首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Large Deviations Rate Function for Polling Systems
Authors:Delcoigne  Franck  de La Fortelle  Arnaud
Institution:(1) Université Paris 10, UFR SEGMI, 200 av. de la République, 92000 Nanterre, France;(2) Domaine de Voluceau, Rocquencourt, INRIA, BP 105, 78153 Le Chesnay Cedex, France
Abstract:In this paper, we identify the local rate function governing the sample path large deviation principle for a rescaled process n –1 Q nt , where Q t represents the joint number of clients at time t in a polling system with N nodes, one server and Markovian routing. By the way, the large deviation principle is proved and the rate function is shown to have the form conjectured by Dupuis and Ellis. We introduce a so called empirical generator consisting of Q t and of two empirical measures associated with S t , the position of the server at time t. One of the main step is to derive large deviations bounds for a localized version of the empirical generator. The analysis relies on a suitable change of measure and on a representation of fluid limits for polling systems. Finally, the rate function is solution of a meaningful convex program. The method seems to have a wide range of application including the famous Jackson networks, as shown at the end of this study. An example illustrates how this technique can be used to estimate stationary probability decay rate.
Keywords:large deviations  local rate function  polling system  fluid limits  empirical generator  change of measure  contraction principle  entropy  convex program
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号