The Distributedk-Server Problem—A Competitive Distributed Translator fork-Server Algorithms

We consider thek-server problem23in a distributed setting. Given a network ofnprocessors andkidentical mobile servers, requests for service appear at the processors and a server must reach the request point. In addition to modeling problems in computer networks wherekidentical mobile resources are shared by the processors of the network, this models a realistic situation where the transfer of information is costly and there is no central control that governs the behavior of servers that move around to satisfy requests for service. We give a general translator to transform any deterministic global-control competitivek-server algorithm into a distributed competitive one. As consequences we get poly(k)-competitive distributed algorithms for the line, trees, and the ring. In contrast to the global-control case where there arek-server algorithms with competitive ratio that depends solely onk, we have a lower bound of Ω(max{k, (1/D) ·(log n/log log n)}) on the competitive ratio of any distributedk-server algorithm, where 1/Dis the ratio between the cost to transmit a message and the cost to move a server over the same distance. We also give a distributed version of the Harmonic randomizedk-server algorithm.