Models of Transit Systems for Optimization of the Grounded Vehicles Fleet

In order to operate a public transportation system, it is necessary to plan the grounded fleet lines among the various origin/destination spread all over the city to better attend population displacement during the day, which uses the bus transportation system. To improve planning operation of the public transportation system, it is proposed a linear programming model to optimize the overall performance of transit systems, by setting the optimum buses fleet for every bus line of each company constrained to an accepted delay between any two bus stop on the bus circuit but with a minimum profit for the companies. As the routes are different for time to time during the day such as rush hour. The proposed model can cope with all the kinds of patterns during the day and the propose is to optimise the whole transportation system. It is discussed also the complexity of the nature of the dynamic of the transportation system. The mathematical modelling can show us correctly a way to qualify and quantify the routes, what helps to understand the dynamic behavior of the population through time, different situations and epochs. Simulations present the viability of implantation for real time system to estimate the transportation system as it changes.