Customer delays in M/M/c repair systems with spares

A service center to which customers bring failed items for repair is considered. The items are exchangeable in the sense that a customer is ready to take in return for the failed item he brought to the center any good item of the same kind. This exchangeability feature makes it possible for the service center to possess spares. The focus of the article is on customer delay in the system—the time that elapses since the arrival of a customer with a failed item and his departure with a good one—when repaired items are given to waiting customers on a FIFO basis. An algorithm is developed for the computation of the delay distribution when the item repair system operates as an M/M/c queue.     

Optimizing search with positive information feedback

A search model is formulated in which positive information may be obtained, through the detection of trails, as to the target's earlier whereabouts. The corresponding Bayesian update formulas for target location probabilities are derived. The model does not appear to be amenable to rigorous optimization. A moving-horizon rule, and a heuristic simplification thereof, are, however, derived. In two numerical examples it is demonstrated that actively designing for detecting trail information, through use of these moving-horizon rules, has substantial potential advantage over using, for example, myopic rules even if the positive information is adaptively incorporated into location probabilities before applying the latter rules in each time period.     

Rectilinear m-Center problem

In this article we consider the unweighted m-center problem with rectilinear distance. We preent an O(n^m–2 log n) algorithm for the m-center problem where m ≥ 4.