Towards a general microeconomic model for the operation of public transport (original) (raw)
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The interplay between congestion and crowding externalities in the design of urban bus systems is identified and analysed. A multimodal social welfare maximisation model with spatially disaggregated demand is developed, in which users choose between travelling by bus, car or walking in a transport corridor. Optimisation variables are bus fare, congestion toll, bus frequency, bus size, fare collection system, bus boarding policy and the number of seats inside buses. We find that optimal bus frequency results from a trade-off between the level of congestion inside buses, i.e., passengers' crowding, and the level of congestion outside buses, i.e., the effect of frequency on slowing down both buses and cars in mixed-traffic roads. A numerical application shows that optimal frequency is quite sensitive to the assumptions on crowding costs, impact of buses on traffic congestion, and overall congestion level. If crowding matters to users, buses should have as many seats as possible, up to a minimum area that must be left free of seats. If for any other reason planners decide to have buses with fewer seats than optimal (e.g., to increase bus capacity), frequency should be increased to compensate for the discomfort imposed on public transport users. Finally, the consideration of crowding externalities (on both seating and standing) imposes a sizeable increase in the optimal bus fare, and consequently, a reduction of the optimal bus subsidy.
Accounting for travel time variability in the optimal pricing of cars and buses
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A number of studies have shown that in addition to the common influences on mode, route and time of day of travel choices such as travel time and cost, travel time variability plays an increasingly important role, especially in the presence of traffic congestion on roads and crowding on public transport. The dominant focus of modelling and implementation of optimal pricing that incorporates trip time variability has been in the context of road pricing for cars. The main objective of this paper is to introduce a non-trivial extension to the existing literature on optimal pricing in a multimodal setting, building in the role of travel time variability as a source of disutility for car and bus users. We estimate the effect of variability in travel time and bus headway on optimal prices (i.e., tolls for cars and fares for buses) and optimal bus capacity (i.e., frequencies and size) accounting for crowding on buses, under a social welfare maximisation framework. Travel time variability is included by adopting the well-known mean-variance model, using an empirical relationship between the mean and standard deviation of travel times. We illustrate our model with an application to a highly congested corridor with cars and buses as travel alternatives in Sydney, Australia. There are three main findings that have immediate policy implications: (i) including travel time variability results in higher optimal car tolls and substantial increases in toll revenue, while optimal bus fares remain almost unchanged; (ii) when bus headways are variable, the inclusion of travel time variability as a source of disutility for users yields higher optimal bus frequencies; and (iii) including both travel time variability and crowding discomfort leads to higher optimal bus sizes.
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European Transport Conference, 2003
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This paper presents the optimization problem of three different on-demand transit systems operated by vehicles of different sizes. This problem is aimed at minimizing the total cost of the system, which consists of the temporal cost experienced by users and the operating cost incurred by transit agencies. A compact set of estimations of the user performance and operating cost is provided, based on geometric probability. The optimization procedure allows the cost comparison of different semi-flexible services. Transit systems operated by cars (shared taxicabs) with flexible layouts are preferable for low demand densities (less than 92 pax/km 2-h). For very high demand (higher than 200 pax/km 2-h), bus systems with fixed layout and variable stop locations present the lowest total cost per passenger. In an intermediate domain, taxi and semiflexible services compete among each other. The estimation of unit operating costs allows decision-makers to calculate the subsidies needed to make the system profitable.
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Research in Transportation Economics, 2019
This paper analyses the interaction between fares and public transport service quality. With higher fares the operator has more resources to provide a better service, while demand in turn depends on both service quality and fare leading therefore to the question as to whether there is an optimal fare for different city scales. The model builds on the work of Daganzo (2010) who determines optimal network headway, stop spacing as well as the ratio of a central dense service area compared to the whole city size. In contrast to Daganzo we include fare and demand elasticity. With this it is possible to obtain some general insights for a range of cities on what type of fare levels are favorable. We focus on a flat fare structure, finding that from the viewpoint of maximizing social welfare, lower fares are preferable. If the operator cost coverage ratio is considered as objective function then there exists an optimal fare above the minimum fare. We illustrate the possible existence of critical fare points, at which the demand and service quality of public transport suddenly drop if an attractive alternative mode exists. We discuss further the impact of city size and demand density on optimal fares and service quality.