Diffusion Approximations for Systems with Shared Resources Offering Guaranteed and Best Effort Service

摘要

This paper considers a Markovian model motivated by communication and in-formation services, where a service provider is assumed to operate a finite set ofprocessing resources and offer guaranteed-rate and best-effort type of service toa market of heterogeneous users. The capacity available to best-effort users isstochastically modulated by the number of guaranteed-rate users in the system.Congestion arises due to the sharing of resources by the best-effort users, and re-sults in a service rate degradation for this class. Exact analysis of this system canonly be obtained via simulation or complicated numerical calculations. In contrast,this paper develops diffusion approximations based on large capacity asymptoticsfor systems operating close to heavy traffic. First, we derive a two-dimensionaldiffusion approximation for the system dynamics, and subsequently a simpler one-dimensional diffusion based on an intuitive perturbation approach. These approx-imations are seen to be very accurate when compared with the behavior of theunderlying stochastic system.