Reliability Analysis of the Retrial Queue with Server Breakdowns and Repairs

Authors:
Jinting Wang;Jinhua Cao;Quanlin Li
Affiliations:
Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, P.R. China;Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, P.R. China;Institute of Automation, Chinese Academy of Sciences, Beijing 100080, P.R. China
Venue:
Queueing Systems: Theory and Applications
Year:
2001

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Abstract

Retrial queues have been widely used to model many problems arising in telephone switching systems, telecommunication networks, computer networks and computer systems, etc. It is of basic importance to study reliability of retrial queues with server breakdowns and repairs because of limited ability of repairs and heavy influence of the breakdowns on the performance measure of the system. However, so far the repairable retrial queues are analyzed only by queueing theory. In this paper we give a detailed analysis for reliability of retrial queues. By using the supplementary variables method, we obtain the explicit expressions of some main reliability indexes such as the availability, failure frequency and reliability function of the server. In addition, some special queues, for instance, the repairable M/G/1 queue and repairable retrial queue can be derived from our results. These results may be generalized to the repairable multi-server retrial models.