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The transient M / G / 1 / 0 queue: some bounds and approximations for light traffic with application to reliability

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  • J. Ben Atkinson

Abstract

We consider the transient analysis of the M / G / 1 / 0 queue, for which P n ( t ) denotes the probability that there are no customers in the system at time t , given that there are n ( n = 0 , 1 ) customers in the system at time 0 . The analysis, which is based upon coupling theory, leads to simple bounds on P n ( t ) for the M / G / 1 / 0 and M / PH / 1 / 0 queues and improved bounds for the special case M / E r / 1 / 0 . Numerical results are presented for various values of the mean arrival rate λ to demonstrate the increasing accuracy of approximations based upon the above bounds in light traffic, i.e., as λ → 0 . An important area of application for the M / G / 1 / 0 queue is as a reliability model for a single repairable component. Since most practical reliability problems have λ values that are small relative to the mean service rate, the approximations are potentially useful in that context. A duality relation between the M / G / 1 / 0 and GI / M / 1 / 0 queues is also described.

Suggested Citation

  • J. Ben Atkinson, 1995. "The transient M / G / 1 / 0 queue: some bounds and approximations for light traffic with application to reliability," International Journal of Stochastic Analysis, Hindawi, vol. 8, pages 1-13, January.
    • Handle: RePEc:hin:jnijsa:818046
    DOI: 10.1155/S1048953395000311
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