Bounded rationality and irreversible network change

A network change is said to be irreversible if the initial network equilibrium cannot be restored by revoking the change. The phenomenon of irreversible network change has been observed in reality. To model this phenomenon, we develop a day-to-day dynamic model whose fixed point is a boundedly rational user equilibrium (BRUE) flow. Our BRUE based approach to modeling irreversible network change has two advantages over other methods based on Wardrop user equilibrium (UE) or stochastic user equilibrium (SUE). First, the existence of multiple network equilibria is necessary for modeling irreversible network change. Unlike UE or SUE, the BRUE multiple equilibria do not rely on non-separable link cost functions, which makes our model applicable to real-world large-scale networks, where well-calibrated non-separable link cost functions are generally not available. Second, travelers’ boundedly rational behavior in route choice is explicitly considered in our model. The proposed model is applied to the Twin Cities network to model the flow evolution during the collapse and reopening of the I-35 W Bridge. The results show that our model can to a reasonable level reproduce the observed phenomenon of irreversible network change.     

The traffic and behavioral effects of the I-35W Mississippi River bridge collapse

On August 1, 2007, the collapse of the I-35W bridge over the Mississippi River in Minneapolis abruptly interrupted the usual route of about 140,000 daily vehicle trips, which substantially disturbed regular traffic flow patterns on the network. It took several weeks for the network to re-equilibrate, during which period travelers continued to learn and adjust their travel decisions. A good understanding of this process is crucial for traffic management and the design of mitigation schemes. Data from loop-detectors, bus ridership statistics, and a survey are analyzed and compared, revealing the evolving traffic reactions to the bridge collapse and how individual choices could help to explain such dynamics. Findings on short-term traffic dynamics and behavioral reactions to this major network disruption have important implications for traffic management in response to future scenarios.     

Network-wide adaptive tolling for connected and automated vehicles

This article proposes Δ-tolling, a simple adaptive pricing scheme which only requires travel time observations and two tuning parameters. These tolls are applied throughout a road network, and can be updated as frequently as travel time observations are made. Notably, Δ-tolling does not require any details of the traffic flow or travel demand models other than travel time observations, rendering it easy to apply in real-time. The flexibility of this tolling scheme is demonstrated in three specific traffic modeling contexts with varying traffic flow and user behavior assumptions: a day-to-day pricing model using static network equilibrium with link delay functions; a within-day adaptive pricing model using the cell transmission model and dynamic routing of vehicles; and a microsimulation of reservation-based intersection control for connected and autonomous vehicles with myopic routing. In all cases, Δ-tolling produces significant benefits over the no-toll case, measured in terms of average travel time and social welfare, while only requiring two parameters to be tuned. Some optimality results are also given for the special case of the static network equilibrium model with BPR-style delay functions.     

Multi-step prediction of experienced travel times using agent-based modeling

This paper develops an agent-based modeling approach to predict multi-step ahead experienced travel times using real-time and historical spatiotemporal traffic data. At the microscopic level, each agent represents an expert in a decision-making system. Each expert predicts the travel time for each time interval according to experiences from a historical dataset. A set of agent interactions is developed to preserve agents that correspond to traffic patterns similar to the real-time measurements and replace invalid agents or agents associated with negligible weights with new agents. Consequently, the aggregation of each agent’s recommendation (predicted travel time with associated weight) provides a macroscopic level of output, namely the predicted travel time distribution. Probe vehicle data from a 95-mile freeway stretch along I-64 and I-264 are used to test different predictors. The results show that the agent-based modeling approach produces the least prediction error compared to other state-of-the-practice and state-of-the-art methods (instantaneous travel time, historical average and k-nearest neighbor), and maintains less than a 9% prediction error for trip departures up to 60 min into the future for a two-hour trip. Moreover, the confidence boundaries of the predicted travel times demonstrate that the proposed approach also provides high accuracy in predicting travel time confidence intervals. Finally, the proposed approach does not require offline training thus making it easily transferable to other locations and the fast algorithm computation allows the proposed approach to be implemented in real-time applications in Traffic Management Centers.     

A Pareto-optimization approach for a fair ramp metering

This paper deals with a fair ramp metering problem which takes into account average travel delay distribution among on-ramps for an expressway system comprising expressways, on-ramps and off-ramps. A novel spatial equity index is defined to measure the evenness of travel delay distribution among on-ramps within the predefined on-ramp groups. An ideal fair ramp metering problem therefore aims to find an optimal dynamic ramp metering rate solution that not only minimizes the total system delay, but also maximizes the equity indexes associated to the groups. Some of these objectives, however, contradict with each other, and their Pareto-optimality is explored. The fair ramp metering problem proposed in this paper is formulated as a multiobjective optimization model incorporating a modified cell-transmission model (MCTM) that captures dynamic traffic flow pattern with ramp metering operations. The MCTM then is embedded in the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to solve the multiobjective optimization model. Finally, the Interstate I-210 W expressway-ramp network in the United States is adopted to assess the methodology proposed in this paper.     

Urban traffic state estimation: Fusing point and zone based data

Loop detectors are the oldest and widely used traffic data source. On urban arterials, they are mainly installed for signal control. Recently state-of-the art Bluetooth MAC Scanners (BMS) has significantly captured the interest of stakeholders for exploiting it for area-wide traffic monitoring. Loop detectors provide flow – a fundamental traffic parameter; whereas BMS provides individual vehicle travel time between BMS stations. Hence, these two data sources complement each other, and if integrated should increase the accuracy and reliability of the traffic state estimation.This paper proposed a model that integrates loops and BMS data for seamless travel time and density estimation for urban signalised network. The proposed model is validated using both real and simulated data and the results indicate that the accuracy of the proposed model is over 90%.     

Modeling stochastic perception error in the mean-excess traffic equilibrium model

In this paper, we extend the α-reliable mean-excess traffic equilibrium (METE) model of Chen and Zhou (Transportation Research Part B 44(4), 2010, 493-513) by explicitly modeling the stochastic perception errors within the travelers’ route choice decision processes. In the METE model, each traveler not only considers a travel time budget for ensuring on-time arrival at a confidence level α, but also accounts for the impact of encountering worse travel times in the (1 − α) quantile of the distribution tail. Furthermore, due to the imperfect knowledge of the travel time variability particularly in congested networks without advanced traveler information systems, the travelers’ route choice decisions are based on the perceived travel time distribution rather than the actual travel time distribution. In order to compute the perceived mean-excess travel time, an approximation method based on moment analysis is developed. It involves using the conditional moment generation function to derive the perceived link travel time, the Cornish-Fisher Asymptotic Expansion to estimate the perceived travel time budget, and the Acerbi and Tasche Approximation to estimate the perceived mean-excess travel time. The proposed stochastic mean-excess traffic equilibrium (SMETE) model is formulated as a variational inequality (VI) problem, and solved by a route-based solution algorithm with the use of the modified alternating direction method. Numerical examples are also provided to illustrate the application of the proposed SMETE model and solution method.     

A finite mixture model of vehicle-to-vehicle and day-to-day variability of traffic network travel times

This study proposes an approach to modeling the effects of daily roadway conditions on travel time variability using a finite mixture model based on the Gamma–Gamma (GG) distribution. The GG distribution is a compound distribution derived from the product of two Gamma random variates, which represent vehicle-to-vehicle and day-to-day variability, respectively. It provides a systematic way of investigating different variability dimensions reflected in travel time data. To identify the underlying distribution of each type of variability, this study first decomposes a mixture of Gamma–Gamma models into two separate Gamma mixture modeling problems and estimates the respective parameters using the Expectation–Maximization (EM) algorithm. The proposed methodology is demonstrated using simulated vehicle trajectories produced under daily scenarios constructed from historical weather and accident data. The parameter estimation results suggest that day-to-day variability exhibits clear heterogeneity under different weather conditions: clear versus rainy or snowy days, whereas the same weather conditions have little impact on vehicle-to-vehicle variability. Next, a two-component Gamma–Gamma mixture model is specified. The results of the distribution fitting show that the mixture model provides better fits to travel delay observations than the standard (one-component) Gamma–Gamma model. The proposed method, the application of the compound Gamma distribution combined with a mixture modeling approach, provides a powerful and flexible tool to capture not only different types of variability—vehicle-to-vehicle and day-to-day variability—but also the unobserved heterogeneity within these variability types, thereby allowing the modeling of the underlying distributions of individual travel delays across different days with varying roadway disruption levels in a more effective and systematic way.     

Multiclass fuzzy user equilibrium with endogenous membership functions and risk‐taking behaviors

Over the last decades, several approaches have been proposed in the literature to incorporate users' perceptions of travel costs, their bounded rationality, and risk‐taking behaviors into network equilibrium modeling for traffic assignment problem. While theoretically advanced, these models often suffer from high complexity and computational cost and often involve parameters that are difficult to estimate. This study proposes an alternative approach where users' imprecise perceptions of travel times are endogenously constructed as fuzzy sets based on the probability distributions of random link travel times. Two decision rules are proposed accordingly to account for users' heterogeneous risk‐taking behaviors, that is, optimistic and pessimistic rules. The proposed approach, namely, the multiclass fuzzy user equilibrium, can be formulated as a link‐based variational inequality model. The model can be solved efficiently, and parameters involved can be either easily estimated or treated as factors for calibration against observed traffic flow data. Numerical examples show that the proposed model can be solved efficiently even for a large‐scale network of Mashhad, Iran, with 2538 links and 7157 origin–destination pairs. The example also illustrates the calibration capability of the proposed model, highlighting that the model is able to produce much more accurate flow estimates compared with the Wardropian user equilibrium model. Copyright © 2016 John Wiley & Sons, Ltd.     

Short-term prediction of border crossing time and traffic volume for commercial trucks: A case study for the Ambassador Bridge

Short-term forecasting of traffic characteristics, such as traffic flow, speed, travel time, and queue length, has gained considerable attention from transportation researchers and practitioners over past three decades. While past studies primarily focused on traffic characteristics on freeways or urban arterials this study places particular emphasis on modeling the crossing time over one of the busiest US–Canada bridges, the Ambassador Bridge. Using a month-long volume data from Remote Traffic Microwave Sensors and a yearlong Global Positioning System data for crossing time two sets of ANN models are designed, trained, and validated to perform short-term predictions of (1) the volume of trucks crossing the Ambassador Bridge and (2) the time it takes for the trucks to cross the bridge from one side to the other. The prediction of crossing time is contingent on truck volume on the bridge and therefore separate ANN models were trained to predict the volume. A multilayer feedforward neural network with backpropagation approach was used to train the ANN models. Predicted crossing times from the ANNs have a high correlation with the observed values. Evaluation indicators further confirmed the high forecasting capability of the trained ANN models. The ANN models from this study could be used for short-term forecasting of crossing time that would support operations of ITS technologies.     

Interactive travel choices and traffic forecast in a doubly dynamical system with user inertia and information provision

This study models the joint evolution (over calendar time) of travelers’ departure time and mode choices, and the resulting traffic dynamics in a bi-modal transportation system. Specifically, we consider that, when adjusting their departure time and mode choices, travelers can learn from their past travel experiences as well as the traffic forecasts offered by the smart transport information provider/agency. At the same time, the transport agency can learn from historical data in updating traffic forecast from day to day. In other words, this study explicitly models and analyzes the dynamic interactions between transport users and traffic information provider. Besides, the impact of user inertia is taken into account in modeling the traffic dynamics. When exploring the convergence of the proposed model to the dynamic bi-modal commuting equilibrium, we find that appropriate traffic forecast can help the system converge to the user equilibrium. It is also found that user inertia might slow down the convergence speed of the day-to-day evolution model. Extensive sensitivity analysis is conducted to account for the impacts of inaccurate parameters adopted by the transport agency.     

Traffic dynamics in a bi-modal transportation network with information provision and adaptive transit services

This paper has two major components. The first one is the day-to-day evolution of travelers’ mode and route choices in a bi-modal transportation system where traffic information (predicted travel cost) is available to travelers. The second one is a public transit operator adjusting or adapting its service over time (from period to period) based on observed system conditions. Particularly, we consider that on each day both travelers’ past travel experiences and the predicted travel cost (based on information provision) can affect travelers’ perceptions of different modes and routes, and thus affect their mode choice and/or route choice accordingly. This evolution process from day to day is formulated by a discrete dynamical model. The properties of such a dynamical model are then analyzed, including the existence, uniqueness and stability of the fixed point. Most importantly, we show that the predicted travel cost based on information provision may help stabilize the dynamical system even if it is not fully accurate. Given the day-to-day traffic evolution, we then model an adaptive transit operator who can adjust frequency and fare for public transit from period to period (each period contains a certain number of days). The adaptive frequency and fare in one period are determined from the realized transit demands and transit profits of the previous periods, which is to achieve a (locally) maximum transit profit. The day-to-day and period-to-period models and their properties are also illustrated by numerical experiments.     

Cellpath: Fusion of cellular and traffic sensor data for route flow estimation via convex optimization

A new convex optimization framework is developed for the route flow estimation problem from the fusion of vehicle count and cellular network data. The issue of highly underdetermined link flow based methods in transportation networks is investigated, then solved using the proposed concept of cellpaths for cellular network data. With this data-driven approach, our proposed approach is versatile: it is compatible with other data sources, and it is model agnostic and thus compatible with user equilibrium, system-optimum, Stackelberg concepts, and other models. Using a dimensionality reduction scheme, we design a projected gradient algorithm suitable for the proposed route flow estimation problem. The algorithm solves a block isotonic regression problem in the projection step in linear time. The accuracy, computational efficiency, and versatility of the proposed approach are validated on the I-210 corridor near Los Angeles, where we achieve 90% route flow accuracy with 1033 traffic sensors and 1000 cellular towers covering a large network of highways and arterials with more than 20,000 links. In contrast to long-term land use planning applications, we demonstrate the first system to our knowledge that can produce route-level flow estimates suitable for short time horizon prediction and control applications in traffic management. Our system is open source and available for validation and extension.     

Estimation of mean and covariance of peak hour origin–destination demands from day-to-day traffic counts

This paper proposes a generalized model to estimate the peak hour origin–destination (OD) traffic demand variation from day-to-day hourly traffic counts throughout the whole year. Different from the conventional OD estimation methods, the proposed modeling approach aims to estimate not only the mean but also the variation (in terms of covariance matrix) of the OD demands during the same peak hour periods due to day-to-day fluctuation over the whole year. For this purpose, this paper fully considers the first- and second-order statistical properties of the day-to-day hourly traffic count data so as to capture the stochastic characteristics of the OD demands. The proposed model is formulated as a bi-level optimization problem. In the upper-level problem, a weighted least squares method is used to estimate the mean and covariance matrix of the OD demands. In the lower-level problem, a reliability-based traffic assignment model is adopted to take account of travelers’ risk-taking path choice behaviors under OD demand variation. A heuristic iterative estimation-assignment algorithm is proposed for solving the bi-level optimization problem. Numerical examples are presented to illustrate the applications of the proposed model for assessment of network performance over the whole year.     

Designing heterogeneous sensor networks for estimating and predicting path travel time dynamics: An information-theoretic modeling approach

With a particular emphasis on the end-to-end travel time prediction problem, this paper proposes an information-theoretic sensor location model that aims to minimize total travel time uncertainties from a set of point, point-to-point and probe sensors in a traffic network. Based on a Kalman filtering structure, the proposed measurement and uncertainty quantification models explicitly take into account several important sources of errors in the travel time estimation/prediction process, such as the uncertainty associated with prior travel time estimates, measurement errors and sampling errors. By considering only critical paths and limited time intervals, this paper selects a path travel time uncertainty criterion to construct a joint sensor location and travel time estimation/prediction framework with a unified modeling of both recurring and non-recurring traffic conditions. An analytical determinant maximization model and heuristic beam-search algorithm are used to find an effective lower bound and solve the combinatorial sensor selection problem. A number of illustrative examples and one case study are used to demonstrate the effectiveness of the proposed methodology.     

A day-to-day route flow evolution process towards the mixed equilibria

This study investigates a travelers’ day-to-day route flow evolution process under a predefined market penetration of advanced traveler information system (ATIS). It is assumed that some travelers equipped with ATIS will follow the deterministic user equilibrium route choice behavior due to the complete traffic information provided by ATIS, while the other travelers unequipped with ATIS will follow the stochastic user equilibrium route choice behavior. The interaction between these two groups of travelers will result in a mixed equilibrium state. We first propose a discrete day-to-day route flow adjustment process for this mixed equilibrium behavior by specifying the travelers’ route adjustment principle and adjustment ratio. The convergence of the proposed day-to-day flow dynamic model to the mixed equilibrium state is then rigorously demonstrated under certain assumptions upon route adjustment principle and adjustment ratio. In addition, without affecting the convergence of the proposed day-to-day flow dynamic model, the assumption concerning the adjustment ratio is further relaxed, thus making the proposed model more appealing in practice. Finally, numerical experiments are conducted to illustrate and evaluate the performance of the proposed day-to-day flow dynamic model.     

Estimating multi-year 24/7 origin-destination demand using high-granular multi-source traffic data

Dynamic origin-destination (OD) demand is central to transportation system modeling and analysis. The dynamic OD demand estimation problem (DODE) has been studied for decades, most of which solve the DODE problem on a typical day or several typical hours. There is a lack of methods that estimate high-resolution dynamic OD demand for a sequence of many consecutive days over several years (referred to as 24/7 OD in this research). Having multi-year 24/7 OD demand would allow a better understanding of characteristics of dynamic OD demands and their evolution/trends over the past few years, a critical input for modeling transportation system evolution and reliability. This paper presents a data-driven framework that estimates day-to-day dynamic OD using high-granular traffic counts and speed data collected over many years. The proposed framework statistically clusters daily traffic data into typical traffic patterns using t-Distributed Stochastic Neighbor Embedding (t-SNE) and k-means methods. A GPU-based stochastic projected gradient descent method is proposed to efficiently solve the multi-year 24/7 DODE problem. It is demonstrated that the new method efficiently estimates the 5-min dynamic OD demand for every single day from 2014 to 2016 on I-5 and SR-99 in the Sacramento region. The resultant multi-year 24/7 dynamic OD demand reveals the daily, weekly, monthly, seasonal and yearly change in travel demand in a region, implying intriguing demand characteristics over the years.     

Path flow estimator for planning applications in small communities

This paper presents an alternative planning framework to model and forecast network traffic for planning applications in small communities, where limited resources debilitate the development and applications of the conventional four-step travel demand forecasting model. The core idea is to use the Path Flow Estimator (PFE) to estimate current and forecast future traffic demand while taking into account of various field and planning data as modeling constraints. Specifically, two versions of PFE are developed: a base year PFE for estimating the current network traffic conditions using field data and planning data, if available, and a future year PFE for predicting future network traffic conditions using forecast planning data and the estimated base year origin–destination trip table as constraints. In the absence of travel survey data, the proposed method uses similar data (traffic counts and land use data) as a four-step model for model development and calibration. Since the Institute of Transportation Engineers (ITE) trip generation rates and Highway Capacity Manual (HCM) are both utilized in the modeling process, the analysis scope and results are consistent with those of common traffic impact studies and other short-range, localized transportation improvement programs. Solution algorithms are also developed to solve the two PFE models and integrated into a GIS-based software called Visual PFE. For proof of concept, two case studies in northern California are performed to demonstrate how the tool can be used in practice. The first case study is a small community of St. Helena, where the city’s planning department has neither an existing travel demand model nor the budget for developing a full four-step model. The second case study is in the city of Eureka, where there is a four-step model developed for the Humboldt County that can be used for comparison. The results show that the proposed approach is applicable for small communities with limited resources.     

Evaluation of different contraflow strategies for hurricane evacuation in Charleston,South Carolina

Abstract

Limited specific evidence is available on the effectiveness of using contraflow as an evacuation traffic management tool. This study was conducted to determine the best combination of strategy options for evacuating Charleston, SC, along route I-26 during the event of a hurricane or other events. PARAMICS microscopic traffic simulator was used to evaluate the impact of each combination of evacuee response timing and traffic control strategy, such as contraflow, with respect to average vehicular travel time and evacuation duration. Analysis revealed the combination of management strategies that created the lowest evacuation durations and travel times for several types of anticipated evacuee responses. Furthermore, a proposed reconfiguration of the I-526/I-26 interchange for contraflow operations produced additional savings in travel times and evacuation durations. These findings support the use of all lanes for contraflow during all evacuations and provide justification to examine a possible reconfiguration of the I-526/I-26 interchange for use during evacuations.     

A day-to-day and within-day dynamic stochastic assignment model

In this article a doubly dynamis assignment model for a general network is presented. It is assumed that users' choices are based on information about travel times and generalized transportation costs occurred in a finite number of previous days and, possibly, in previous periods of the same day. The information may be supplied and managed by an informative system. In this context, path and link flows vary for different subperiods of the same day (within-day dynamics) and for different days (day-to-day dynamics). The proposed model follows a nonequilibrium approach in which both within-day and day-to-day flow fluctuations are modelled as a stochastic process. A model of dynamic network loading for computing within-day variable arc flows from path flows is also presented. The model deals explicitly with queuing at oversaturated intersections and can be formulated as a fixed point problem. A solution scheme for the doubly dynamic assignment model is presented embedding a solution algorithm for the fixed-point problem.