Abstract

Currently, the modern networks including Internet and ATM are based on packet-switched technology. In this technology, the arriving packets are statistically multiplexed to achieve high bandwidth gain, also the output ports of routers may be modeled as multiplexers. As a result, in this type of networks, a packet goes through a number of multiplexers as it transits from source to destination. Because of this, the study of tandem networks of multiplexers is very important; as it will give us the information regarding the traffic shaping that occurs along the route. Due to the lack of exact analysis methods, most of the previous work in the analysis of tandem networks is based on either simulation or approximate models. This thesis presents an exact performance analysis of tandem networks with arbitrary number of multiplexers. Since, the traffic generated by multimedia sources in the real networks is correlated, the binary Markov On/Off source model is assumed for the input traffic to the network. The objective of the analysis is to determine the Probability Generating Function (PGF) of the queue length of each multiplexer in the tandem network as well as the corresponding performance measures. The complicated dependency among tandem multiplexers results in unknown boundary functions, determination of which is the main source of difficulty in the exact performance analysis. In this thesis, at first a straightforward solution technique is used to determine the PGF of the queue lengths and number of On sources for a tandem network with two multiplexers. Unfortunately, this solution does not extend to tandem networks with higher number of multiplexers. As a result, an alternative method has been developed, which determines the unknown boundary functions by using busy periods of multiplexers. The PGF of the queue length and number of On sources is obtained for each multiplexer in a tandem network with arbitrary number of multiplexers. Following that, the mean and variance of queue lengths as well as the packet delay at each multiplexer have been determined. A proof of this solution is given to show that the analysis is correct. Then, the solution has been extended to a more general tandem network, where each multiplexer is fed by multiple types of traffic. Finally, numerical results regarding the analysis are presented and compared with those of the simulation. The analysis shows network traffic gets smoother when it goes through higher number of multiplexers, this smoothing effect is more obvious in heterogeneous traffic case. It also shows that under constant traffic load, as the number of sources increases, the delay and queue length increase. The analysis results enable to explain the delicate interaction between traffic smoothing and source burstiness.