OPTIMAL DISPATCHING OF A POISSON PROCESS
Abstract
Items arrive at a processing plant at a Poisson rate lambda. At time T, all items are dispatched from the system. An intermediate dispatch time is to be chosen to minimize the total wait of all items. It is shown that if the dispatch time must be chosen at time 0 then T/2 not only minimizes the expected total wait but it also maximizes the probability that the total wait is less than a for every a > 0. If the intermediate dispatch time is allowed to be a (random) stopping time, then it is shown that the policy which dispatches at time t if N(t) = or > lambda (T - t) is optimal, where N(t) denotes the number of items present at time t. The distribution of the optimal dispatch time and the optimal expected total wait are determined. A generalization to the case of a nonhomogeneous Poisson Process, a time lag, and batch arrivals is given. Finally, the case where the process goes on indefinitely and any number of dispatches are allowed (at a cost K per dispatch) is considered.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1968
- Accession Number
- AD0685254
Entities
People
- Sheldon M. Ross
Organizations
- University of California, Berkeley