi-server queueing system with server failures

Authors:
Xiaolan Yang;Attahiru Sule Alfa
Affiliations:
School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, PR China;Department of Electrical & Computer Engineering, University of Manitoba, Winnipeg, Man., Canada R3T 5V6
Venue:
Computers and Industrial Engineering
Year:
2009

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Abstract

A multi-server queueing system with identical unreliable servers with phase type distributed service times is considered. The servers are subject to random breakdowns and repairs when a repair person is available. We consider both the cases of infinite and finite buffers. Job arrivals are Poisson and server inter-failure and repair times follow exponential distributions. The infinitesimal generator matrix has a block tri-diagonal structure. The stability condition for the infinite case and the loss probability for the finite buffer case are obtained. We use a matrix-geometric approach to analyze the infinite buffer problem. Numerical examples are presented for both cases.