AbstractIn this paper we deal with a generalization of the k-server problem (Manasse 1988), in which the servers are unequal. In the weighted server model each of the servers is assigned a positive weight. The cost associated with moving a server equals the product of the distance traversed and the server weight.A weighted k-server algorithm is called competitive if the competitive ratio depends only upon the number of servers (i.e., the competitive ratio is independent of the weights associated with the servers and the number of points in the metric space).For the uniform metric space, we give super exponential 22O(k)-competitive algorithms for any set of weights. If the servers have one of two possible weights, we give deterministic expon...