Workload models for stochastic networks: value functions and performance evaluation

This paper concerns control and performance evaluation for stochastic network models. Structural properties of value functions are developed for controlled Brownian motion (CBM) and deterministic (fluid) workload-models, leading to the following conclusions: Outside of a null-set of network parameters, the following hold. i) The fluid value-function is a smooth function of the initial state. Under further minor conditions, the fluid value-function satisfies the derivative boundary conditions that are required to ensure it is in the domain of the extended generator for the CBM model. Exponential ergodicity of the CBM model is demonstrated as one consequence. ii) The fluid value-function provides a shadow function for use in simulation variance reduction for the stochastic model. The resulting simulator satisfies an exact large deviation principle, while a standard simulation algorithm does not satisfy any such bound. iii) The fluid value-function provides upper and lower bounds on performance for the CBM model. This follows from an extension of recent linear programming approaches to performance evaluation.