Statistical Multiplexing of Homogeneous Streams results in Linear Bandwidth Gains

Abstract

Statistical multiplexing of traffic streams results in reduced network bandwidth requirement. The resulting gain increases with the increase in the number of streams being multiplexed together. However, the exact shape of the gain curve, as more and more streams are multiplexed together, is not known. In this paper, we first present the generalized result that the statistical gain of combining homogeneous traffic streams, of any traffic type, is a linear function of the number of streams being multiplexed. That is, given a fixed Quality of Service (QoS) constraint, like percentile delay, D, the bandwidth requirement of n streams to satisfy the delay constraint D is n x R x c where R is the bandwidth requirement of a single stream that satisfies the constraint D and c e (0,1]. We present the linear bandwidth gain result, using an extensive simulation study for video traces, specifically, streaming video (IPTV traces) and interactive video (CISCO Telepresence traces). The linear bandwidth gain result is then verified using analytical tools from two different domains. First, we validate the linearity using Queueing Theory Analysis, specifically using Interrupted Poisson Process (IPP) and Markov Modulated Poisson Process (MMPP) modeling. Second, we formally prove the linear behavior using the Asymptotic Analysis of Algorithms, specifically, the Big-O analysis.