Eric J. Gonzales

The potential of parsimonious models for understanding large scale transportation systems and answering big picture questions

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.

Modeling Taxi Trip Demand by Time of Day in New York City

Identifying the factors that influence taxi demand is very important for understanding where and when people use taxis. A large set of GPS data from New York City taxis is used along with demographic, socioeconomic, and employment data to identify the factors that drive taxi demand. A technique was developed to measure and map transit accessibility on the basis of transit access time (TAT) to understand the relationship between taxi use and transit service. The taxi data were categorized by pickups and drop-offs at different times of day. A multiple linear regression model was estimated for each hour of the day to model pickups and another to model drop-offs. Six important explanatory variables that influence taxi trips were identified: population, education, age, income, TAT, and employment. The influence of these factors on taxi pickups and drop-offs changed at different times of the day. The number of jobs in each industry sector was an indication of the types of economic activities occurring at a location, and in some sectors the number of jobs were strongly associated with taxi use. This study demonstrates the temporal and spatial variation of taxi demand and shows how transit accessibility and other factors affect it.

On the allocation of city space to multiple transport modes

Abstract This paper analyzes urban multimodal transportation systems in an aggregated way. To describe the aggregate behavior of traffic in cities, use is made of an idea that is now receiving some attention: the macroscopic fundamental diagram (MFD). We demonstrate through simulation how the MFD can be used to monitor and control a real network, in this case a portion of San Francisco, using readily available input data. We then show how different modes interact on the same network and discuss how these interactions might be incorporated into an MFD for multimodal networks. The work unveils two main results: first, it confirms recent results showing that restricting access to a citys congested areas can improve mobility for all travelers, including those who endure the restrictions; and second, that dedicating street space to collective transport modes can improve accessibility for all modes, even those from which space is taken away.

Analytical equilibrium of bicriterion choices with heterogeneous user preferences: application to the morning commute problem

ABSTRACT The morning commute problem, introduced in Vickrey [1969. “Congestion Theory and Transport Investment.” American Economic Review 56: 251–260], addresses the equilibrium trip schedule of the users for commuting through a single bottleneck with fixed capacity over the morning peak. In this paper, we adapt the concept of the efficient frontier from Portfolio Theory [Markowitz, H. 1952. “Portfolio Selection.” The Journal of Finance 7 (1): 77–91] to propose an analytical solution to the morning commute problem with a general distribution of the schedule preferences over time and a continuous joint distribution of schedule penalty preferences over the population of the commuters. On this basis, we analytically derive the equilibrium arrivals of the heterogeneous commuters to the bottleneck given the independent probability distributions of earliness and lateness penalty factors. We also propose a method to retrieve independent probability distributions of the schedule penalty factors in the equilibrium condition from a joint distribution. The proposed model can be inversely used to approximate the independent distribution of schedule penalty preferences of the user for the early and late commuters using empirical arrival time data from the network. The result is also used to propose a dynamic pricing strategy to optimize the system by avoiding the formation of a queue, which can also be extended to design a dynamic pricing strategy on the network level using the macroscopic fundamental diagram (MFD). To provide an example, the approach is employed to derive a closed-form solution when the probability distribution of the preferences is uniform. A numerical example is also presented using the proposed model to compare the solutions for different distributions of the schedule deviation penalty preferences.

Modeling Taxi Demand and Supply in New York City Using Large-Scale Taxi GPS Data

Data from taxicabs equipped with Global Positioning Systems (GPS) are collected by many transportation agencies, including the Taxi and Limousine Commission in New York City. The raw data sets are too large and complex to analyze directly with many conventional tools, but when the big data are appropriately processed and integrated with Geographic Information Systems (GIS), sophisticated demand models and visualizations of vehicle movements can be developed. These models are useful for providing insights about the nature of travel demand as well as the performance of the street network and the fleet of vehicles that use it. This paper demonstrates how big data collected from GPS in taxicabs can be used to model taxi demand and supply, using 10 months of taxi trip records from New York City. The resulting count models are used to identify locations and times of day when there is a mismatch between the availability of taxicabs and the demand for taxi service in the city. The findings are useful for making decisions about how to regulate and manage the fleet of taxicabs and other transportation systems in New York City.

Comparison of Mode Cost by Time of Day for Nondriving Airport Trips to and from New York City's Pennsylvania Station

A novel methodology used taxi global position system data and high-resolution transit schedule information to compare travel times and travel fares of the two main nondriving travel modes for airport ground access: taxi and transit. Five origin–destination pairs between Pennsylvania Station in New York City and three airports in the New York region were used as an example to demonstrate these methods. An analysis of total trip cost considered both travel time and expenditures on fare. A binary logit model was used to model the mode choice of travelers. The results indicate that transit is the more likely choice during most of the day except the midnight period when transit service has longer headways. A sensitivity analysis shows the relationship between the value of time and total trip cost per passenger for different numbers of passengers traveling together and at different times of day. The higher the value of time and the number of passengers in a group, the more likely it is that a taxi is chosen for airport trips. The attractiveness of one mode relative to the other varies spatially and temporally according to the travel time and price. This paper focuses on understanding temporal variation of total cost of each mode and the effect that this variation is likely to have on mode share.

Empirical assessment of bottleneck congestion with a constant and peak toll: San Francisco–Oakland Bay Bridge

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.

The Evening Commute with Cars and Transit: Duality Results and User Equilibrium for the Combined Morning and Evening Peaks

Abstract This paper extends Vickreys (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.

Evaluating Potential Demand and Operational Effects of Coordinated Americans with Disabilities Act Paratransit and Taxi Service

This paper presents an evaluation of the potential implications of using taxis along with conventional paratransit to serve customers eligible for demand responsive service through the Americans with Disabilities Act (ADA). Subsidizing a taxi service to carry some paratransit demand could potentially reduce the total cost of the service if diverted trips are inexpensive to serve by taxi and the remaining paratransit operations remain efficient. This study makes use of ADA paratransit operations and demand data from the Pioneer Valley Transit Authority (PVTA) in the greater Springfield, Massachusetts, region to develop an algorithm for optimally allocating paratransit demand to conventional paratransit services and taxis. First, a model is presented to optimize the spatial extent of the ADA paratransit service area, assuming that all trips outside the service region can be incentivized to use taxis. A more detailed investigation makes use of survey data from PVTA to estimate which trips could potentially be diverted to taxis or transportation network companies (TNCs) based on the type of disability that a customer has. The result is a model that shows which trips could be incentivized to switch to taxi and the magnitude of total operating cost savings that may be achieved from such a program.

Real-time signal control accounting for urban freight deliveries

Freight vehicles often block lanes of traffic on signalized arterials when double-parking to make deliveries in urban areas. When delivery vehicles block lanes of traffic near signalized intersections, the capacity of the intersection is affected. Current practice is for traffic signals to be timed assuming that each approach can serve vehicles at the unobstructed saturation flow. This paper presents a model for adapting the traffic signal timing in real time for signal cycles during which a delivery blocks a link upstream of the intersection. The model requires real-time information about the location of the double-parked delivery vehicle, which is assumed to be available from connected vehicle data from urban freight vehicles or from another detection system. The results show that for low levels of traffic demand, the signal control method reduces intersection delay compared to a signal that is timed for unblocked traffic. The algorithm also keeps the intersection approach undersaturated for higher levels of demand, which is important because deliveries can last for many signal cycles.