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2 results

  • The queue GI/Hm/s in continuous time

  • Jos H. A. De smit
  • Journal:
    Journal of Applied Probability / Volume 22 / Issue 1 / March 1985
    Published online by Cambridge University Press:
    14 July 2016, pp. 214-222
    Print publication:
    March 1985

  • This is an extension of our previous paper [4] on the queue GI/Hm/s. In that paper we have derived results for the actual waiting time, the number of customers in the system at arrival epochs and the number of customers during a busy cycle. Here we obtain results for the virtual waiting time and the number of customers in the system at arbitrary times.

  • The queue GI/M/s with customers of different types or the queue GI/Hm/s

  • Jos H. A. De Smit
  • Journal:
    Advances in Applied Probability / Volume 15 / Issue 2 / June 1983
    Published online by Cambridge University Press:
    01 July 2016, pp. 392-419
    Print publication:
    June 1983

  • We study the queue GI/M/s with customers of m different types. An arriving customer is of type i with probability pi and the types of different customers are independent. A customer of type i requires a service time which is exponentially distributed with parameter bi. This model is equivalent to the queue GI/Hm/s, where Hm denotes a mixture of m different exponential distributions. We are primarily interested in the distributions of waiting times and queue lengths. Using a probabilistic argument we reduce the problem to the solution of a system of Wiener-Hopf-type equations. This system is solved by a factorization method. Thus we obtain explicit results for the stationary distributions of waiting times and queue lengths.