### 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 language | English (US) |
---|---|

Pages (from-to) | 308-318 |

Number of pages | 11 |

Journal | Operations Research Letters |

Volume | 30 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 2002 |

### Fingerprint

### 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

*Operations Research Letters*,

*30*(5), 308-318. https://doi.org/10.1016/S0167-6377(02)00175-X

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

Research output: Contribution to journal › Article

*Operations Research Letters*, vol. 30, no. 5, pp. 308-318. https://doi.org/10.1016/S0167-6377(02)00175-X

}

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

VL - 30

SP - 308

EP - 318

JO - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

IS - 5

ER -