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1 results

  • On regenerative and ergodic properties of the k-server queue with non-stationary Poisson arrivals

  • Hermann Thorisson
  • Journal:
    Journal of Applied Probability / Volume 22 / Issue 4 / December 1985
    Published online by Cambridge University Press:
    14 July 2016, pp. 893-902
    Print publication:
    December 1985

  • We consider the stable k-server queue with non-stationary Poisson arrivals and i.i.d. service times and show that the non-time-homogeneous Markov process Zt = (the queue length and residual service times at time t) can be subordinated to a stable time-homogeneous regenerative process. As an application we show that if the system starts from given conditions at time s then the distribution of Zt stabilizes (but depends on t) as s tends backwards to –∞. Also moment and stochastic domination results are established for the delay and recurrence times of the regenerative process leading to results on uniform rates of convergence.