This project analyzes the performance of discrete-time queueing systems, appearing in packet communication networks, under dependent and/or slow (or fast) packet arrival processes. Packet processes in today's networking structures are usually dependent and they may deliver packets which are at least tau time units apart (slow lines) or they may deliver multiple packets almost simultaneously (fast lines). Such processes will be described by an m-state tau-idle Markov Modulated r-Bernoulli model (m/tau/MM/r/B). The appropriateness of the m/tau/MM/r/B modeling for complex packet processes is being established and (a) statistical multiplexers and (b) token ring networks, under m/tau/MM/r/B packet arrival processes, are being studied. The analysis approach is based on the formulation of appropriate discrete-time queueing models. The buffer occupancy process, for system (a), and the cycle time process for system (b), are described. Based on these processes, packet delay results are obtained. The following is being achieved: - A powerful class of models for complex packet processes, which has the potential of leading to analytically tractable system modeling, will be introduced and its superiority to previously adopted models will be established. - Important systems appearing in complex networking structures will be analyzed under certain models from the proposed class of models. - Techniques for the anlysis of queueing systems under m/tau/MM/r/B modeling will be developed.
