On the distribution of search cost for the move-to-front rule

A file of records, each with an associated request probability, is dynamically maintained as a serial list. Successive requests are mutually independent. The list is reordered according to the move-to-front (MTF) rule: The requested record is moved to the front of the list. We derive the stationary distribution of search cost (=depth of requested item) by embedding in Poisson processes and derive certain finite-time stochastic ordering results for the MTF chain so embedded. A connection with cache fault probabilities is discussed. We also establish a Schur-concavity result for stationary expected search cost. © 1996 John Wiley & Sons, Inc.