An adaptive routing approach for personal rapid transit

Personal Rapid Transit (PRT) is a public transportation mode, in which small automated vehicles transport passengers on demand. Central control of the vehicles leads to interesting possibilities for optimized routings. The complexity of the involved routing problems together with the fact that routing algorithms for PRT essentially have to run in real-time often leads to the choice of fast greedy approaches. The most common routing approach is arguably a sequential one, where upcoming requests are greedily served in a quickest way without interfering with previously routed vehicles. The simplicity of this approach stems from the fact that a chosen route is never changed later. This is as well the main drawback of it, potentially leading to large detours. It is natural to ask how much one could gain by using a more adaptive routing strategy. This question is the main motivation of this article. In this paper, we first suggest a simple mathematical model for PRT, and then introduce a new adaptive routing algorithm that repeatedly uses solutions to an LP as a guide to route vehicles. Our routing approach incorporates new requests in the LP as soon as they appear, and reoptimizes the routing of all currently used vehicles, contrary to sequential routing. We provide preliminary computational results that give first evidence of the potential gains of an adaptive routing strategy, as used in our algorithm.National Science Foundation (U.S.) (Grants CCF-1115849 and CCF-0829878)United States. Office of Naval Research (Grants N00014-11-1-0053 and N00014-09-1-0326

Bayesian sequential change diagnosis

Sequential change diagnosis is the joint problem of detection and identification of a sudden and unobservable change in the distribution of a random sequence. In this problem, the common probability law of a sequence of i.i.d. random variables suddenly changes at some disorder time to one of finitely many alternatives. This disorder time marks the start of a new regime, whose fingerprint is the new law of observations. Both the disorder time and the identity of the new regime are unknown and unobservable. The objective is to detect the regime-change as soon as possible, and, at the same time, to determine its identity as accurately as possible. Prompt and correct diagnosis is crucial for quick execution of the most appropriate measures in response to the new regime, as in fault detection and isolation in industrial processes, and target detection and identification in national defense. The problem is formulated in a Bayesian framework. An optimal sequential decision strategy is found, and an accurate numerical scheme is described for its implementation. Geometrical properties of the optimal strategy are illustrated via numerical examples. The traditional problems of Bayesian change-detection and Bayesian sequential multi-hypothesis testing are solved as special cases. In addition, a solution is obtained for the problem of detection and identification of component failure(s) in a system with suspended animation