Large loss networks

Large loss networks

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Article ID: iaor19951137
Country: Netherlands
Volume: 53
Issue: 2
Start Page Number: 363
End Page Number: 378
Publication Date: Oct 1994
Journal: Stochastic Processes and Their Applications
Authors: ,
Keywords: loss networks
Abstract:

A general loss network is considered in the limit as the arrival rates and link capacities become large with their ratio held fixed. The authors 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 equ1, 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, the authors give examples and show that commonly employed fixed point approximations are not valid in this limit.

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