Heavy and Light Traffic

Title of Dissertation: HEAVY AND LIGHT TRAFFIC REGIMES FOR M |G|∞ TRAFFIC MODELS Konstantinos P. Tsoukatos, Doctor of Philosophy, 1999 Dissertation directed by: Professor Armand M. Makowski Department of Electrical Engineering The M |G|∞ busy server process provides a class of structural models for communication network traffic. In this dissertation, we study the asymptotic behavior of a network multiplexer, modeled as a discrete–time queue, driven by an M |G|∞ correlated arrival stream. The asymptotic regimes considered here are those of heavy and light traffic. In heavy traffic, we show that the arising limits are described in terms of the classical Brownian motion and the α–stable Lévy motion, under short– and long–range dependence, respectively. Salient features are then effectively captured by the exponential distribution and the Mittag–Leffler special function. In light traffic, the analysis reveals the effect of two aspects of the M |G|∞ process, i.e., the session duration distribution G and the gradual nature of the arrivals, as opposed to the instantaneous inputs of a standard GI|GI|1 queue. We exploit these asymptotic results to construct interpolation approximations for system quantities of interest, applicable to all traffic intensities. HEAVY AND LIGHT TRAFFIC REGIMES FOR M |G|∞ TRAFFIC MODELS by Konstantinos P. Tsoukatos Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 1999 Advisory Committee: Professor Armand M. Makowski, Chairperson/Advisor Professor Prakash Narayan Associate Professor Adrian Papamarcou Associate Professor Leandros Tassiulas Professor A. Udaya Shankar, University Representative c ©Copyright by Konstantinos P. Tsoukatos 1999