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Approximate analysis of exponential queueing systems with blocking

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Summary

A network of service stations Q 0 Q 1,...,QM is studied. Requests arrive at the centers according to independent Poisson processes; they travel through (part of) the network demanding amounts of service, with independent and negative exponentially distributed lengths, from those centers which they enter, and finally depart from the network. The waiting rooms or buffers at each service station in this exponential service system are finite. When the capacity at Q i is reached, service at all nodes which are currently processing a request destined next for Q i is instantaneously interrupted. The interruption lasts until the service of the request in the saturated node Q i is. completed. This blocking phenomenon makes an exact analysis intractable and a numerical solution computationally infeasible for most exponential systems. We introduce an approximation procedure for a class of exponential systems with blocking and show that it leads to accurate approximations for the marginal equilibrium queue length distributions. The applicability of the approximation method may not be limited to blocking systems.

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Author notes

  1. Onno J. Boxma

    Present address: Mathematical Institute, State University of Utrecht, Utrecht, The Netherlands

Authors and Affiliations

  1. Mathematical Sciences Department, IBM Thomas J. Watson Research Center, PO Box 218, 10598, Yorktown Heights, New York, USA

    Onno J. Boxma & Alan G. Konheim

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  1. Onno J. Boxma
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  2. Alan G. Konheim
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Mathematical Sciences Department Postdoctoral Fellow 1978–79.

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Boxma, O.J., Konheim, A.G. Approximate analysis of exponential queueing systems with blocking. Acta Informatica 15, 19–66 (1980). https://doi.org/10.1007/BF00269808

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