Online Problems in Timetabling: Bus Priority at signalised junctions

The aim of this study is to create and study a model, using Matlab, to solve the problem of prioritising delayed buses at signalised junctions; in particular, we discuss an on-line algorithm that adjusts the traffic lights of a certain city crossroads in such a way that the waiting times of delayed buses are reduced. Hence the objective is the study of on-line problems in timetabling, where the timetable is updated repeatedly following the repeated revelation of uncertainty, where a finite number of such recourse actions are evaluated over a finite horizon, while considering the distance from the previously announced timetable. Dynamic Programming is used to solve the problem under consideration. It consists in breaking down the problem into a collection of simpler subproblems, solving each of them just once in inverse temporal order, and storing their solutions. Then the algorithm examines the previously solved subproblems and combines their solutions to give the best one. In particular, the strategy consists in computing a solution for all the possible distributions of cars and buses in the network. After that, reality is observed and the optimal traffic lights configuration computed in the previous step is chosen. In order to realize the first step a Bellman type equation is solved going backward in time. Then the path is chosen in a forward way waiting for the revelation of reality. Finally, an interactive platform is created in order to manage the obtained solutions.