tailieunhanh - Mạng lưới giao thông và đánh giá hiệu suất P6

Recently, there has been much interest in the behavior of queues with heavy-tailed service time distributions. This interest has been triggered by a large number of traf®c measurements on modern communication network traf®c (., see Willinger et al. [38] for Ethernet LAN traf®c, Paxson and Floyd [30] for WAN traf®c, and Beran et al. [3] for VBR video traf®c; see also various chapters in this volume). | Self-Similar Network Traffic and Performance Evaluation Edited by Kihong Park and Walter Willinger Copyright 2000 by John Wiley Sons Inc. Print ISBN 0-471-31974-0 Electronic ISBN 0-471-20644-X 6 THE SINGLE SERVER QUEUE HEAVY TAILS AND HEAVY TRAFFIC O. J. Boxma Department of Mathematics and Computing Science Eindhoven University of Technology 5600 MB Eindhoven The Netherlands and CWI . Box 94079 1090 GB Amsterdam The Netherlands J. W. Cohen CWI . Box 94079 1090 GB Amsterdam The Netherlands INTRODUCTION Recently there has been much interest in the behavior of queues with heavy-tailed service time distributions. This interest has been triggered by a large number of traffic measurements on modem communication network traffic . see Willinger et al. 38 for Ethernet LAN traffic Paxson and Floyd 30 for WAN traffic and Beran et al. 3 for VBR video traffic see also various chapters in this volume . These measurements and their statistical analysis . see Leland et al. 26 suggest that modem communication traffic often possesses the properties of selfsimilarity and long-range dependence. A natural possibility to introduce long-range dependence in an input traffic process is to take a fluid queue and to assume that at least one of the input quantities I on or off periods in the fluid queue fed by on off sources has the following heavy-tail behavior P Z t fr. 143 144 THE SINGLE SERVER QUEUE HEAVY TAILS AND HEAVY TRAFFIC with h . a positive constant and 1 v 2 here and later f fli gti stands for f t g t 1 with t and many-valued functions like t are defined by their principal value so t is real for t positive . In this context regularly varying and subexponential distributions 5 have received special attention. We refer to Boxma and Dumas 12 for a survey on fluid queues with heavy-tailed on-period distributions. In this chapter we concentrate on the ordinary single server queue with regularly varying service and or interarrival time distribution. The fluid queue