Mean first passage times in fluid queues

Vidyadhar G. Kulkarni, Elena Tzenova

Research output: Contribution to journalArticlepeer-review


A stochastic fluid queueing system describes the input-output flow of a fluid in a storage device, called a buffer. The rates at which the fluid enters and leaves the buffer depend on a random environment process. The external governing process is an irreducible CTMC and the fluid from the buffer is emptied at a constant rate μ. Let X(t) denote the buffer content at time t and I(t) denote the state of the random environment at time t. In this paper we present a method for computing the mean first passage times in the (X(t), t ≥ 0) process, as well as in the bivariate ((X(t), I(t)), t ≥ 0) process. We derive a system of first-order non-homogeneous linear differential equations for the mean first passage times which can easily be solved using well-known techniques. The method developed here can be readily implemented for computational purposes. We present two examples illustrating how to find explicitly the analytical solution to a small two-state problem and how to obtain numerical solutions to a multistate problem.

Original languageEnglish (US)
Pages (from-to)308-318
Number of pages11
JournalOperations Research Letters
Issue number5
StatePublished - Oct 2002


  • Buffer
  • First passage times
  • Fluid models

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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