Near optimal control of queueing networks over a finite time horizon

Yoni Nazarathy, Gideon Weiss

Research output: Contribution to journalArticlepeer-review


We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class queueing network by a fluid network and formulate a fluid optimization problem which we solve as a separated continuous linear program. The optimal fluid solution partitions the time horizon to intervals in which constant fluid flow rates are maintained. We then use a policy by which the queueing network tracks the fluid solution. To that end we model the deviations between the queuing and the fluid network in each of the intervals by a multi-class queueing network with some infinite virtual queues. We then keep these deviations stable by an adaptation of a maximum pressure policy. We show that this method is asymptotically optimal when the number of items that is processed and the processing speed increase. We illustrate these results through a simple example of a three stage re-entrant line.

Original languageEnglish
Pages (from-to)233-249
Number of pages17
JournalAnnals of Operations Research
Issue number1
StatePublished - Sep 2009

Bibliographical note

Funding Information:
Research supported in part by Israel Science Foundation Grant 249/02 and 454/05 and by European Network of Excellence Euro-NGI.


  • Continuous linear programming
  • Fluid approximations
  • Infinite virtual queues
  • Maximum pressure policies
  • Multi-class queueing networks
  • Queueing control

ASJC Scopus subject areas

  • General Decision Sciences
  • Management Science and Operations Research


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