Queueing Analysis of High-Speed Multiplexers including Long-Range Dependent Arrival Processes.

With the advent of high-speed networks, a single link will carry hundreds or even thousands of applications. This results in a very natural application of the Central Limit Theorem, to model the network traffic by Gaussian stochastic processes. In this paper we study the tail probability P({Q>x})of a queueing system when the input process is assumed to be a very general class of Gaussian processes which includes a large class of self-similar or other types of long-range dependent Gaussian processes. For example, past work on Fractional Brownian Motion, and variations therein, are but a small subset of the work presented in this paper. Our study is based on Extreme Value Theory and we show that log P({Q>x})+m x/2grows at most on the order of log x,wherem x corresponds to the reciprocal of the maximum (normalized) variance of a Gaussian process directly related to the aggregate input process. Our result is considerably stronger than the existing results in the literature based on Large D..

Investigation of delay jitter of heterogeneous traffic in broadband networks

Scope and Methodology of Study: A critical challenge for both wired and wireless networking vendors and carrier companies is to be able to accurately estimate the quality of service (QoS) that will be provided based on the network architecture, router/switch topology, and protocol applied. As a result, this thesis focuses on the theoretical analysis of QoS parameters in term of inter-arrival jitter in differentiated services networks by deploying analytic/mathematical modeling technique and queueing theory, where the analytic model is expressed in terms of a set of equations that can be solved to yield the desired delay jitter parameter. In wireless networks with homogeneous traffic, the effects on the delay jitter in reference to the priority control scheme of the ARQ traffic for the two cases of: 1) the ARQ traffic has a priority over the original transmission traffic; and 2) the ARQ traffic has no priority over the original transmission traffic are evaluated. In wired broadband networks with heterogeneous traffic, the jitter analysis is conducted and the algorithm to control its effect is also developed.Findings and Conclusions: First, the results show that high priority packets always maintain the minimum inter-arrival jitter, which will not be affected even in heavy load situation. Second, the Gaussian traffic modeling is applied using the MVA approach to conduct the queue length analysis, and then the jitter analysis in heterogeneous broadband networks is investigated. While for wireless networks with homogeneous traffic, binomial distribution is used to conduct the queue length analysis, which is sufficient and relatively easy compared to heterogeneous traffic. Third, develop a service discipline called the tagged stream adaptive distortion-reducing peak output-rate enforcing to control and avoid the delay jitter increases without bound in heterogeneous broadband networks. Finally, through the analysis provided, the differential services, was proved not only viable, but also effective to control delay jitter. The analytic models that serve as guidelines to assist network system designers in controlling the QoS requested by customer in term of delay jitter