Modelling and Optimization of Commuter Flows as Queuing System Considering Customer and Environmental Costs: a Case Study

Passenger flows in transportation systems need to be controlled in such a way that costs are minimized. To be able to do it, discrete event systems can be used for the first model and then optimize in transportation systems. Queuing systems in particular are often the means of choice to model transportation systems in order to minimize costs. In the past, the focus has been on minimizing customer or supplier costs. In this paper, the theory of queuing systems is applied to model commuter flows between a fixed origin and destination, considering the L-BFGS-B optimization algorithm. It is known that limited-memory BFGS (L-BFGS or LM-BFGS) is an optimization algorithm in the family of quasi-Newton methods and that the L-BFGS-B algorithm extends L-BFGS to handle simple box constraints variables. Due to climate change, environmental factors are increasingly important, which is why not only customer costs but also environmental costs are considered in the novel model, presented in this paper.