Variational Bounds and Sensitivity Analysis of TrafficProcesses in Continuous Flow Models
Discrete Event Dynamic Systems
Perturbation Analysis of Multiclass Stochastic Fluid Models
Discrete Event Dynamic Systems
Introduction to Discrete Event Systems
Introduction to Discrete Event Systems
IPA for continuous stochastic marked graphs
Automatica (Journal of IFAC)
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Stochastic Flow Models (SFMs) are stochastic hybrid systems that abstract the dynamics of many complex discrete event systems and provide the basis for their control and optimization. SFMs have been used to date to study systems with a single user class or some multiclass settings in which performance metrics are not class-dependent. In this paper, we develop a SFM framework for multiple classes and class-dependent performance objectives, where competing classes employ threshold control policies and service is provided on a First Come First Serve (FCFS) basis. In this framework, we analyze new phenomena that result from the interaction of the different classes and give rise to a new class of "induced" events that capture delays in the SFM dynamics. We derive Infinitesimal Perturbation Analysis (IPA) estimators for derivatives of various class-dependent objectives, and use them as the basis for on-line optimization algorithms that apply to the underlying discrete event system (not the SFM). This allows us to contrast system-centric and user-centric objectives, thus putting the resource contention problem in a game framework. The unbiasedness of IPA estimators is established and numerical results are provided to illustrate the effectiveness of our method for the case where there are no constraints on the controllable thresholds and to demonstrate the gap between the results of system-centric optimization and user-centric optimization.