### Abstract

Motivated by a practical situation for the production/assembly of printed circuit boards, we study a generalized shortest queue system. This system consists of parallel servers, which all have their own queue. The system serves several types of jobs, which arrive according to Poisson processes. Because of technical reasons, most or all types of arriving jobs can only be served by a restricted set of servers. All jobs have the same exponential service time distribution, and, in order to minimize its own service time, each arriving job joins (one of) the shortest queue(s) of all queue(s) where the job can be served. The behavior of the resulting queueing system may be described by a multi-dimensional Markov process. Since an analytical solution for this Markov process is hard to obtain, we present flexible bound models in order to find the most relevant performance measures, viz. the waiting times for each of the job types separately and for all job types together. The effectiveness of the flexible bound models is shown by some numerical results.

Original language | English |
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Title of host publication | Ten years LNMB |

Subtitle of host publication | Ph.D. research and graduate courses of the Dutch Network of Operations Research |

Editors | W.K. Klein Haneveld, O.J. Vrieze, L.C.M. Kallenberg |

Publisher | Centrum voor Wiskunde en Informatica |

Pages | 151-160 |

ISBN (Print) | 90 6196 475X |

Publication status | Published - 1997 |

### Publication series

Name | CWI Tract |
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Publisher | CWI |

Number | 122 |

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## Cite this

van Houtum, G. J. (1997). Analysis of a generalized shortest queue system by flexible bound models. In W. K. Klein Haneveld, O. J. Vrieze, & L. C. M. Kallenberg (Eds.),

*Ten years LNMB: Ph.D. research and graduate courses of the Dutch Network of Operations Research*(pp. 151-160). (CWI Tract; No. 122). Centrum voor Wiskunde en Informatica.