STOCHASTIC DISCRETIZATION FOR THE LONG-RUN AVERAGE REWARD IN FLUID MODELS

  • Authors:

  • I. J. B. F. Adan;J. A. C. Resing;V. G. Kulkarni

  • Affiliations:

  • Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands, E-mail: i.j.b.f.adan@tue.nl;Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands, E-mail: j.a.c.resing@tue.nl;Department of Operations Research, University of North Carolina, Chapel Hill, NC 27599, E-mail: vkulkarn@email.unc.edu

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2003

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Abstract

Stochastic discretization is a technique of representing a continuous random variable as a random sum of i.i.d. exponential random variables. In this article, we apply this technique to study the limiting behavior of a stochastic fluid model. Specifically, we consider an infinite-capacity fluid buffer, where the net input of fluid is regulated by a finite-state irreducible continuous-time Markov chain. Most long-run performance characteristics for such a fluid system can be expressed as the long-run average reward for a suitably chosen reward structure. In this article, we use stochastic discretization of the fluid content process to efficiently determine the long-run average reward. This method transforms the continuous-state Markov process describing the fluid model into a discrete-state quasi-birth–death process. Hence, standard tools, such as the matrix-geometric approach, become available for the analysis of the fluid buffer. To demonstrate this approach, we analyze the output of a buffer processing fluid from K sources on a first-come first-served basis.