Telecommunication Systems 29:3, 181–197, 2005 c  2005 Springer Science + Business Media, Inc. Manufactured in The Netherlands. Loss Probability for a Finite Buffer Multiplexer with the M/ G /∞ Input Process GEORGE C. LIN ∗ george.lin@ieee.org; glin@ics.uci.edu ViaSat, Inc., Carlsbad, CA 92009 USA TATSUYA SUDA suda@ics.uci.edu Department of Information and Computer Science, University of California, Irvine, CA 92697-3425, USA FUMIO ISHIZAKI fumio@ieee.org Telecommunication Mathematics Research Center, Department of Mathematics, Korea University, 1, 5-Ka, Anam-dong, Sungbuk-gu, Seoul 136-701, Korea Received December 5, 2004; Revised March 15, 2005 Abstract. This paper studies the impact of long-range-dependent (LRD) traffic on the performance of a network multiplexer. The network multiplexer is characterized by a multiplexing queue with a finite buffer and an M/ G/∞ input process. Our analysis expresses the loss probability bounds using a simple relationship between loss probability and buffer full probability. Our analysis also derives an exact expression for the buffer full probability and consequently calculates the loss probability bounds with excellent precision. Through numerical calculations and simulation examples, we show that existing asymptotic analyses lack the precision for calculating the loss probability over realistic ranges of buffer capacity values. We also show that existing asymptotic analyses may significantly overestimate the loss probability and that designing networks using our analysis achieves efficient resource utilization. Keywords: long-range-dependence, self-similarity, fluid flow queue, multiplexing, queueing theory 1. Introduction Recent traffic measurements of existing packet networks and their applications (includ- ing Ethernet LANs, WANs, WWW, and VBR video over ATM) show that packet traffic exhibits the bursty property over multiple time scales, namely the long-range-dependent (LRD) property (e.g., [2,4,6,10,18,28,33]). The conventional Markov traffic models, however, do not adequately capture the LRD property (e.g., [4,18]), and network designs ∗ Corresponding author. George C. Lin was with the Department of Information and Computer Science, University of California, Irvine, CA 92697-3425, USA. Fumio Ishizaki was with the Department of Information and Telecommunication Engineering, Nanzan University, 27 Seirei, Seto, Aichi 489-0863, Japan