Statistical multiplexing of regulated flows in networks: Some structural properties and a framework for end-to-end performance analysis

Yu Ying, Purdue University

Abstract

An important, yet challenging, issue in the traffic engineering of high-speed networks is to determine the statistical performance when bursty traffic are multiplexed. Important performance metrics are the end-to-end delay and packet loss characteristics. The key to resolving the performance is the buffer occupancy distribution at the nodes. While this is fairly well understood in single buffers, the end-to-end problem is largely unsolved in the statistical context. A useful heuristic is the so-called Negligible Jitter conjecture that states that the end-to-end performance is bounded by the performance in a network assuming Better than Poisson (BTP) traffic at each node and then using the standard M/G/1 analysis with independence assumptions. The crucial question that arises is whether the BTP assumption is realistic and the applicability is broad. This dissertation is devoted to this important issue and to develop a framework for analyzing the end-to-end statistical performance for flows regulated by leaky bucket regulators as in real networks. We consider the problem for networks with FIFO scheduling and independent input streams at the network ingress. We show that the BTP holds for regulated sources and obtain explicit and accurate estimates for the tail and mean distributions of the workload. Furthermore, we study the burstiness behavior of regulated traffic inside the network. We show that a single flow inherits its initial bursty properties with a distribution converging to the burst size it initially obtains at the network access provided its contribution is small with respect to the aggregate. We also obtain explicit models for the burstiness of aggregate flows. These results lead to explicit bounds for the end-to-end mean delay performance. All these performance bounds give insights for network QoS provisioning and designing admission control strategy. Finally we consider concentrator networks as a special, but important, case. We show that the workload increases in distribution when their input flows are replaced by the original independent traffic streams. This result gives a very simple but effective approach to estimate the statistical performance of such networks. The ash exhibited a high acid neutralizing capacity that increased with retention time, and neutralization of ground and surface water was observed at the site. However, pore-water within the ash fill contained potentially hazardous constituents, most of which were depleted slowly from ash and reached higher aqueous concentrations at extended retention times. The two main constituents of concern were arsenic and boron. Arsenic transport was highly attenuated by soil with As(III) being more mobile than As(V). Arsenic has not been detected in downgradient monitoring wells and its transport is highly dependent on preferential flow conditions. Boron exhibited low sorption to soil and its transport lagged slightly behind groundwater flow. Thus, release of boron from ash and groundwater flow rate control its mobility. A fraction of the boron in ash was solubilized immediately upon water contact and other fractions were released more slowly, consistent with boron partitioning during combustion. Over 50% of the total boron was released slowly indicating that ash may be a long-term source. For both elements, groundwater flow rates, preferential flow, and dilution are critical in evaluating environmental impacts. Assuming no preferential flow, boron and arsenic require over 100 and 30,000 years to reach a downgradient creek which is utilized by wildlife. A creek flow rate of at least 1.6 L/s, which is reasonable, would dilute both elements to acceptable levels.

Degree

Ph.D.

Advisors

Shroff, Purdue University.

Subject Area

Electrical engineering

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