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2 results

  • A martingale approach to the slow server problem

  • Richard H. Stockbridge
  • Journal:
    Journal of Applied Probability / Volume 28 / Issue 2 / June 1991
    Published online by Cambridge University Press:
    14 July 2016, pp. 480-486
    Print publication:
    June 1991

  • A Markov queueing system having heterogeneous servers under a long-run average criterion is analyzed. A direct proof of the optimality of a stationary, Markov policy is given using martingale methods. Simultaneously, the problem is reduced to a linear programming problem. Analysis of the LP for a system having finite queueing length shows the optimal policy is not always of threshold type.

  • Controlled queues in heavy traffic

  • John H. Rath
  • Journal:
    Advances in Applied Probability / Volume 7 / Issue 3 / September 1975
    Published online by Cambridge University Press:
    01 July 2016, pp. 656-671
    Print publication:
    September 1975

  • This paper studies a controlled queueing system in which the decisionmaker may change servers according to rules which depend only on the queue length. It is proved that for a given control policy a properly normalised sequence of these controlled queue length processes converges weakly to a controlled diffusion process as the queueing systems approach a state of heavy traffic.