Adaptation of the Service Capacity in a Queueing Systems which is Subjected to a Change in the Arrival Rate at Unknown Epoch.
CASE WESTERN RESERVE UNIV CLEVELAND OHIO DEPT OF MATHEMATICS AND STATISTICS
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The paper studies the problem of optimal adaptation of an MM1 queueing station, when the arrival rate lambda sub zero of customers shifts at unknown epoch, tau to a known value, lambda sub 1. The service intensity of the system starts at mu 0 and can be increased at most n times to mu 1 mu2 ... mu N. The cost structure consists of the cost of changing mui to muj i1 or j or N of maintaining service at rate mu per unit of time and of holding customers at the station per unit of time. Adaptation policies are constrained by the fact that mu can be only increased. A Bayes solution is derived, under the prior assumption that tau has an exponential distribution. This solution minimizes the total expected discounted cost for the entire future. Author
- Statistics and Probability