Determination of efficient frontiers for urban public transport system configurations
Authors:   , Basnak Klajn Paul Alexander 
Published: November 2023

One of the fundamental aspects when planning an urban public transport system is to define which modes provide the greatest benefit both for the city residents and for the system operators. Two relevant questions arise from this: What characteristics of cities and their people are relevant to define these modes? What are the efficiency frontiers – that is, the minimum and maximum values of these relevant characteristics – for the different modal configurations that an urban public transport system should have? The available literature addresses these questions through recommendations based on existing systems and mathematical optimization models. However, recommendations based on existing systems are often limited to simple criteria based on the population of cities an the income of their residents, which ignores the relevance of other factors explaining public transport trips in lines or networks. For their part, optimization models have been widely used to define the ideal fundamental characteristics that a given transport service or network should have, such as frequency, density of lines and distance between stops, but they usually lack in linking the real characteristics of cities with the transport technologies that allow minimizing total costs. In addition, there are no known systematic efforts to link both mentioned approaches, considering the behaviour of people in their mode choice. The general objective of this research is to develop classification and optimization models to recommend which public transport modes a city should have according to their basic characteristics. Moreover, the proposed models are applied in simple representations of cities with low-capacity modes and in transit lines with high-capacity modes. Based on this general aim, the main objectives are the following: a) Estimate aggregate classification models at the city level to determine which geographic and socioeconomic factors of cities and their residents define the existing modal supply in their public transport systems. b) Provide recommendations about the set of modes to be used in cities below 200,000 inhabitants, by applying social cost minimization models in simplified representations of such cities. c) Propose improved demand thresholds that set the recommendation between high-capacity modes (bus, Bus Rapid Transit [BRT], Metro) through optimization models in transit lines. To achieve this objective, a stated preference study was first performed, which allowed for improving the perception of the penalty for crowding in public transport vehicles. Once these valuations were obtained, cost minimization models were applied in corridors to update the demand thresholds to allow a better selection of the most efficient technology. In conclusion, we identified common determinants of higher capacity transit modes in cities, both for the existing and recommended systems, such as a higher population, income, and linear form. From the onset of COVID-19, users were found to penalize traveling in crowded transit vehicles with non-linear functions increasing with density of passengers in the vehicle and the proportion of users not wearing facemasks. When applying these valuations to line optimization models, the minimum demand that justifies building a BRT over a standard bus line is reduced when facemask use compliance is lower, and directionality of demand is less significant than if pre-pandemic values were used.