 Large loss networksP. J. Hunt and T. G. Kurtz Stochastic Processes and their Applications, 1994, vol. 53, issue 2, 363-378 Abstract: A general loss network is considered in the limit as the arrival rates and link capacities become large with their ratio held fixed. We show that the network obeys a functional law of large numbers (along a subsequence) and that the free circuit process acts as a control for the network. The network exhibits a separation of time-scales, with the free circuit process operating on the fast time-scale as a random walk on +J, and this leads to an interesting conjecture for transient random walks. The techniques used to prove the results are of independent interest and can be applied to a wide range of models in which a similar separation of time-scale occurs, or in which the transition rates of the process undergo a discontinuity at or near a boundary. Finally, we give examples and show that commonly employed fixed point approximations are not valid in this limit. Keywords: Loss; network; Functional; law; of; large; numbers; Time-scale; separation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:53:y:1994:i:2:p:363-378 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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