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Explicit solutions for the steady state distributions in M/PH/1 queues with workload dependent balking

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Abstract

We consider an M/PH/1 queue with balking based on the workload. An arriving customer joins the queue and stays until served only if the system workload is below a fixed level at the time of arrival. The steady state workload distribution in such a system satisfies an integral equation. We derive a differential equation for Phase type service time distribution and we solve it explicitly, with Erlang, Hyper-exponential and Exponential distributions as special cases. We illustrate the results with numerical examples.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, N.C., 27599-3180

    Liqiang Liu & Vidyadhar G. Kulkarni

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  1. Liqiang Liu
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  2. Vidyadhar G. Kulkarni
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Liu, L., Kulkarni, V.G. Explicit solutions for the steady state distributions in M/PH/1 queues with workload dependent balking. Queueing Syst 52, 251–260 (2006). https://doi.org/10.1007/s11134-006-6084-3

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  • DOI: https://doi.org/10.1007/s11134-006-6084-3

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