2004/05/01 by Franck Delcoigne, Arnaud de La Fortelle
Business, Management and Accounting · Decision Sciences · Engineering · Mathematics · #Advanced Queuing Theory Analysis #Probability and Risk Models #Reliability and Maintenance Optimization #math.PR #msc:60F10 #msc:60K30.
paper · pdf · doi:10.1214/105051604000000198
published as Annals of Probability 2004, Vol. 14, No. 2, 1006-1028
openalex publication_date 2004/05/01 · arxiv created 2004/06/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We are interested in analyzing the effect of bandwidth sharing for telecommunication networks. More precisely, we want to calculate which routes are bottlenecks by means of large deviations techniques. The method is illustrated in this paper on a star network, where the bandwidth is shared between customers according to the so-called min policy. We prove a sample path large deviation principle for a rescaled process n−1Qnt, where Qt represents the joint number of connections at time t. The main result is to compute the rate function explicitly. The major step consists in deriving large deviation bounds for an empirical generator constructed from the join number of customers and arrivals on each route. The rest of the analysis relies on a suitable change of measure together with a localization procedure. An example shows how this can be used practically.