论文信息 - PROBABILISTIC ANALYSIS OF THE K-SERVER PROBLEM ON THE CIRCLE

PROBABILISTIC ANALYSIS OF THE K-SERVER PROBLEM ON THE CIRCLE

We consider a stochastic version of the k-server problem, in which k servers move on a circle to satisfy randomly generated requests. The requests are independent and identically distributed, according to an arbitrary distribution that is either discrete or continuous. The cost of serving a request is the distance that a server needs to travel in order to reach the request. The goal is to minimize the steady-state expected cost induced by the sequence of requests. We study the performance of a greedy strategy focusing, in particular, on its convergence properties and the interplay between the discrete and continuous versions of the process. Finally, we show that in the case of k = 2 servers the greedy policy is optimal.

Eli Upfal | Aris Anagnostopoulos | Clément Dombry

[1] D. Vere-Jones. Markov Chains , 1972, Nature.

[2] Allan Borodin,et al. Online computation and competitive analysis , 1998 .

[3] S. Meyn,et al. Spectral theory and limit theorems for geometrically ergodic Markov processes , 2002, math/0209200.

[4] Lyle A. McGeoch,et al. Competitive Algorithms for Server Problems , 1990, J. Algorithms.

[5] Christos H. Papadimitriou,et al. On the k-server conjecture , 1995, JACM.

[6] Lyle A. McGeoch,et al. Competitive algorithms for on-line problems , 1988, STOC '88.

[7] R. Bass,et al. Review: P. Billingsley, Convergence of probability measures , 1971 .

[8] Richard L. Tweedie,et al. Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[9] Amir Dembo,et al. Large Deviations Techniques and Applications , 1998 .

[10] John Maindonald,et al. Data Analysis and Graphics Using R: An Example-based Approach (Cambridge Series in Statistical and Probabilistic Mathematics) , 2003 .