### Abstract

We examine the resource allocation problem of partitioning identical servers into two parallel pooling centers, and simultaneously assigning job types to pooling centers. Each job type has a distinct Poisson arrival rate and a distinct holding cost per unit time. Each pooling center becomes a queueing system with an exponential service time distribution. The goal is to minimize the total holding cost. The problem is shown to be polynomial if a job type can be divided between the pooling centers, and NP-hard if dividing job types is not possible. When there are two servers and jobs cannot be divided, we demonstrate that the two pooling center configuration is rarely optimal. A heuristic which checks the single pooling center has an upper bound on the relative error of 4/3. The heuristic is extended for the multiple server problem, where relative error is bounded above by the number of servers.

Original language | English |
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Pages (from-to) | 179-194 |

Number of pages | 16 |

Journal | Queueing Systems |

Volume | 55 |

Issue number | 3 |

DOIs | |

State | Published - 1 Mar 2007 |

### Keywords

- Parallel queueing system
- Resources allocation
- Work-in-process cost
- Workload allocation problem

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## Cite this

*Queueing Systems*,

*55*(3), 179-194. https://doi.org/10.1007/s11134-007-9015-z