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Weak reversibility is a crucial structural property of chemical reaction networks with mass action kinetics, because it has major implications related to the existence, uniqueness and stability of equilibrium points and to the boundedness of solutions. In this paper, we present two new algorithms to find dynamically equivalent weakly reversible realizations of a given chemical reaction network. They are based on linear programming (LP) and thus have polynomial time-complexity. Hence, these algorithms can deal with large-scale biochemical reaction networks, too. Furthermore, one of the methods is able to deal with linearly conjugate networks.

In this paper we present a railway traffic model and a model predictive controller for online railway traffic management of railway networks with a periodic timetable. The main aim of the controller is to recover from delays in an optimal way by changing the departure of trains, by breaking connections, by splitting joined trains, and -in the case of multiple tracks between two stations -by redistributing the trains over the tracks. The railway system is described by a switching max-plus-linear model. We assume that measurements of current running and dwell times and estimates of future running times and dwell times are continuously available so that they can be taken into account in the optimization of the system's control variables. The switching max-plus-linear model railway model is used to determine optimal dispatching actions, based on the prediction of the future arrival and departure times of the trains, by recasting the dispatching problem as a Mixed Integer Linear Programming (MILP) problem and solving it. Moreover, we use properties from max-plus algebra to rewrite and reduce the model such that the MILP problem can be solved in less time. We also apply the algorithm to a model of the Dutch railway network.Keywords Max-plus algebra · Railway networks · Rescheduling · Model reduction · MILP B. Kersbergen ( ) · T. van den Boom · B. De Schutter

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