Istituto di Scienza e Tecnologie dell'Informazione     
Bortolussi L., Hayden R. A. Bounds on the deviation of discrete-time Markov chains from their mean-field model. In: Performance Evaluation, vol. 70 (10) pp. 736 - 749. Elsevier, 2013.
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 ofsuchsteadystates, 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.
URL: http://www.sciencedirect.com/science/article/pii/S0166531613000904
DOI: 10.1016/j.peva.2013.08.012
Subject Mean-field approximation
Discrete time Markov chains
B.8.2 Performance Analysis and Design Aids
60Jxx Markov processes

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