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1 results

  • The backlog and depletion-time process for M/G/1 vacation models with exhaustive service discipline

  • Julian Keilson, Ravi Ramaswamy
  • Journal:
    Journal of Applied Probability / Volume 25 / Issue 2 / June 1988
    Published online by Cambridge University Press:
    14 July 2016, pp. 404-412
    Print publication:
    June 1988

  • The vacation model studied is an M/G/1 queueing system in which the server attends iteratively to ‘secondary' or ‘vacation' tasks at ‘primary' service completion epochs, when the primary queue is exhausted. The time-dependent and steady-state distributions of the backlog process [6] are obtained via their Laplace transforms. With this as a stepping stone, the ergodic distribution of the depletion time [5] is obtained. Two decomposition theorems that are somewhat different in character from those available in the literature [2] are demonstrated. State space methods and simple renewal-theoretic tools are employed.