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

  • Authors:

  • Catherine Rainer;Ravi R. Mazumdar

  • Affiliations:

  • Département de Mathématics, Université de Bretagne Ouest, 29285 Brest Cedex, France E-mail: rainer@univ-brest.fr;Department of Mathematics, University of Essex, Colchester CO4 3SQ, UK E-mail: mazum@essex.ac.uk

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 1998

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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.