A discrete‐time on–off source queueing system with negative customers

A discrete‐time on–off source queueing system with negative customers

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Article ID: iaor201110325
Volume: 61
Issue: 4
Start Page Number: 1226
End Page Number: 1232
Publication Date: Nov 2011
Journal: Computers & Industrial Engineering
Authors: , ,
Keywords: markov processes
Abstract:

This paper studies a discrete‐time single‐server infinite‐capacity queueing system with correlated arrivals, geometrically distributed service times and negative customers. Positive customers are generated by a Bernoulli bursty source, with geometrically distributed lengths of the on‐periods and off‐periods. Negative customers arrive to the system according to a geometrical arrival process which is independent of the positive arrival process. A negative customer removes a positive customer in service if any, but has no effect on the system if it finds the system empty. We analyze the Markov chain underlying the queueing system and evaluate the performance of the system based on generating functions technique. Closed‐form expressions of some performance measures of the system are obtained, such as stationary probability generating functions of queue length, unfinished work, sojourn time distribution and so on. Finally, the effect of several parameters on the system is shown numerically.

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