Traditional teletraffic engineering is essentially based on the exponential distribution and its variants. The recent measurement studies indicate that models based on this approach may be less useful than expected. Our goal in this research is to present new perspectives on teletraffic engineering and the concept of Quality of Service in high speed networks. Toward this aim, we have developed novel and easily tractable methodologies for the teletraffic engineering of high speed networks with multiple time-scale traffic. Our analytical procedures are useful for the design and performance evaluation of both single queues and queueing networks. Note that parts of this research appear also in [StS98a, StS98b, StS99a, StS99b].
In Chapter 2, we focus on the single-node engineering. We propose a new methodology for the modeling and analysis of heavy-tailed distributions, such as the Pareto distribution, in a queueing system. Our main thesis is that classical teletraffic methods can be employed for analyzing such distributions. Our approach is based on a fitting algorithm which approximates a heavy-tailed distribution by a hyperexponential distribution. This algorithm possesses several key properties. First, the approximation can be achieved within any desired degree of accuracy. Second, the fitted hyperexponential distribution depends only on a few parameters. Third, only a small number of exponentials are required in order to obtain an accurate approximation over many time scales. Once equipped with a fitted hyperexponential distribution, we have an integrated framework for analyzing queueing systems with heavy-tailed distributions. We consider the GI/G/1 queue with Pareto distributed service time and show how our approach allows to derive both quantitative numerical results and asymptotic closed-form results (note that the performance of a GI/G/1 queue with Pareto distributed service time is closely related to the performance of a queue fed by an On/Off fluid process with Pareto distributed activity period and arbitrarily distributed inactive period [Box96]). This derivation provides new insight into the impact of system characteristics on performance measures, such as the relation between the inter-arrival time distribution and the waiting time distribution. Moreover, it enables to state the domain of validity of asymptotic results.
In the second part of this work, which appears in Chapter 3, we introduce a comprehensive framework for evaluating the impact of multiple time-scale traffic on important QoS performance measures in a communication network. Our approach is based on a new network calculus, termed Stochastically Bounded Burstiness (SBB) calculus, which provides statistical upper bounds on various performance metrics such as delay, at each node of a feedforward network. This calculus is based on an appropriate characterization of the processes feeding the network. This characterization is achieved by stochastically bounding the ``burstiness'', which in our context means an ensemble of linear envelop processes, by general decreasing functions. The SBB methodology is useful for a large class of exogenous arrival processes, including important processes exhibiting ``subexponentially bounded burstiness'' such as fractional Brownian motion. Moreover, it allows to judiciously capture the salient features of real-time traffic, such as the ``cell'' and ``burst'' characteristics of multiplexed voice traffic. This accurate characterization is achieved by setting the bounding function as a sum of exponentials. We compare our methodology with previous approaches and show that it can substantially improve the utilization of networks implementing services based on statistical guarantees.
The last chapter of this work is devoted to discussion on the findings of this thesis and future areas of research.