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4395 results in Advances in Applied Probability

Page 214 of 220

  • On the many server queue with exponential service times

  • J. H. A. De Smit
  • Journal:
    Advances in Applied Probability / Volume 5 / Issue 1 / April 1973
    Published online by Cambridge University Press:
    01 July 2016, pp. 170-182
    Print publication:
    April 1973

  • The general theory for the many server queue due to Pollaczek (1961) and generalized by the author (de Smit (1973)) is applied to the system with exponential service times. In this way many explicit results are obtained for the distributions of characteristic quantities, such as the actual waiting time, the virtual waiting time, the queue length, the number of busy servers, the busy period and the busy cycle. Most of these results are new, even for the special case of Poisson arrivals.

  • Some general results for many server queues

  • J. H. A. De Smit
  • Journal:
    Advances in Applied Probability / Volume 5 / Issue 1 / April 1973
    Published online by Cambridge University Press:
    01 July 2016, pp. 153-169
    Print publication:
    April 1973

  • Pollaczek's theory for the many server queue is generalized and extended. Pollaczek (1961) found the distribution of the actual waiting times in the model G/G/s as a solution of a set of integral equations. We give a somewhat more general set of integral equations from which the joint distribution of the actual waiting time and some other random variables may be found. With this joint distribution we can obtain distributions of a number of characteristic quantities, such as the virtual waiting time, the queue length, the number of busy servers, the busy period and the busy cycle. For a wide class of many server queues the formal expressions may lead to explicit results.

Page 214 of 220