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Size- and state-aware dispatching problem with queue-specific job sizes


  • Hyytiä, Esa
  • Penttinen, Aleksi
  • Aalto, Samuli


We consider the dispatching problem in a size- and state-aware multi-queue system with Poisson arrivals and queue-specific job sizes. By size- and state-awareness, we mean that the dispatcher knows the size of an arriving job and the remaining service times of the jobs in each queue. By queue-specific job sizes, we mean that the time to process a job may depend on the chosen server. We focus on minimizing the mean sojourn time (i.e., response time) by an MDP approach. First we derive the so-called size-aware relative values of states with respect to the sojourn time in an M/G/1 queue operating under FIFO, LIFO, SPT or SRPT disciplines. For FIFO and LIFO, the size-aware relative values turn out to be insensitive to the form of the job size distribution. The relative values are then exploited in developing efficient dispatching rules in the spirit of the first policy iteration.

Suggested Citation

  • Hyytiä, Esa & Penttinen, Aleksi & Aalto, Samuli, 2012. "Size- and state-aware dispatching problem with queue-specific job sizes," European Journal of Operational Research, Elsevier, vol. 217(2), pages 357-370.
  • Handle: RePEc:eee:ejores:v:217:y:2012:i:2:p:357-370
    DOI: 10.1016/j.ejor.2011.09.029

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    References listed on IDEAS

    1. Wu, Rong & Down, Douglas G., 2009. "Round robin scheduling of heterogeneous parallel servers in heavy traffic," European Journal of Operational Research, Elsevier, vol. 195(2), pages 372-380, June.
    2. Becker, K. J. & Gaver, D. P. & Glazebrook, K. D. & Jacobs, P. A. & Lawphongpanich, S., 2000. "Allocation of tasks to specialized processors: A planning approach," European Journal of Operational Research, Elsevier, vol. 126(1), pages 80-88, October.
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    Cited by:

    1. Dinard van der Laan, 2015. "Assigning Multiple Job Types to Parallel Specialized Servers," Tinbergen Institute Discussion Papers 15-102/III, Tinbergen Institute.


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