A coupling approach to estimating the Lyapunov exponent of stochastic max-plus linear systems

Rob M.P. Goverde , Bernd Heidergott , Glenn Merlet (1)

1 I2M - Institut de Mathématiques de Marseille

This paper addresses the problem of approximately computing the Lyapunov exponent of stochastic max- plus linear systems. Our approach allows for an efficient simulation of bounds for the Lyapunov expo- nent. We provide sufficient conditions for the convergence of the bounds. In particular, a perfect sampling scheme for the Lyapunov exponent is established. We illustrate the effectiveness of our bounds with an application to (real-life) railway systems.

Mots clés: Max-plus algebra; Stochastic DES; Lyapunov exponent; Simulation; Railway systems

Domaines: Mathématiques [math]; Recherche opérationnelle [math.OC]; Probabilités [math.PR]; Mathématique discrète [cs.DM]

Rob M.P. Goverde, Bernd Heidergott, Glenn Merlet. A coupling approach to estimating the Lyapunov exponent of stochastic max-plus linear systems. European Journal of Operational Research, 2011, ⟨10.1016/j.ejor.2010.09.035⟩. ⟨hal-01263221⟩