A Pareto-improving and revenue-neutral scheme to manage mass transit congestion with heterogeneous commuters☆
Introduction
Demand for public transportation is growing faster than transit capacity in many metropolises. Mass transit operators are thus facing the significant challenge of managing peak-hour demand and overcrowding. When passenger density is low and everyone can board the first arriving train, the expected usual waiting time at a station is approximately half the headway of the service. However, during peak hours, the high occupancy of trains with limited capacity results in on-platform queueing and passenger discomfort. Oldfield and Bly (1988) discussed the effects of bus occupancy and frequency on average waiting time if passengers failed to board the first bus. In Beijing’s subway system, 47% of daily trips are made in peak hours and some lines are overloaded and extremely crowded; the queueing time at the station platform is estimated to be up to 25 minutes. Crowding control measures are implemented at 96 entry stations, about 30% overall (China Intelligent Transportation System Association, 2018). The peak-hour congestion has negative effects on both transit operators and users which decreases the stability and reliability of transit services, and reduces user satisfaction.
Policymakers are now giving increasing consideration to the peak-hour congestions and demand management strategies which take two main forms: increasing the service supply and reducing travel demand at peak times. Increasing the service supply is often done through adjusting the service frequency to accommodate variable passenger demand. These adjustments affect both service capacity and passenger waiting time (service quality). Notably, applying the bottleneck model (Vickrey, 1969, Arnott et al., 1990) to mass transit, Kraus and Yoshida (2002) determined the optimal fares and service frequency for minimizing long-term system costs. On the other hand, reducing peak demand is often done through fare differentials to spread demand, which may involve peak-fare charging, off-peak discounting and combinations of the above (Liu and Charles, 2013, Lehe, 2019). Halvorsen et al. (2016) investigated the Early Bird discount promotion on Hong Kong’s MTR system that prevented peak hour ridership from growing much. However, off-peak discounts or free fare strategies come at the expense of the government or transit operator. Due to their limited sources in funding, governments and transit operators would rather charge passenger high fares than to lose revenue which can raise issues of equity and customer acceptability. Adding a surcharge to travel in peak periods is rarely seen as acceptable by users, particularly as those who work in lower-paid jobs (Faber Maunsell Ltd., 2007).
With regard to the efficiency and public acceptability, it is therefore important to explore alternatives and more acceptable congestion management strategies. Such proposals have been explored for road traffic in theory and in practice. One direction is the tradable credit or permits schemes in the static equilibrium model as well as in the dynamic bottleneck model (Yang and Wang, 2011, Nie and Yin, 2013, Akamatsu and Wada, 2017). Another idea focuses on the charges in combinations of the rewards, subsidies or refunding such as the theoretical analysis on the pareto-improving toll strategies (Daganzo and Garcia, 2000, Lawphongpanich and Yin, 2010), pricing and revenue-refunding (Guo and Yang, 2010, Rouwendal et al., 2012), and the recent congestion pricing and incentives in e-hailing and ridesharing market (Angelopoulos et al., 2018, He et al., 2018).
While combined strategies for demand management in road traffic is well researched, its investigations and applications for mass transit system are still emerging. One reason is that the behaviors of mass transit travelers are affected by service such as the fare costs and the timetables. Besides, the revenue and costs can be an important aspect to influence transit operator’s willingness to implement the congestion management strategies. Among the few existing studies on combined strategies in public transport system, Whelan and Johnson (2004) showed that a combined strategy of increased peak fares and reduced off-peak fares have a larger effect than just a single policy. Douglas et al. (2011) further simulated passenger assignment under different fares and found that the combination of discount and surcharge was the most effective one to reduce peak loads. Different from the anonymous fare strategies, Yang and Tang (2018) proposed an individual-based fare-reward scheme (FRS) with homogeneous commuters in which a commuter is rewarded with one free trip during pre-specified shoulder periods after taking a certain number of paid trips during the peak hours. The theoretical analysis demonstrated the effective reduction of the time costs depending on the original fares. Previous studies opened various avenues for further research on the combined strategies for demand management in public transport system. With the fast population and spatial growth in many mature cities, such demand management strategies become increasingly concerned and important.
In this paper, we consider the continuous heterogeneity in commuters’ scheduling flexibility and propose an incentive-based hybrid fare scheme (HFS) with a revenue-neutral property. The HFS combines the fare-reward scheme (H-FRS) with a non-rewarding uniform fare scheme (H-UFS). In the FRS originally proposed by Yang and Tang (2018), commuters need to occasionally change their scheduling decisions (departure times or arrival times) to make use of their free rides. This may not be acceptable by all users, because some users tend to have less flexibility in their departure times.
The HFS provides a more flexible and acceptable design to various users having different scheduling flexibility. The scheduling flexibility is defined as an arrival time flexibility interval (or departure time flexibility interval by the first-in first-out principle). The value of time for traveling outside one’s arrival time flexibility interval (ATFI) is greater than traveling inside the ATFI. Hence the length of the ATFI represents a commuter’s scheduling flexibility as a commuter prefers to travel inside the ATFI because of the lower schedule delay penalty. Commuters will join either scheme according to the design of the H-FRS and the H-UFS, and their ATFIs. The HFS will differentiate and determine the fares for paid rides under the H-FRS and the fares for the H-UFS to ensure equity and flexibility while preserving the operator’s revenue. In addition, the fare differentials will be selected to incentivize commuters with flexible scheduling decisions to join the H-FRS. Commuters who voluntarily continue to use the H-UFS may need to pay a marginally higher fare each time (to maintain the operator’s revenue) than before, but they are still better off with the hybrid scheme due to the overall improvement (reduced queuing time costs and thus reduced individual trip costs in peak-hour transit services).
This paper is organized as follows. Section 2 describes the mathematical formulation of the heterogeneity of commuter’s ATFI and introduces the framework of the urban rail transit bottleneck with batch arrivals at stations and the problem of departure time equilibrium with heterogeneous commuters under a uniform fare. Section 3 investigates the equilibrium solution and its properties of the HFS model within the framework of the transit bottleneck. Section 4 assesses the system performance and conducts sensitivity analysis of the HFS in comparison with the original bottleneck. Conclusions and recommendations for further development and implementations are provided in Section 5.
Section snippets
Commuter’s scheduling flexibility and the arrival time flexibility interval
Following investigations of departure times (Vickrey, 1969, Small, 1982), various empirical studies have been conducted on scheduling decision (departure times or arrival times) and the flexibility of commuters. It is found in the behavioral survey in Seattle that commuter’s departure time changes were affected by the length of the travel time and work schedule flexibility, where 62.6% of commuters have at least some flexibility in departure times in home-to-work trips, within which 20.9% of
Basic considerations and design criteria
The hybrid fare scheme (HFS) consists of a fare-reward scheme (H-FRS) and a non-rewarding uniform fare scheme (H-UFS). Commuters have opportunity to join either scheme according to their arrival time flexibility interval (ATFI).
In the H-FRS, a commuter will be rewarded with one free ride during a pre-specified shoulder peak interval after taking a certain number of paid trips at a new fare during the period central to peak hours. Implementation of the H-FRS changes the original uniform fare
Performance of the hybrid fare scheme
The hybrid fare scheme affects the system total time costs and the individual equilibrium trip costs. To assess the performance of the hybrid fare scheme, we introduce the following set of performance measures, and conduct sensitivity analysis of the performance with respect to the exogenous system settings.
The absolute reduction of the system total time costs (TTC) at the optimal FFI ratio is defined as
The absolute reduction of the individual average equilibrium costs (AEC) at
Conclusions
The hybrid fare scheme (HFS) developed in this paper is incentive compatible and balances the competing claims of efficiency, simplicity and fairness. It captures the heterogeneity in commuter’s scheduling flexibility and provides diverse options for commuters with a fare-reward scheme (H-FRS) and a non-rewarding uniform fare scheme (H-UFS). Commuters have the opportunity to join either scheme according to their flexibility in scheduling decisions. The hybrid fare scheme is an individual-based
Acknowledgements
The authors wish to express their thanks to editors and three anonymous reviewers, whose useful comments have improved the exposition of the study. This research was supported by a grant from the Hong Kong’s Research Grants Council (HKUST16211218) and a grant from National Natural Science Foundation of China (71890974/71890970). The first author also wishes to acknowledge the support of the Hong Kong PhD Fellowship Scheme by Hong Kong’s Research Grants Council.
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This paper has been accepted for a podium presentation at the 23rd International Symposium on Transportation and Traffic Theory (ISTTT23) July 24–26, 2019 in Lausanne, CH.