Why buffers in switching systems do not essentially improve QoS: An analytical case study for On-Off source traffic

摘要

Traffic models with a rate varying according to a Gaussian distribution are commonly used to evaluate statistical multiplexing in telecommunication systems. The superposition of a sufficient large number of homogeneous Markovian On-Off sources asymptotically approaches an Ornstein-Uhlenbeck process (OUP) which represents a Gaussian process with exponential autocorrelation function. We derive a simple expression for the bandwidth demand under QoS constraints which is close to numerical OUP/D/1 analysis results over the entire parameter region with relevance to applications. In comparison, results of the fluid flow method for fixed aggregation level are used to verify the OUP/D/1 asymptotics and to estimate its accuracy depending on the number of aggregated flows. Moreover, the OUP/D/1 asymptotics provides a useful check of the accuracy of bounds and approximations proposed in the literature in order to improve the effective bandwidth principle. Based on analytical evaluation, the efficiency of buffers for voice traffic is finally shown to be very limited, i.e. no more than 2% of bandwidth can be saved owing to buffers with regard to real time constraints and a predefined loss probability as QoS demands for voice.