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This paper presents a continuum approximation model for the operating cost of demand responsive transit (DRT) systems in large urban networks. Applications of the proposed model shed light on ways demand and characteristics of the DRT system affect major components of cost: fleet, vehicle hours, and vehicle miles traveled. Verifying the relationship with empirical data, results show an accurate approximation of the operating cost for the paratransit system in New Jersey. Furthermore, we develop a systematic approach for evaluating the efficiency of policy implementations for DRTs. Finally, the circumstances where coordinated taxis could be a cost reduction strategy are identified.

Travelers consider the average duration and the reliability of travel time when choosing their route. However, the relative importance of average travel time and reliability not only depends on the purpose of the trip, but also varies from one person to another. Users seek to minimize their travel costs leading to an equilibrium condition in which they choose routes in such a way that they cannot reduce the general cost of their own trip. In this paper, we adopt the concept of the efficient frontier to represent the equilibrium route choice of the heterogeneous users in a network under travel time variability. Then, we use the primary properties of the efficient frontier to propose a mathematical formulation for the route choice problem for a discrete or continuous distribution of sensitivity of users to variations in route travel times. An analytical-based algorithm is designed to assign the heterogeneous demand to the network. Efficiency of the proposed algorithm in solving the route choice problem is also compared in a numerical example with a classic iterative method with a smoothing factor.

The land-use pattern for many cities is a central business district surrounded by sprawling suburbs. This pattern can lead to an inefficient and congestion-prone transportation system due to a reliance on automobiles. This is because high-capacity transit is inefficient in low-density areas where insufficient travelers can access transit. This also poses an equity concern as the monetary cost of faster and more expensive travel disproportionately burdens low income travelers, especially when fixed congestion pricing is imposed. This paper presents a deterministic approximation of a discrete choice model for mixed access and mainline transportation modes, meaning that travelers may use different modes to access a mainline system, such as transit. The purpose is to provide a tractable computationally efficient model to address the first/last mile problem using a system-wide pricing policy that can account for heterogeneous values of time; a problem that is difficult to solve efficiently using a stochastic model. The model is structured for a catchment area around a central access point for a mainline mode, approximating choice by comparing modal utility costs. The underlying utility model accommodates both fixed prices (e.g., parking, fixed tolls, and fares) and distance-based unit prices (e.g. taxi fare, bike-share, and distance tolls) that may be set in a coordinated way with respect to value of time. Using numerical analysis to assess accuracy, the deterministic model achieved results within 3% of a stochastic logit-based model, and within 7% of measured values. The optimization of prices using the final model achieved a 22% reduction in generalized travel time and a 30% improvement in the Gini inequity measure from 0.2 to 0.14.

The operating cost of a demand responsive transit (DRT) system strictly depends on the quality of service that it offers to its users. An operating agency seeks to minimize operating costs while maintaining the quality of service while users experience costs associated with scheduling, waiting, and traveling within the system. In this paper, an analytical model is employed to approximate the agency's operating cost for running a DRT system with dynamic demand and the total generalized cost that users experience as a result of the operating decisions. The approach makes use of Vickrey's (1969) congestion theory to model the dynamics of the DRT system in the equilibrium condition and approximate the generalized cost for users when the operating capacity is inadequate to serve the time-dependent demand over the peak period without excess delay. The efficiency of the DRT system can be improved by optimizing one of three parameters that define the agency's operating decision: (1) the operating capacity of the system, (2) the number of passengers that have requested a pick-up and are awaiting service, and (3) the distribution of requested times for service from the DRT system. A schedule management strategy and dynamic pricing strategies are presented that can be implemented to manage demand and reduce the total cost of the DRT system by keeping the number of waiting requests optimized over the peak period. In the end, proposed optimization strategies are compared using a numerical example.

Highlights • Measuring crowding through archived and real-time data using object detection tools. • Object detection tools with surveillance video to quantify transit performance. • Logistic regression models with automatic passenger counts and train operations data. • Estimation of left-behind passengers at stations with farecard use only at entrance. • Estimation and evaluation of waiting time as a transit service reliability measure., Crowding is one of the most common problems for public transportation systems worldwide, and extreme crowding can lead to passengers being left behind when they are unable to board the first arriving bus or train. This paper combines existing data sources with an emerging technology for object detection to estimate the number of passengers that are left behind on subway platforms. The methodology proposed in this study has been developed and applied to the subway in Boston, Massachusetts. Trains are not currently equipped with automated passenger counters, and farecard data is only collected on entry to the system. An analysis of crowding from inferred origin–destination data was used to identify stations with high likelihood of passengers being left behind during peak hours. Results from North Station during afternoon peak hours are presented here. Image processing and object detection software was used to count the number of passengers that were left behind on station platforms from surveillance video feeds. Automatically counted passengers and train operations data were used to develop logistic regression models that were calibrated to manual counts of left behind passengers on a typical weekday with normal operating conditions. The models were validated against manual counts of left behind passengers on a separate day with normal operations. The results show that by fusing passenger counts from video with train operations data, the number of passengers left behind during a day’s rush period can be estimated within 10% of their actual number.

Extensive theoretical research has been conducted on the morning commute problem building on the bottleneck model (Vickrey in Am Econ Rev 59(2):251–260, 1969). There have been far fewer studies assessing the bottleneck model and its extensions using real data. This paper presents an analysis of empirical data from the toll plaza of the San Francisco–Oakland Bay Bridge, which is a major regional bottleneck. The Bay Bridge transitioned from a constant toll to a peak step toll on July 1, 2010, so the site is well-suited for assessing many relevant extensions to the classic bottleneck model for the morning commute, including theories for congestion pricing. This paper uses traffic data from the Bay Bridge to address two areas of theoretical work on bottleneck congestion: (1) heterogeneous schedule preferences, and (2) equilibrium response to step tolls. The results suggest that the predicted equilibrium for the morning commute is consistent with observed traffic patterns, especially at the beginning of the rush. The data can be analyzed through the lens of relevant theories to quantify commuters’ value of earliness and lateness relative to queuing delay. The pattern of queuing suggests that the peak step toll has not been implemented in a socially optimal way.

Urban street networks exhibit hypercongested traffic states in which flow and speed drop as vehicles crowd the network. An important feature of aggregate traffic models based on the macroscopic fundamental diagram is that the dynamics of congestion are represented in a physically realistic way. For peak demand in a city in which all travelers use cars, hypercongested states are known to be unstable in equilibrium. In real cities travelers are able to choose whether to use cars or public transit during a peak period. This paper presents a model of the equilibrium for cars and transit, recognizing that hypercongestion often arises when modes are not priced. It is shown that hypercongested traffic can be part of a stable, steady equilibrium state when cars and high-capacity transit are used simultaneously. The paper also shows that coordinated fixed prices for cars and transit can always prevent hypercongested traffic states from developing.

Identifying the generators of paratransit trips by persons with disabilities is important to comprehend the current demand patterns and forecast future demand. Only a handful of studies have been conducted so far to identify the generators of paratransit trips and most focused on the home end of the trips. Given some of the inconsistencies in past studies and the scarcity of studies on the generators of trips away from home, this study attempts to identify the generators of paratransit trips beginning and ending at clients’ homes and away from home. It uses an extremely large dataset consisting of 1.91 million trips made by NJ TRANSIT’s Access Link clients, socioeconomic data from the American Community Survey, employment data from the Longitudinal Employer-Household Dynamics, and establishment data from Dun and Bradstreet. The analytical methods include an ordinary least squares model (OLS) and several spatial generalized linear mixed models (GLMM) to identify the characteristics of census block groups associated with Access Link trip generation at home and away from home, Geographic Information System (GIS) analysis to identify the types of establishments located in the immediate vicinity of drop-offs, and a multinomial logit model (MNL) to examine the relationship between the characteristics of the establishments in the vicinity of drop-offs and the characteristics of the dropped-off clients. Together, the various analyses provide useful insights about paratransit trip generators at the macro and micro levels. Some implications of the findings are discussed.

This paper extends Vickrey's (1969) commute problem for commuters wishing to pass a bottleneck for both cars and transit that share finite road capacity. In addition to this more general framework considering two modes, the paper focuses on the evening rush, when commuters travel from work to home. Commuters choose which mode to use and when to travel in order to minimize the generalized cost of their own trips, including queueing delay and penalties for deviation from a preferred schedule of arrival and departure to and from work. The user equilibrium for the isolated morning and evening commutes are shown to be asymmetric because the schedule penalty in the morning is the differ- ence between the departure and wished curves, and the schedule penalty in the evening is the difference between the arrival and wished curves. It is shown that the system optimum in the morning and evening peaks are symmetric because queueing delay is eliminated and the optimal arrival curves are the same as the departure curves. The paper then considers both the morning and evening peaks together for a single mode bottleneck (all cars) with identical travelers that share the same wished times. For a schedule penalty function of the morning departure and evening arrival times that is positive definite and has certain properties, a user equilibrium is shown to exist in which commuters travel in the same order in both peaks. The result is used to illustrate the user equilibrium for two cases: (i) commuters have decoupled schedule preferences in the morning and evening, and (ii) commuters must work a fixed shift length but have flexibility when to start. Finally, a special case is considered with cars and transit: commuters have the same wished order in the morning and evening peaks. Commuters must use the same mode in both directions, and the complete user equilibrium solution reveals the number of commuters using cars and transit and the period in the middle of each rush when transit is used.

This paper extends Vickrey's (1969) commute problem for commuters wishing to pass a bottleneck for both cars and transit that share finite road capacity. In addition to this more general framework considering two modes, the paper focuses on the evening rush, when commuters travel from work to home. Commuters choose which mode to use and when to travel in order to minimize the generalized cost of their own trips, including queueing delay and penalties for deviation from a preferred schedule of arrival and departure to and from work. The user equilibrium for the isolated morning and evening commutes are shown to be asymmetric because the schedule penalty in the morning is the difference between the departure and wished curves, and the schedule penalty in the evening is the difference between the arrival and wished curves. It is shown that the system optimum in the morning and evening peaks are symmetric because queueing delay is eliminated and the optimal arrival curves are the same as the departure curves. The paper then considers both the morning and evening peaks together for a single mode bottleneck (all cars) with identical travelers that share the same wished times. For a schedule penalty function of the morning departure and evening arrival times that is positive definite and has certain properties, a user equilibrium is shown to exist in which commuters travel in the same order in both peaks. The result is used to illustrate the user equilibrium for two cases: (i) commuters have decoupled schedule preferences in the morning and evening, and (ii) commuters must work a fixed shift length but have flexibility when to start. Finally, a special case is considered with cars and transit: commuters have the same wished order in the morning and evening peaks. Commuters must use the same mode in both directions, and the complete user equilibrium solution reveals the number of commuters using cars and transit and the period in the middle of each rush when transit is used.

The morning commute problem for a single bottleneck is extended to model mode choice in an urban area with time-dependent demand. This extension recognizes that street space is shared by cars and public transit. It is assumed that transit is operated independently of traffic conditions, and that when it is operated it consumes a fixed amount of space. As a first step, a single fixed-capacity bottleneck that can serve both cars and transit is studied. Commuters choose which mode to use and when to travel in order to minimize the generalized cost of their own trip. The transit agency chooses the headway and when to operate. Transit operations reduce the bottleneck’s capacity for cars by a fixed amount. The following results are shown for this type of bottleneck: 1. If the transit agency charges a fixed fare and operates at a given headway, and only when there is demand, then there is a unique user equilibrium. 2. If the transit agency chooses its headway and time of operation for the common good, then there is a unique system optimum. 3. Time-dependent prices exist to achieve system optimum. Finally, it is also shown that results 2 and 3 apply to urban networks.

A model with few variables is said to be parsimonious. If it is also analytically tractable, physically realistic, and conceptually insightful, it is said to be effective. Effective parsimonious models have long been used in fields such as economics and applied physics to describe the aggregate behavior of systems as opposed to the behavior of their individual parts. In transportation, these models are particularly well suited to address big picture questions because they provide insights that might be lost when focusing on details. This paper presents an abbreviated history of effective parsimonious models in the transportation field, classified by sub-area: regional and urban economics, traffic flow, queuing theory, network dynamics, town planning, public transportation, logistics, and infrastructure management. The paper also discusses the benefits of these models—fewer data requirements, reduced computational complexity, improved system representation, insightfulness—and ways of constructing them. Two examples, one from logistics and one from urban transportation, are used to illustrate these points. Finally, the paper discusses ways of expanding the application of effective parsimonious models in the transportation field.

Recent experimental work has shown that the average flow and average density within certain urban networks are related by a unique, reproducible curve known as the Macroscopic Fundamental Diagram (MFD). For networks consisting of a single route this MFD can be predicted analytically; but when the networks consist of multiple overlapping routes experience shows that the flows observed in congestion for a given density are less than those one would predict if the routes were homogeneously congested and did not overlap. These types of networks also tend to jam at densities that are only a fraction of their routes’ average jam density. This paper provides an explanation for these phenomena. It shows that, even for perfectly homogeneous networks with spatially uniform travel patterns, symmetric equilibrium patterns with equal flows and densities across all links are unstable if the average network density is sufficiently high. Instead, the stable equilibrium patterns are asymmetric. For this reason the networks jam at lower densities and exhibit lower flows than one would predict if traffic was evenly distributed. Analysis of small idealized networks that can be treated as simple dynamical systems shows that these networks undergo a bifurcation at a network-specific critical density such that for lower densities the MFDs have predictably high flows and are univalued, and for higher densities the order breaks down. Microsimulations show that this bifurcation also manifests itself in large symmetric networks. In this case though, the bifurcation is more pernicious: once the network density exceeds the critical value, the stable state is one of complete gridlock with zero flow. It is therefore important to ensure in real-world applications that a network’s density never be allowed to approach this critical value. Fortunately, analysis shows that the bifurcation’s critical density increases considerably if some of the drivers choose their routes adaptively in response to traffic conditions. So far, for networks with adaptive drivers, bifurcations have only been observed in simulations, but not (yet) in real life. This could be because real drivers are more adaptive than simulated drivers and/or because the observed real networks were not sufficiently congested.

In this research, we develop an optimal credit-based pricing scheme for a single bottleneck with time-dependent demand and heterogeneous user preferences. For this purpose, we first propose an analytical model for dynamically pricing the bottleneck. Accounting for the independent distributions of the schedule penalty factors and the value of time of the commuters can significantly improve the accuracy of the pricing strategy. Moreover, implementing such a strategy using a revenue-neutral credit-based pricing scheme allows the value of the credits to be determined by the interaction between the users in the equilibrium condition of the market. Hence, there would be no need to charge all commuters over the peak period. Instead, the proposed strategy allocates the money raised from the “credit buyers” to subsidize the commutes of the “credit sellers” in order to incentivize the commuters to form a uniform distribution of arrival times over the peak period. Using tradable credits to design a revenue-neutral pricing strategy for the bottleneck can raise public support by improving the social welfare of the users. The proposed credit-based pricing strategy also have broad applications for optimizing the urban networks using the concept of the macroscopic fundamental diagram (see Amirgholy et al., 2017).