KEYWORDS: Video, Systems modeling, Video compression, Multiplexing, Data modeling, Stars, Multiplexers, Image compression, Performance modeling, Computing systems
We study modeling approaches for traffic characteristics of real time video traffic including the distribution function of the size of each group of pictures in MPEG coding and their short term correlation. A numerical solution of the steady state workload distribution is computed for semi-Markovian state models in discrete time. A verification step based on interval arithmetic is able to enclose the numerical result within tight bounds for many cases. We compare the delay and loss performance in data forwarding by a buffered switch as predicted by the model to direct evaluation of publicly available video traces.
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 MarkovianOn-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.
Non-renewal processes are relevant in queueing analysis to include various types of traffic arising in integrated services communication networks. We consider a workload based approach to the single server queue in discrete time domain with semi-Markov arrivals (SMP/G/1). Starting from a subdivision of the busy periods, we generalize a computationally attractive algorithm for the discrete time GI/G/1 queue. The stationary distributions of the waiting and idle time as well as the moments of the busy period are computed. Performance results are given for deterministic servers with autoregressive input and the output process of a server is modeled by adapting a SMP of small size.
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