Statistical Analysis of Long-Range Dependent Processes via a Stochastic Intensity Approach, with Applications in Networking

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Title: Statistical Analysis of Long-Range Dependent Processes via a Stochastic Intensity Approach, with Applications in Networking
Author: Tan, Phaik-Hoon
Advisors: James R. Wilson, Chair
Thom J. Hodgson, Minor Representative, Member
Arne A. Nilsson, Member
Henry L. W. Nuttle, Member
Abstract: The objective of this research is to develop a flexible stochastic intensity-function model for traffic arrivals arising in an Ethernet local area network. To test some well-known Bellcore datasets for long-rangedependence or nonstationarity, a battery of statistical tests was applied---including a new extensionof the classical Priestley-Rao test for nonstationarity; and the results of this analysis revealedpronounced nonstationarity in all of the Bellcore datasets. To model such teletraffic arrivalprocesses accurately, a stochastic intensity function was formulated as a nonlinear extension of theCox regression model that incorporates a general time trend together with cyclic effects andpacket-size effects. The proposed intensity-function model has anexponential-polynomial-trigonometric form that includes a covariate representing the latest packet size. Maximum likelihoodestimates of the unknown continuous parameters of the stochastic intensity function areobtained numerically, and the degrees of the polynomial time and packet-size components aredetermined by a likelihood ratio test. Although this approach yielded excellent fits to the Bellcoredatasets, it also yielded the surprising conclusion that packet size has a negligible effect on thepacket arrival rate. A follow-up analysis of the packet-size process confirmed this conclusion andshed additional light on the packet-generation mechanism in Ethernet local area networks. This research also includes the development of procedures for simulating traffic processes having a stochastic intensity function of the proposed form. An extensive Monte Carlo performanceevaluation demonstrates the effectiveness of the proposed procedure for modeling and simulation ofteletraffic arrival processes.
Date: 1999-07-07
Degree: PhD
Discipline: Industrial Engineering
URI: http://www.lib.ncsu.edu/resolver/1840.16/3435


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