Introduction to Shape Stability for a Storage Model

M. V. Menshikov (), V. V. Sisko () and M. Vachkovskaia ()
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M. V. Menshikov: University of Durham
V. V. Sisko: Federal University of Fluminense
M. Vachkovskaia: University of Campinas – UNICAMP

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 1, 125-146

Abstract: 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.

Keywords: Storage model; Recurrence; transience; join the shortest queue; routing policy; 60J25; 60K25 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s11009-011-9229-8

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