240,369 research outputs found
Limiting behavior of the search cost distribution for the move-to-front rule in the stable case
Move-to-front rule is a heuristic updating a list of n items according to
requests. Items are required with unknown probabilities (or popularities). The
induced Markov chain is known to be ergodic. One main problem is the study of
the distribution of the search cost dened as the position of the required item.
Here we first establish the link between two recent papers that both extend
results proved by Kingman on the expected stationary search cost. Combining
results contained in these papers, we obtain the limiting behavior for any
moments of the stationary seach cost as n tends to innity
Limiting behavior of the search cost distribution for the move-to-front rule in the stable case
Move-to-front rule is a heuristic updating a list of n items according to requests. Items are required with unknown probabilities (or popularities). The induced Markov chain is known to be ergodic. One main problem is the study of the distribution of the search cost defined as the position of the required item. Here we first establish the link between two recent papers of Barrera and Paroissin and Lijoi and Pruenster that both extend results proved by Kingman on the expected stationary search cost. Combining results contained in these papers, we obtain the limiting behavior for any moments of the stationary seach cost as n tends to infinity.Normalized random measure, Random discrete distribution, Stable subordinator, Problem of heaps
Limiting behavior of the search cost distribution for the move-to-front rule in the stable case
Move-to-front rule is a heuristic updating a list of n items according to requests. Items are required with unknown probabilities (or ppopularities). The induced Markov chain is known to be ergodic [4]. One main problem is the study of the distribution of the search cost defined as the position of the required item. Here we first establish the link between two recent papers [3, 8] that both extend results proved by Kingman [7] on the expected stationary search cost. Combining results contained in these papers, we obtain the limiting behavior for any moments of the stationary seach cost as n tends to infinity.normalized random measure; random discrete distribution; stable subordinator; problem of heaps
Limiting behaviour of the stationary search cost distribution driven by a generalized gamma process
Consider a list of labeled objects that are organized in a heap. At each time, object j is selected with probability pj and moved to the top of the heap. This procedure defines a Markov chain on the set of permutations which is referred to in the literature as Move-to-Front rule. The present contribution focuses on the stationary search cost, namely the position of the requested item in the heap when the Markov chain is in equilibrium. We consider the scenario where the number of objects is infinite and the probabilities pj's are defined as the normalization of the increments of a subordinator. In this setting, we provide an exact formula for the moments of any order of the stationary search cost distribution. We illustrate the new findings in the case of a generalized gamma subordinator and deal with an extension to the two-parameter Poisson-Dirichlet process, also known as Pitman-Yor process
Limiting search cost distribution for the move-to-front rule with random request probabilities
Consider a list of files whose popularities are random. These files are
updated according to the move-to-front rule and we consider the induced Markov
chain at equilibrium. We give the exact limiting distribution of the
search-cost per item as tends to infinity. Some examples are supplied.Comment: move-to-front, search cost, random discrete distribution, limiting
distribution, size biased permutatio
Ant colony system-based applications to electrical distribution system optimization
Chapter 16, February 201
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