Nonlinear differential equations and dynamical systems
Nonlinear differential equations and dynamical systems
Discrete flow networks: bottleneck analysis and fluid approximations
Mathematics of Operations Research
Stability and instability of fluid models for reentrant lines
Mathematics of Operations Research
Sequencing and Routing in Multiclass Queueing Networks Part I: Feedback Regulation
SIAM Journal on Control and Optimization
Value iteration and optimization of multiclass queueing networks
Queueing Systems: Theory and Applications
Performance Evaluation and Policy Selection in Multiclass Networks
Discrete Event Dynamic Systems
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
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Fluid limit techniques have become a central tool to analyze queueing networks over the last decade, with applications to performance analysis, simulation, and optimization.In this paper some of these techniques are extended to a general class of skip-free Markov chains. As in the case of queueing models, a fluid approximation is obtained by scaling time, space, and the initial condition by a large constant. The resulting fluid limit is the solution of an ODE in "most" of the state space. Stability and finer ergodic properties for the stochastic model then follow from stability of the set of fluid limits. Moreover, similar to the queueing context where fluid models are routinely used to design control policies, the structure of the limiting ODE in this general setting provides an understanding of the dynamics of the Markov chain. These results are illustrated through application to Markov Chain Monte Carlo.