Abstract

Broadband networks are integrating different applications such as data, voice and video in a single network. The priority mechanism allows differentiating among services such that they can meet their QoS requirements. Since a switch output port may be considered as a statistical multiplexer, and the packets coming from an application are correlated, it is very important to obtain a good understanding of the statistical multiplexing with priority queues and correlated arrivals. In this thesis, we present performance analysis of a discrete-time system with two priority queues and correlated arrivals. A packet is transmitted during a slot if there are packets available in either queue. The packets in the low-priority queue are transmitted only if the high-priority queue is empty. The arrival process to each priority queue consists of the superposition of the traffic generated by a number of independent binary Markov sources and the arrivals to the two queues are independent of each other. The joint Probability Generating Function (PGF) of the two queue lengths and the number of sources is derived and the unknown boundary function is determined using the busy period distribution of the high-priority queue. From here, we determine closed form expressions for mean and variance of queue lengths as well as mean packet delay. Also we show the correspondence of our results with previous work by reducing our solution to the results of a multiplexer without priority in many special cases. At last we present numerical results, which show the effect of the high-priority traffic on the low-priority traffic and demonstrate the significance of the correlation on the performance of the system.