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Nonstationary queues with Interrrupted Poisson arrivals and unreliable/repairable servers

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Abstract

A queueing model having a nonstationary Interrupted Poisson arrival process (IPP(t)),s time-dependent exponential unreliable/repairable servers and finite capacityc is introduced, and an approximation method for analysis of it is developed and tested. Approximations are developed for the time-dependent queue length moments and the system viewpoint waiting time distributions and moments. The approximation involves state-space partitioning and numerically integrating partial-moment differential equations (PMDEs). Surrogate distribution approximations (SDA's) are used to close the system of PMDEs. The approximations allow for analysis using only (s + 1)(s + 6) differential equations for the queue length moments rather than the 2(c + 1)(s +1) equations required by the classic method of numerically integrating the full set of Kolmogorov-forward equations. Effectively hours of cpu time are reduced to minutes for even modest capacity systems. Approximations for waiting time distributions and moments are developed.

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Authors and Affiliations

  1. BDM Corporation, 22102-3396, McLean, Virginia, USA

    Kim L. Ong

  2. School of Industrial Engineering, Purdue University, 47907, West Lafayette, Indiana, USA

    Michael R. Taaffe

Authors
  1. Kim L. Ong
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  2. Michael R. Taaffe
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This research was partially funded by National Science Foundation grant ECS-8404409.

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Ong, K.L., Taaffe, M.R. Nonstationary queues with Interrrupted Poisson arrivals and unreliable/repairable servers. Queueing Syst 4, 27–46 (1989). https://doi.org/10.1007/BF01150854

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  • DOI: https://doi.org/10.1007/BF01150854

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