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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. 0 1996 John Wiley & Sons, Inc.

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Consider the pieces of a randomly broken stick. How long is the j th longest piece? How many breaks are necessary for getting all pieces less than a given length? These and related questions are studied in particular when the number of pieces is large. Using simple properties of the exponential distribution new proofs are given of old results and new results are obtained.

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