KALASHNIKOV MEMORIAL SEMINAR Performance of the Leaky Bucket System with Long–range Depend.pdfVIP

Информационные процессы, Том 2, № 2, 2002, стр. 186–189. c ´ ´ 2002 Gonzalez-Arevalo, Samorodnitsky. KALASHNIKOV MEMORIAL SEMINAR Performance of the Leaky Bucket System with Long–range Dependent Input Traffic B. Gonzalez-Arevalo and G. Samorodnitsky Cornell University email: bpg5@, gennady@ Received October 14, 2002 The study of traffic on data networks has changed substantially since the appearance of modern com- munication systems, which are essentially different from the traditional voice traffic networks. The main difference that appears in modern networks is the dependence structure of the data. While traditional models are based on assumptions of short range dependence, recent measurements (see [Leland et al.(1994)Leland, Taqqu, Willinger and Wilson], [Paxson and Floyd(1994)], [Cunha et al.(1995)Cunha, Bestavros and Crov- ella], [Crovella and Bestavros(1996)]) show the presence of long–range dependence and self–similarity in the data of network traffic. Presently it is believed that these phenomena are caused by the presence of heavy tails in the distribution of the service times, which cause the long–range dependence. In this study we consider a fluid version of a leaky bucket flow control protocol, with an input process in which the distribution of the session lengths is heavy tailed, causing it to be long–range dependent. The leaky bucket is a flow control mechanism that is designed to reduce the effect of the inevitable variability in the input stream into a node of a communication network. Let us consider two types of input processes: an On–Off process and a M/G/∞ type process. Recently there has been a lot of work concerning fluid models fed by On–Off or M/G/∞ t