The most promising switching technique for B-ISDN (broadband integrated service digital network) is the ATM (asynchronous transfer mode). In an ATM network, all information, data, voice and video, is packetized and divided into fixed length data blocks called cells. The cells from different connections are carried through a multiplexer, and asynchronously transmitted through the network. Statistical multiplexing of cells allows the possible reduction of the bandwidth assigned to each single source. That increased flexibility with respect to the bandwidth requirement provides a chance for better, more economical utilization of the network resources. On the other hand, severe network congestion can occur when a large number of traffic sources become active simultaneously. Since most traffic sources in ATM networks are bursty, some congestion control must be applied to each source in order to maintain the required GOS (grade of service) and provide fairness among the users. We introduce the discrete batch Markovian arrival process, which is a versatile and tractable class of Markov renewal processes. This class of processes provides a very powerful modeling tool. The Palm measure, variance time curve, asymptotic normality of the counts are derived. The interarrival time distribution for the single arrivals case are discussed. We also address some issues related to the simulation of this class of processes. Two traffic shaping, or smoothing schemes are investigated in this dissertation: jumping windows with regular placement and an input rate control model, introduced by Ohta et al. (21). The discrete Markovian arrival process with single arrivals serves as the model for the arrival process. In the first model, analytical expressions for the loss probability, packet delay and the interarrival times for the shaped process in steady state are derived. The second model leads to a highly degenerate partitioned Markov chain of QBD (Quasi-Birth-and-Death) type. Special algorithms involving matrices of lower order are obtained by exploiting the special structure of the Markov chain. Some performance measurements are derived. The algorithmic implementation of these results is also discussed. Finally, we examine some specific examples, applying both the analytical results and simulation, to demonstrate the effectiveness of the two traffic shaping schemes.
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