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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Mikhail Menshikov

Menshikov, M.V., Sisko, V.V. & Vachkovskaia, M. (2013). Introduction to shape stability for a storage model. Methodology and Computing in Applied Probability 15(1): 125-146.

Author(s) from Durham


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.