Stability Of Load-balanced Network And Bandwidth Sharing Network Under Special Conditions

Stochastic network is a usual simulation tool of the systems, and the question wh-en it is stable not only is essential to their capacity planning, but also directly affects t-he benefit of the service company. So the stability analysis of stochastic network is es-sential in both theory aspect and practical aspect.Based on analyzing and summarizing the research achievements of predecessorson the stability of the queuing network, this paper analyzes the stability of two-stationload-balanced network with each station containing two servers, two-station load-balanced network with each station containing three servers, and bandwidth sharing netw-ork under general document size distributions with weighted alpha fair allocation. Themain content is as follows:First of all, this paper introduces the domestic and foreign research situation of c-orresponding subject, Poisson process, usual limits and continuity definitions, strong l-aw of large numbers, and Markov process.Secondly, this paper analyzes the stability of two-station load-balanced networkwith each station containing two servers. This paper derives the dynamic behavior rel-ations of the network by the load-balanced model, service discipline and JSQ routingchoice policy. This paper proves that each undelayed fluid limit satisfies fluid model r-elations through fluid limit to the relations and that each fluid limit with fixed initial s-tate satisfies augmented fluid model relations under the assumption that the network isstable. This paper gets three necessary and sufficient conditions such that the networkis stable through the method of fluid limit, and confirms the conjecture that Suhov YM and Vvedenskaya N D proposed in2002under each station containing two servers.When each station contains3servers, this paper gets the same conclusion.Finally, this paper analyzes the stability of bandwidth sharing network under gen-eral file size distributions with weighted alpha fair allocation. This paper proves fluidlimit theorem, the network is stable if corresponding fluid limit model is stable, and n-ormal capacity condition is necessary and sufficient condition such that the network is stable, and confirms the conjecture that Walton N S and Mandjes M R H proposed in2011under weighted alpha fair allocation.