Uniform service systems with k servers

We consider the problem of Ic servers situated on a uniform metric space that must serve a sequence of requests, where each request consists of a see of locations of the metric space and can be served by moving a server to any of the nodes of the set. The goal is to minimize the total distance traveled by the servers. This problem generalizes a problem presented by Chrobak and Larmore in [7]. We give lower and upper bounds on the competitive ratio achievable by on-line algorithms for this problem, and consider also interesting particular cases.