### Abstract

Original language | English |
---|---|

Place of Publication | Enschede |

Publisher | Universiteit Twente |

Number of pages | 35 |

Publication status | Published - 2000 |

### Publication series

Name | BETA working paper |
---|---|

Publisher | University of Twente, Department of Technology and Management |

No. | WP-49 |

Volume | WP-49 |

### Fingerprint

### Keywords

- IR-95548
- METIS-128027

### Cite this

*On multi-class multi-server queueing and spare parts management*. (BETA working paper; Vol. WP-49, No. WP-49). Enschede: Universiteit Twente.

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*On multi-class multi-server queueing and spare parts management*. BETA working paper, no. WP-49, vol. WP-49, Universiteit Twente, Enschede.

**On multi-class multi-server queueing and spare parts management.** / van Harten, Aart; Sleptchenko, Andrei.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - On multi-class multi-server queueing and spare parts management

AU - van Harten, Aart

AU - Sleptchenko, Andrei

PY - 2000

Y1 - 2000

N2 - Multi-class multi-server queuing problems are a generalization of the wellknown M/M/k situation to arrival processes with clients of N types that require exponentially distributed service with different averaged service time. Problems of this sort arise naturally in various applications, such as spare parts management, for example. In this paper we give a procedure to construct exact solutions of the stationary state equations. Essential in this procedure is the reduction of the problem for n = the number of clients in the system > k to a backwards second order difference equation with constant coefficients for a vector in a linear space with dimension depending on Nand k, denoted by d(N,k). Precisely d(N,k) of its solutions have exponential decay for n 00. Next, using this as input, the equations for n ::; k can be solved by backwards recursion. It follows that the exact solution does not have a simple product structure as one might expect intuitively. Further, using the exact solution several interesting performance measures related to spare parts management can be computed and compared with heuristic approximations. This is illustrated with numerical results.

AB - Multi-class multi-server queuing problems are a generalization of the wellknown M/M/k situation to arrival processes with clients of N types that require exponentially distributed service with different averaged service time. Problems of this sort arise naturally in various applications, such as spare parts management, for example. In this paper we give a procedure to construct exact solutions of the stationary state equations. Essential in this procedure is the reduction of the problem for n = the number of clients in the system > k to a backwards second order difference equation with constant coefficients for a vector in a linear space with dimension depending on Nand k, denoted by d(N,k). Precisely d(N,k) of its solutions have exponential decay for n 00. Next, using this as input, the equations for n ::; k can be solved by backwards recursion. It follows that the exact solution does not have a simple product structure as one might expect intuitively. Further, using the exact solution several interesting performance measures related to spare parts management can be computed and compared with heuristic approximations. This is illustrated with numerical results.

KW - IR-95548

KW - METIS-128027

M3 - Report

T3 - BETA working paper

BT - On multi-class multi-server queueing and spare parts management

PB - Universiteit Twente

CY - Enschede

ER -