Mean first passage times in fluid queues

Vidyadhar G. Kulkarni, Elena Tzenova

Research output: Contribution to journalArticle

Abstract

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
Volume30
Issue number5
DOIs
StatePublished - Jan 1 2002

Fingerprint

Fluid Queue
Mean First Passage Time
Buffer
Fluid
Fluids
Random Environment
Denote
Multi-state
Queueing System
Rate Constant
Linear differential equation
Analytical Solution
Differential equations
Numerical Solution
First-order
First passage time
Queue
Computing
Output

Keywords

  • Buffer
  • First passage times
  • Fluid models

ASJC Scopus subject areas

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

Cite this

Mean first passage times in fluid queues. / Kulkarni, Vidyadhar G.; Tzenova, Elena.

In: Operations Research Letters, Vol. 30, No. 5, 01.01.2002, p. 308-318.

Research output: Contribution to journalArticle

Kulkarni, Vidyadhar G. ; Tzenova, Elena. / Mean first passage times in fluid queues. In: Operations Research Letters. 2002 ; Vol. 30, No. 5. pp. 308-318.
@article{81da8e5363e04a62a38cee126f55db47,
title = "Mean first passage times in fluid queues",
abstract = "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.",
keywords = "Buffer, First passage times, Fluid models",
author = "Kulkarni, {Vidyadhar G.} and Elena Tzenova",
year = "2002",
month = "1",
day = "1",
doi = "10.1016/S0167-6377(02)00175-X",
language = "English (US)",
volume = "30",
pages = "308--318",
journal = "Operations Research Letters",
issn = "0167-6377",
publisher = "Elsevier",
number = "5",

}

TY - JOUR

T1 - Mean first passage times in fluid queues

AU - Kulkarni, Vidyadhar G.

AU - Tzenova, Elena

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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.

AB - 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.

KW - Buffer

KW - First passage times

KW - Fluid models

UR - http://www.scopus.com/inward/record.url?scp=0036793137&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036793137&partnerID=8YFLogxK

U2 - 10.1016/S0167-6377(02)00175-X

DO - 10.1016/S0167-6377(02)00175-X

M3 - Article

AN - SCOPUS:0036793137

VL - 30

SP - 308

EP - 318

JO - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

IS - 5

ER -