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1 results

  • On the stationary workload distribution of work-conserving single-server queues: a general formula via stochastic intensity

  • Part of
  • Naoto Miyoshi
  • Journal:
    Journal of Applied Probability / Volume 38 / Issue 3 / September 2001
    Published online by Cambridge University Press:
    14 July 2016, pp. 793-798
    Print publication:
    September 2001

  • It is well known that a simple closed-form formula exists for the stationary distribution of the workload in M/GI/1 queues. In this paper, we extend this to the general stationary framework. Namely, we consider a work-conserving single-server queueing system, where the sequence of customers’ arrival epochs and their service times is described as a general stationary marked point process, and we derive a closed-form formula for the stationary workload distribution. The key to our proof is two-fold: one is the Palm-martingale calculus, that is, the connection between the notion of Palm probability and that of stochastic intensity. The other is the preemptive-resume last-come, first-served discipline.