Large deviations problems for star networks: The min policy

• 成果类型: Article
• 署名作者: Delcoigne, F; De La Fortelle, A
• 署名单位: Electricite de France (EDF); Inria
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000198
• 发表日期: 2004
• 页码: 1006-1028
• 关键词: discontinuous statistics; MARKOV-PROCESSES

摘要

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(-1) Q(nt), where Q(t) 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.