Mathematical model to set frequencies on a massive public transport system

Abstract

This paper proposes a mathematical model to estimate the frequency setting of the buses for a specific route on any given hour in public transportation systems. This model can be used for four different purposes: determine how many buses a route needs to fully satisfy its demand, estimate an optimal bus frequency to satisfy the maximum amount of demand when the number of buses is fixed, estimate an optimal bus frequency to satisfy a given percentage of demand and define how much buses would it take on an specific route to reach a provided average waiting time. It receives three entries: number of buses assigned to the route, which can vary or not depends on its purpose, the latitude and longitude of the route’s initial and final point and the route’s demand. A series of equations are proposed using a heuristic method, which allows calculating the frequency of a route at any given hour of the day and, using this, define all the different uses exposed previously. A use case experiment is applied to help understand how to use the model on it’s different suggested uses. Additionally, exposes how the proposed model could improve an actual one. The results of this experiment case showed that the demand could be fulfilled using one of this model’s cases.