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A note on the conservation law for continuous reflected processes and its application to queues with fluid inputs

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Abstract

In this note we provide a new derivation of a conservation law for stationary continuous reflected processes which arise in the context of fluid queueing models. This readily gives the so-called Little's law for fluid queues as a special case. We then apply the result to compute the Laplace transform of the stationary workload distribution for a queue with fluid ON-OFF inputs in terms of the Palm distribution associated with the beginning of ON periods.

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Authors and Affiliations

  1. Département de Mathématics, Université de Bretagne Ouest, 29285, Brest Cedex, France

    Catherine Rainer

  2. Department of Mathematics, University of Essex, Colchester, CO4 3SQ, UK

    Ravi R. Mazumdar

Authors
  1. Catherine Rainer
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  2. Ravi R. Mazumdar
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Rainer, C., Mazumdar, R.R. A note on the conservation law for continuous reflected processes and its application to queues with fluid inputs. Queueing Systems 28, 283–291 (1998). https://doi.org/10.1023/A:1019103323831

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  • DOI: https://doi.org/10.1023/A:1019103323831