The Client the Problem

Virtually all previous research in on-line algorithms has f ocused onsingle-threaded systemswhere only asinglesequence of requests compete for system resources. To model multi-threaded on-line systems , we define and analyze the k-client problem, a dual of the well-studiedk-server problem. In the basic k-client problem, there is a single server and k clients, each of which generates a sequence of requests for s ervice in a metric space. The crux of the problem is deciding which client’s request the si ngle server should service rather than which server should be used to service the current reque st. We also consider variations where requests have non-zero processing times and where the re are multiple servers as well as multiple clients. We evaluate the performance of algorithms using several cos t functions including maximum completion time and average completion time. Two of the m ain results we derive are tight bounds on the performance of several commonly studied isk scheduling algorithms and lower bounds oflg k 2 + 1 on the competitive ratio of any on-line algorithm for the maximum completion time and average completion time cost fu nctions whenk is a power of 2. Most of our results are essentially identical for the ma xi um completion time and average completion time cost functions.