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

This paper considers a Markovian model motivated by communication and information services, where a service provider is assumed to operate a finite set of processing resources and offer guaranteed-rate and best-effort type of service to a market of heterogeneous users. The capacity available to best-effort users is stochastically 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 results in a service rate degradation for this class. Exact analysis of this system can only be obtained via simulation or complicated numerical calculations. In contrast, this paper develops diffusion approximations based on large capacity asymptotics for systems operating close to heavy traffic. First, we derive a two-dimensional diffusion approximation for the system dynamics, and subsequently a simpler onedimensional diffusion based on an intuitive perturbation approach. These approximations are seen to be very accurate when compared with the behavior of the underlying stochastic system.