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2 results

  • On the optimal assignment of customers to parallel servers

  • Richard R. Weber
  • Journal:
    Journal of Applied Probability / Volume 15 / Issue 2 / June 1978
    Published online by Cambridge University Press:
    14 July 2016, pp. 406-413
    Print publication:
    June 1978

  • We consider a queuing system with several identical servers, each with its own queue. Identical customers arrive according to some stochastic process and as each customer arrives it must be assigned to some server's queue. No jockeying amongst the queues is allowed. We are interested in assigning the arriving customers so as to maximize the number of customers which complete their service by a certain time. If each customer's service time is a random variable with a non-decreasing hazard rate then the strategy which does this is one which assigns each arrival to the shortest queue.

  • Optimality of the shortest line discipline

  • Wayne Winston
  • Journal:
    Journal of Applied Probability / Volume 14 / Issue 1 / March 1977
    Published online by Cambridge University Press:
    14 July 2016, pp. 181-189
    Print publication:
    March 1977

  • We consider a queuing system consisting of a finite number of identical exponential servers. Each server has its own queue, and upon arrival each customer must be assigned to some server's queue. Under the assumption that no jockeying between queues is permitted, it is shown that the intuitively satisfying rule of assigning each arrival to the shortest line maximizes, with respect to stochastic order, the discounted number of customers to complete their service in any time t.