Abstract

In this dissertation, we propose a new approach for the queueing analysis of discrete-time queues with correlated arrivals, arising in the ATM environment. In the first part of this work, we focus on the discrete-time transient analysis of a single server ATM multiplexer, where the arrival process consists of the super-position of the traffic generated by a homogeneous as well as by a heterogeneous set of independent binary Markov sources. We propose a new approach in the derivation of the transient joint probability generating function of the buffer content and the number of active sources. From this, time-dependent performance measures such as mean, variance and distribution of the queue length can be derived. Further, the transient analysis allows us to derive closed form expressions for the steady-state probability generating functions of the queue length, packet delay, as well as their corresponding first moments. We also present the idle and busy period analysis of the system. In the second part of this dissertation, we extend the approach to the transient and steady-state analysis of a multiserver ATM multiplexer and finally, in the third part, we demonstrate the applicability of the proposed approach in the steady-state analysis of a tandem queuing network with correlated arrivals. First we derive the steady-state joint generating function of the contents of the queues and the number of active sources. From this any moment of the queue length at each node can be extracted. In addition we derive explicit expressions for the average delay at each node as well as for the total average delay in the network. The main contribution of the first two parts of this work is to show how to extend the queueing analysis of the GI/D/c queue in order to handle the correlation in the arrival process. The advantage behind the proposed approach is that it places the ATM multiplexer analysis on the same platform as that of the GI/D/c queue. The main contribution of the third part of this work is to establish a general framework, under which an exact performance analysis can be carried out, at the network level, in an ATM environment.