Statistical Models of Internet Traffic and Queueing Analysis

Purdue University, West Lafayette IN

Investigators

Abstract

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The investigator will construct different statistical models for the general Internet traffic and traffic from one extremely time-sensitive application, Voice over Internet Protocol (VoIP), due to the different traffic generation mechanism: A VoIP call creates a unique ON-OFF traffic process and the superposed VoIP traffic is generated following a call arrival process. On the other hand the general Internet traffic is a superposed packet stream where individual connection can be treated as a marked point process. The statistical models for both types of traffic will reflect the effect of superposition of multiple connections. The number of connections will be an important parameter in all the models under consideration. Stochastic processes theory will be extensively used to create statistical models of the non-linear long range dependent Internet traffic. The investigator will conduct a queueing study for VoIP, using the proposed VoIP traffic model as the arrival process at a queue. The queueing study will not be limited to the tail probabilities, and will provide results for the entire output process to better understand the effect of superposition on queueing behavior. Statistical models of Internet traffic are critical for computer network design and capacity planning purpose. Parsimonious models which accurately capture the Internet traffic properties will assist network engineers to design future networks with the ability to accommodate user traffic growing quickly beyond the scope of what is being observed today. The models will have simple structure that provides intuition and formulas for the traffic statistical properties, and serve as a tractable basis for further mathematical study of the Internet traffic. Because Quality of Service (QoS) criteria for the general Internet traffic can be a little relaxed while VoIP must comply with very strict QoS standards, the queueing study for VoIP will demonstrate how much VoIP traffic a network can support while maintaining the QoS standards. The proposed research requires knowledge in both statistical theory and computation. Students directly involved in the project will gain experience of statistical computing, and learn the knowledge of stochastic processes and queueing theory.