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Introduction to Shape Stability for a Storage Model

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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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Durham, South Road, Durham, DH1 3LE, UK

    M. V. Menshikov

  2. Institute of Mathematics and Statistics, Federal University of Fluminense, R. Mário Santos Braga, s/n, 24020-140, Niterói, RJ, Brazil

    V. V. Sisko

  3. Department of Statistics, Institute of Mathematics, Statistics and Scientific Computation, University of Campinas – UNICAMP, rua Sérgio Buarque de Holanda 651, 13083–859, Campinas SP, Brazil

    M. Vachkovskaia

Authors
  1. M. V. Menshikov
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  2. V. V. Sisko
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  3. M. Vachkovskaia
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Correspondence to M. V. Menshikov.

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Menshikov, M.V., Sisko, V.V. & Vachkovskaia, M. Introduction to Shape Stability for a Storage Model. Methodol Comput Appl Probab 15, 125–146 (2013). https://doi.org/10.1007/s11009-011-9229-8

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  • DOI: https://doi.org/10.1007/s11009-011-9229-8

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