• 1 Department of Informatics and System Sciences
• 2 Laboratoire de Mathématiques et Applications [LMA [Poitiers]]
• 3 Laboratoire de mathématiques et applications [UMR 7348] [LMA [Poitiers]]
• 4 Institut Camille Jordan
• 5 Department of Informatics [Athens]
• 6 Department of Computer Science

We consider a stochastic version of the $k$-server problem in which $k$ servers move on a circle to satisfy stochastically generated requests. The requests are independent and identically distributed according to an arbitrary distribution on a circle, which is either discrete or continuous. The cost of serving a request is the distance that a server needs to move to reach the request. The goal is to minimize the steady-state expected cost induced by the 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.