TY - GEN
T1 - On the approximation error of mean-field models
AU - Ying, Lei
N1 - Publisher Copyright:
© 2016 Copyright held by the owner/author(s). Publication rights licensed to ACM.
PY - 2016/6/14
Y1 - 2016/6/14
N2 - Mean-field models have been used to study large-scale and complex stochastic systems, such as large-scale data centers and dense wireless networks, using simple deterministic models (dynamical systems). This paper analyzes the approximation error of mean-field models for continuous-time Markov chains (CTMC), and focuses on mean-field models that are represented as finite-dimensional dynamical systems with a unique equilibrium point. By applying Stein's method and the perturbation theory, the paper shows that under some mild conditions, if the mean-field model is glob- Ally asymptotically stable and locally exponentially stable, the mean square difference between the stationary distribution of the stochastic system with size M and the equilibrium point of the corresponding mean-field system is O(1/M). The result of this paper establishes a general theorem for establishing the convergence and the approximation error (i.e., the rate of convergence) of a large class of CTMCs to their mean-field limit by mainly looking into the stability of the mean-field model, which is a deterministic system and is often easier to analyze than the CTMCs. Two applications of mean-field models in data center networks are presented to demonstrate the novelty of our results.
AB - Mean-field models have been used to study large-scale and complex stochastic systems, such as large-scale data centers and dense wireless networks, using simple deterministic models (dynamical systems). This paper analyzes the approximation error of mean-field models for continuous-time Markov chains (CTMC), and focuses on mean-field models that are represented as finite-dimensional dynamical systems with a unique equilibrium point. By applying Stein's method and the perturbation theory, the paper shows that under some mild conditions, if the mean-field model is glob- Ally asymptotically stable and locally exponentially stable, the mean square difference between the stationary distribution of the stochastic system with size M and the equilibrium point of the corresponding mean-field system is O(1/M). The result of this paper establishes a general theorem for establishing the convergence and the approximation error (i.e., the rate of convergence) of a large class of CTMCs to their mean-field limit by mainly looking into the stability of the mean-field model, which is a deterministic system and is often easier to analyze than the CTMCs. Two applications of mean-field models in data center networks are presented to demonstrate the novelty of our results.
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U2 - 10.1145/2896377.2901463
DO - 10.1145/2896377.2901463
M3 - Conference contribution
AN - SCOPUS:84978640617
T3 - SIGMETRICS/ Performance 2016 - Proceedings of the SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Science
SP - 285
EP - 297
BT - SIGMETRICS/ Performance 2016 - Proceedings of the SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Science
PB - Association for Computing Machinery, Inc
T2 - 13th Joint International Conference on Measurement and Modeling of Computer Systems, ACM SIGMETRICS / IFIP Performance 2016
Y2 - 14 June 2016 through 18 June 2016
ER -