Cost sharing of cooperating queues in a Jackson network

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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 languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages15
Publication statusPublished - Dec 2011

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherUniversity 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.
Timmer, Judith B. ; Scheinhardt, Willem R.W. / Cost sharing of cooperating queues in a Jackson network. Enschede : University of Twente, Department of Applied Mathematics, 2011. 15 p. (Memorandum / Department of Applied Mathematics; 1969).
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Timmer, JB & Scheinhardt, WRW 2011, Cost sharing of cooperating queues in a Jackson network. Memorandum / Department of Applied Mathematics, no. 1969, University of Twente, Department of Applied Mathematics, Enschede.

Cost sharing of cooperating queues in a Jackson network. / Timmer, Judith B.; Scheinhardt, Willem R.W.

Enschede : University of Twente, Department of Applied Mathematics, 2011. 15 p. (Memorandum / Department of Applied Mathematics; No. 1969).

Research output: Book/ReportReportProfessional

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Timmer JB, Scheinhardt WRW. Cost sharing of cooperating queues in a Jackson network. Enschede: University of Twente, Department of Applied Mathematics, 2011. 15 p. (Memorandum / Department of Applied Mathematics; 1969).