Queueing theory is one of the most important branches of modern probability theory which has many applications in operation research and communication networks. Statistical multiplexing is one of core techniques behind the concept of ATM networks in B-ISDN. Since one of important problems in statistical multiplexing is modeling of the superposed input traffic, the characterization of the superposed traffic may be one of the most essential issues in the performance evaluation of statistical multiplexers. One voice source is modeled by 2-state Markov model in the most studies on statistical multiplexing. Recently experimental results show that the 3-state Markov model is more reasonable than 2-state Markov model in voice source.
In this thesis, as superposed input traffic of voice sources, we characterize arrival processes to a statistical multiplexing of independent identical 3-state Markov models, and obtain the distribution of buffer contents, loss probability and the distribution of packet delay. Also, as input traffic of MPEG video source, we propose a new stochastic process called the P-MMBBP, and obtain the autocorrelation function of the P-MMBBP and performance evaluation of P-MMBBP/D/1 queueing system.
In chapter 3, we consider queueing model for a statistical multiplexer model with finite buffer capacity and a finite number of independent identical 3-state bursty voice sources. One voice source is modeled as 3-state MMBP by describing both two different active periods (at the rate of one packet per slot) and one passive period during which no packets are generated. For queueing model for statistical multiplexer of a finite buffer capacity and a finite number of independent identical 3-state bursty voice sources, we derive the recursive algorithm for the probability mass functions of the buffer contents. We also loss probability and the distribution of packet delay.
In chapter 4, we consider the same statistical multiplexer model as in chapter 3 excep...