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Introduction to shape stability for a storage model

Menshikov, M.V.; Sisko, V.V.; Vachkovskaia, M.

Authors

V.V. Sisko

M. Vachkovskaia



Abstract

We consider a new idea for a storage model on n nodes, namely stability of shape. These nodes support K neighborhoods S i  ⊂ {1, ..., n} and items arrive at the S i as independent Poisson streams with rates λ i , i = 1, ... , K . Upon arrival at S i an item is stored at node j ∈ S i where j is determined by some policy. Under natural conditions on the λ i we exhibit simple local policies such that the multidimensional process describing the evolution of the number of items at each node is positive recurrent (stable) in shape.

Citation

Menshikov, M., Sisko, V., & Vachkovskaia, M. (2013). Introduction to shape stability for a storage model. Methodology and Computing in Applied Probability, 15(1), 125-146. https://doi.org/10.1007/s11009-011-9229-8

Journal Article Type Article
Publication Date Mar 1, 2013
Deposit Date May 8, 2014
Publicly Available Date Mar 29, 2024
Journal Methodology and Computing in Applied Probability
Print ISSN 1387-5841
Electronic ISSN 1573-7713
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 15
Issue 1
Pages 125-146
DOI https://doi.org/10.1007/s11009-011-9229-8
Keywords Storage model, Recurrence, Transience, Join the shortest queue, Routing policy, 60J25, 60K25.

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