Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Integrating streaming and file-transfer Internet traffic: fluid and diffusion approximations
Queueing Systems: Theory and Applications
A Generic Mean Field Convergence Result for Systems of Interacting Objects
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
Journal of Computer and System Sciences
A class of mean field interaction models for computer and communication systems
Performance Evaluation
Performance analysis of contention based medium access control protocols
IEEE Transactions on Information Theory
Mean-Field Analysis for the Evaluation of Gossip Protocols
QEST '09 Proceedings of the 2009 Sixth International Conference on the Quantitative Evaluation of Systems
Dynamical Systems and Stochastic Programming: To Ordinary Differential Equations and Back
Transactions on Computational Systems Biology XI
Accurate hybridization of nonlinear systems
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
A fluid analysis framework for a Markovian process algebra
Theoretical Computer Science
Computing reachable states for nonlinear biological models
Theoretical Computer Science
Fluid computation of passage-time distributions in large Markov models
Theoretical Computer Science
Input-to-state stability for discrete-time nonlinear systems
Automatica (Journal of IFAC)
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
Performance Specification and Evaluation with Unified Stochastic Probes and Fluid Analysis
IEEE Transactions on Software Engineering
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We consider a generic mean-field scenario, in which a sequence of population models, described by discrete-time Markov chains (DTMCs), converges to a deterministic limit in discrete time. Under the assumption that the limit has a globally attracting equilibrium, the steady states of the sequence of DTMC models converge to the point-mass distribution concentrated on this equilibrium. In this paper we provide explicit bounds in probability for the convergence of such steady states, combining the stochastic bounds on the local error with control-theoretic tools used in the stability analysis of perturbed dynamical systems to bound the global accumulation of error. We also adapt this method to compute bounds on the transient dynamics. The approach is illustrated by a wireless sensor network example.