### Abstract

We consider networks of queues in which the independent operators of individual queues may cooperate to reduce the amount of waiting. More specifically, we focus on Jackson networks in which the total capacity of the servers can be redistributed over all queues in any desired way. If we associate a cost to waiting that is linear in the queue lengths, it is known how the operators should share the available service capacity to minimize the long run total cost.
We answer the question whether or not (the operators of) the individual queues will indeed cooperate in this way, and if so, how they will share the cost in the new situation. One of the results is an explicit cost allocation that is beneficial for all operators. The approach used also works for other cost functions, such as the server utilization.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 15 |

Publication status | Published - Dec 2011 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
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Publisher | University of Twente, Department of Applied Mathematics |

No. | 1969 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- IR-79012
- Game Theory
- Cost allocation
- Capacity allocation
- EWI-21078
- METIS-284937
- Jackson network
- Co-operation

## Cite this

Timmer, J. B., & Scheinhardt, W. R. W. (2011).

*Cost sharing of cooperating queues in a Jackson network*. (Memorandum / Department of Applied Mathematics; No. 1969). Enschede: University of Twente, Department of Applied Mathematics.