OPTIMAL DISPATCHING OF A POISSON PROCESS
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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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 T2 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 Nt or lambda T - t is optimal, where Nt 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.
- Operations Research