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1 results

  • Interchange arguments in stochastic scheduling

  • Philippe Nain, Pantelis Tsoucas, Jean Walrand
  • Journal:
    Journal of Applied Probability / Volume 26 / Issue 4 / December 1989
    Published online by Cambridge University Press:
    14 July 2016, pp. 815-826
    Print publication:
    December 1989

  • Interchange arguments are applied to establish the optimality of priority list policies in three problems. First, we prove that in a multiclass tandem of two ·/M/1 queues it is always optimal in the second node to serve according to the cµ rule. The result holds more generally if the first node is replaced by a multiclass network consisting of ·/M/1 queues with Bernoulli routing. Next, for scheduling a single server in a multiclass node with feedback, a simplified proof of Klimov's result is given. From it follows the optimality of the index rule among idling policies for general service time distributions, and among pre-emptive policies when the service time distributions are exponential. Lastly, we consider the problem of minimizing the blocking in a communication link with lossy channels and exponential holding times.