Heavy and Light Traffic Regimes for M/G/infinity Traffic Models
Abstract
The M | G | infinity 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 and M | G | infinity 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 alpha-stable Levy 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 | infinity 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1999
- Accession Number
- ADA442643
Entities
People
- Konstantinos P. Tsoukatos
Organizations
- University of Maryland