Introduction to shape stability for a storage model

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

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: May 21, 2014
• 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.