Online dial-a-ride problem with time-windows under a restricted information model

In online dial-a-ride problem with time-windows, requests for rides consist of two points in a metric space, a source and a destination. One server with some finite capacity is required to transports a specified amount of goods for requests from the sources to the destinations. Calls for rides come in while the server is travelling. Each request also specifies a deadline. If a request is not be served by its deadline, it will be called off. The server travels at unit speed in the metric space and the goal is to plan the motion of the server in an online way so that the maximum number of requests (or the maximum quantity of goods) is met by the deadlines of the requests. Usually it is assumed that the server knows the complete information on the ride when the requests are presented. We study this problem under a restricted information model. At the release time of one request, only the information on the source is presented. The server does not have the information on the destination until it reaches the source of the request. This models, e.g. the taxi problem, or elevator problem. We study the problem in the uniform metric space and K-constrained metric space. We perform competitive analysis of two deterministic strategies in the two types of metric spaces, The competitive ratios of the strategies are obtained. We also prove a lower bound on the competitive ratio of any deterministic algorithm of Z for the uniform metric space and of KZ for the K-constrained metric space, where Z denotes the capacity of the server and K denotes the diameter of the metric space.