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Diffusion Approximations for a Multiclass Markovian Service System with "Guaranteed" and "Best-Effort" Service Levels

Graduate School of Business, Columbia University, 3022 Broadway, New York, New York 10027
Graduate School of Business, Columbia University, 3022 Broadway, New York, New York 10027
c.maglaras{at}gsb.columbia.edu
assaf{at}gsb.columbia.edu

This paper considers a Markovian model of a service system motivated by communication and information services. The system has finite processing capacity and offers multiple grades of service. The highest priority users receive a "guaranteed" processing rate, while lower priority users share residual capacity according to their priority level and therefore may experience service degradation (hence the term "best effort"). This paper focuses on performance analysis for this class of systems. We consider the Halfin-Whitt heavy-traffic regime, where the arrival rate and system processing capacity both grow large in a way that the traffic intensity approaches one. We first derive a multidimensional diffusion approximation for the system dynamics and subsequently obtain a more tractable diffusion limit based on an intuitive "perturbation approach." This method enables us to compute various closed form approximations to steady-state as well as transient congestion-related performance measures. Numerical examples illustrate the accuracy of these approximations.

Key Words: diffusion approximations; service systems; static priorities; shared resources; differentiated services; many server limits; Halfin-Whitt regime; parameter perturbations
History: Received: December 20, 2002; revision received: August 4, 2003;

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