Journal
APPLIED MATHEMATICAL MODELLING
Volume 36, Issue 1, Pages 255-269Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2011.05.047
Keywords
Stationary system size distribution; Random breakdown; Delay time; Repair time; Retrial time; Reliability indices
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This paper deals with the steady state behaviour of an M-x/G/1 queue with general retrial time and Bernoulli vacation schedule for an unreliable server, which consists of a breakdown period and delay period. Here we assume that customers arrive according to compound Poisson processes. While the server is working with primary customers, it may breakdown at any instant and server will be down for short interval of time. Further concept of the delay time is also introduced. The primary customer finding the server busy, down or vacation are queued in the orbit in accordance with FCFS (first come first served) retrial policy. After the completion of a service, the server either goes for a vacation of random length with probability p or may continue to serve for the next customer, if any with probability (1 - p). We carry out an extensive analysis of this model. Finally, we obtain some important performance measures and reliability indices of this model. (C) 2011 Elsevier Inc. All rights reserved.
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