Showing papers by "Lars Holst published in 1996"
TL;DR: The stationary distribution of search cost is derived by embedding in Poisson processes and certain finite-time stochastic ordering results for the MTF chain so embedded are derived.
Abstract: 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.
60 citations
TL;DR: The model considered in this paper has arisen in a number of completely separate contexts: release of neurotransmitter at neuromuscular synapses, unravelling of strands of DNA, differentiation of cells into heterocysts in algae and growth of crystals.
Abstract: The model considered here has arisen in a number of completely separate contexts: release of neurotransmitter at neuromuscular synapses, unravelling of strands of DNA, differentiation of cells into heterocysts in algae and growth of crystals. After a shear transformation the model becomes a Markov process, based on a Poisson process on the upper half plane, homogeneous in the horizontal (time) direction, which increases at unit rate except for occasional "drops." By considering the process separately when it is above or below a given "level," for any interval on the time axis, we obtain in particular exact moment results and prove asymptotic normality for long time intervals for the number of downcrossings in the interval, the total time in the interval when the process is below the specified level and the number of drops in the interval. Limit distributions as the length of interval tends to infinity are obtained for the level at which the interval is "covered." It is shown that several problems considered in the literature have analytic solutions as special cases of the general model. The numerical results from one special case are compared to statistics obtained from experimental data from neurobiology.
24 citations