Cycle time of stochastic max-plus linear systems.

Cycle time of stochastic max-plus linear systems

We analyze the asymptotic behavior of sequences of random variables (x(n))n∈N defined by an initial condition and the induction formula xi(n + 1) = maxj (Aij(n) + xj(n)), where (A(n))n∈N is a stationary and ergodic sequence of random matrices with entries in R ∪ {−∞}. This type of recursive sequences are frequently used in applied probability as they model many systems as some queueing networks...

Finite Abstractions of Stochastic Max-Plus-Linear Systems

This work investigates the use of finite abstractions to study the finite-horizon probabilistic invariance problem over Stochastic MaxPlus-Linear (SMPL) systems. SMPL systems are probabilistic extensions of discrete-event MPL systems that are widely employed in the engineering practice for timing and synchronisation studies. We construct finite abstractions by re-formulating the SMPL system as ...

Model predictive control for stochastic switching max-plus-linear systems

Railway Timetable Stability Analysis Using Stochastic Max-Plus Linear Systems

Stability and robustness of a railway timetable are essential properties for punctual and reliable operations. Timetable performance evaluation is therefore an important aspect in the timetable design process. In particular, the stability and recoverability properties of a timetable with respect to daily process time variations must be well analysed. The timetable must be able to recover from p...

Approximation Methods in Stochastic Max-Plus Systems

Cover design: Maryam (Narjes) Shojai Kaveh Cover illustrations: The robot is called Zebro and is designed at DCSC robotic laboratory. The other photos are downloaded from Wikipedia. " Fences are made for those who cannot fly. "