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• Studies network Macroscopic Fundamental Diagram of urban network with hierarchical streets. • Presence of hierarchy leads to non-unimodal patterns in MFD when hierarchical streets present and users route according to UE principles. • Findings obtained with simple analytical model and confirmed with simulations and empirical data. Unimodal, concave relationships between average network productivity and accumulation or density aggregated across spatially compact regions of urban networks—so called network Macroscopic Fundamental Diagrams (MFDs)—have recently been shown to exist on homogeneous street networks. When present, MFD relationships facilitate the modeling of traffic congestion at a regional level and have led to the development of various regional traffic control strategies. However, real street networks are not homogeneous—they generally have a hierarchical structure where some streets (e.g., arterials) promote higher mobility than others (e.g., local roads). This paper examines how the presence of hierarchical roadway structures may potentially cause non-unimodal patterns in a network's MFD. These are observed using three types of tools: analytical models of simple network structures, simulations of various idealized roadway networks, and empirical data. The impacts of street hierarchy depend on how vehicles use different roadway types to move within the network; i.e., their routing strategy. The findings suggest that the presence of roadway hierarchies may lead to MFDs that have non-unimodal or non-concave patterns on the free-flow branch when vehicles route themselves according to user equilibrium principles, which is closest to what would be observed in realistic situations. Such patterns are contrary to what is traditionally assumed in most MFD-based modeling frameworks. However, the unimodal and concave MFD should be expected under system optimal routing conditions that maximize network productivity for a given traffic state. [ABSTRACT FROM AUTHOR]

Traffic at urban intersections constitute a series of complex conflicting vehicular movements and contribute greatly to the problems of traffic congestion and air pollution. The emerging of connected and automated vehicle (CAV) technologies inspires innovative ideas in traffic management at intersections; it not only enables new control paradigms, but also allows for possibilities to revolutionize the geometric layouts of intersections. This study proposes a novel intersection design called knotted intersection (KI), to resolve the complexity of conflicting relations at intersections in a full CAV environment. This new design is associated with a set of neat control rules for vehicles to realize the smooth traffic operation at these intersections. The design problem of intersection geometry and control strategy is optimized jointly and formulated as a mixed-integer linear program (MILP), and some basic theoretical properties of KI design are derived, including nearly throughput-maximizing property and bounded within-intersection delay of vehicles. Furthermore, the KI design is then extended to a road network composed of multiple intersections to improve the overall efficiency. The optimal design of multiple knotted intersections (MKI) is developed to coordinate the traffic organization methods among intersections and a two-level solution method is proposed to solve the optimization efficiently. Numerical and simulation experiments are conducted at both the intersection level and network level under various cases, and the results validate the superior performance of the proposed methods compared to classical traffic signal control (TSC) strategies. • Knotted intersection design for resolving the complexity of intersection conflicts • Joint design of intersection geometric layout and traffic control strategy • Theoretical properties for nearly-maximum throughput and bounded delay • Optimal design of multiple knotted intersections to enhance network efficiency [ABSTRACT FROM AUTHOR]

Two new synchronization strategies are developed for signalized grids of two-directional streets. Both strategies are found to reduce congestion significantly more than do other approaches. One of the strategies is static and the other adaptive. Both use a common timing pattern for all signals on the grid but use a different offset for each. The static strategy serves the morning rush by providing perfect forward progression on all streets in the directions that point toward a reference intersection, one that is located near the center of gravity of all workplaces. For the evening rush, perfect progression is achieved for all travel directions that point away from the reference intersection. The adaptive strategy toggles between this forward synchronization mode and a second mode suited for congestion, but only in a pre-determined district surrounding the reference intersection. Toggling is based on the district's real-time traffic density. The paper shows how to switch quickly between the two synchronization modes without resorting to unacceptably short phases. It also shows that if the grid is formed by two intersecting sets of parallel streets, even if unevenly spaced, then every street can be perfectly synchronized in one of its directions. As a result, an inbound driver in the morning, or an outbound driver in the evening, is guaranteed to encounter synchronized signals over the full length of her trip. Although this is not possible for more irregular grids, the paper shows how to modify the two strategies for this case, so that they still perform well. The strategies were benchmarked with simulations against a fixed, zero-offset strategy for many scenarios, because zero-offsets are known to work well under congestion. In one important scenario representing a severely congested morning rush, both strategies were also benchmarked against a state-of-the-practice computer program. While the state-of-the-practice program reduced the zero-offset delay by a modest 7%, the proposed strategies reduced it by 21% (static) and 32% (adaptive); i.e., improving on the state-of-the-practice program by 14% and 25%. These improvements considerably exceed the 1% to 5% reductions typically reported in the literature for other state-of-the-art methods that have been compared with state-of-the-practice programs. Similarly good results were obtained for the other scenarios, which included the morning and evening rushes, various distributions of workplaces, and both regular and irregular grids. [ABSTRACT FROM AUTHOR]

Abstract Uniqueness of the dynamic user-equilibrium assignment is still an important issue. This paper proves uniqueness with a milder condition compared to past studies and shows another counterexample to the uniqueness. A unidirectional network , in which any node on any shortest route has a unique node potential, is introduced. Orders of vehicles are determined by this node potential so that, given any two vehicles passing through the same node, the lower potential vehicle arrives at the node before the higher potential vehicle. It is shown that, for a unidirectional network in equilibrium, the link travel times and traffic volumes of congested links are uniquely determined. Moreover, a simple non-unidirectional network having multiple equilibria is introduced. This example exhibits importance of unidirectional-network structure to prove uniqueness. [ABSTRACT FROM AUTHOR]

Highlights • Presents a Continuum Percolation based approach to determine the effects of the vehicular density and communication range on the connectivity level. • Investigates string stability under different communication ranges and market penetration rates of connected and autonomous vehicles. Abstract Connectivity and automation are expected to enhance safety and efficiency in transportation systems. Connectivity will provide information to drivers/autonomous vehicles to enhance decision-making reliability at the operational and tactical levels. Consequently, drivers are more likely to execute safe and efficient maneuvers and autonomous vehicles will have a more accurate perception of the traffic condition and an "error-free" execution of the driving maneuvers. At the operational level, ensuring string stability is a key consideration since unstable traffic flow results in shockwave propagation and possibly crashes. While several studies have examined the effects of information availability on string stability in a connected environment, most of the approaches are focused on automated driving (e.g., Cooperative Adaptive Cruise Control systems) and do not consider a mixed environment with regular, connected, and autonomous vehicles. To ensure connectivity in such a mixed environment, the correlation between communication range and connected vehicles density should be considered. To capture the effects of this correlation, this study uses the Continuum Percolation theory to determine the effects of the vehicular density and communication range on the connectivity level in telecommunications network and consequently, on the string stability of traffic flow. Based on the Continuum Percolation theory, there is a critical density of connected vehicles above which the entire system is connected. This critical density also depends on the communication range. This study presents an analytical derivation of this critical density. Moreover, this study evaluates the string stability under different communication ranges and market penetration rates of connected and autonomous vehicles. Results revealed that as communication range increases, the system becomes more stable and at high communication ranges, the system performs similar to the system with full connectivity. Moreover, results indicated the existence of an optimal communication range to maximize stability and ensure information delivery. [ABSTRACT FROM AUTHOR]

Highlights • Consider coordinated traffic signal controls under both deterministic and stochastic demands. • A new mixed integer linear programming (MILP) for deterministic optimization is proposed. • The MILP has a network structure and its size is smaller than the existing formulations. • The problem is extended to treat the stochastic fluctuations in traffic demand. • An accurate and efficient approximation method of expected delays is developed. • Optimal control parameters for deterministic and stochastic controls are examined. Abstract This study considers an optimal coordinated traffic signal control under both deterministic and stochastic demands. We first present a new mixed integer linear programming (MILP) for the deterministic signal optimization wherein traffic flow is modeled based on the variational theory and the constraints on a signal control pattern are linearly formulated. The resulting MILP has a clear network structure and requires fewer binary variables and constraints as compared with those in the existing formulations. We then extend the problem so as to treat the stochastic fluctuations in traffic demand. We here develop an accurate and efficient approximation method of expected delays and a solution method for the stochastic version of the signal optimization by exploiting the network structure of the problem. Using a set of proposed methods, we finally examine the optimal control parameters for deterministic and stochastic coordinated signal controls and discuss their characteristics. [ABSTRACT FROM AUTHOR]

Abstract We study a parsimonious theory that synthesizes short-term traffic demand management (TDM) policies with long-term endogenous heterogeneities of demand. In a corridor network with multiple discrete bottlenecks, we study a model of system optimal assignment that integrates the short-term problem (departure time choice with tolling) and the long-term problem (job and residential location choice). For the short-term departure-time-choice equilibrium, under mild assumptions on schedule delay function, we derive analytical solutions under a first-best TDM scheme. Investigating properties of long-term equilibria, we found that the overall equilibrium pattern exhibits remarkable spatio-temporal sorting properties. It is further shown that a lack of integration of the short- and the long-term policy results in excessive investments for long-term road construction. [ABSTRACT FROM AUTHOR]

Abstract The Macroscopic Fundamental Diagram (MFD) framework has been widely utilized to describe traffic dynamics in urban networks as well as to design perimeter flow control strategies under stationary (constant) demand and deterministic settings. In real world, both the MFD and demand however suffer from various intrinsic uncertainties while travel demand is of time-varying nature. Hence, robust control for traffic networks with uncertain MFDs and demand is much appealing and of greater interest in practice. In literature, there would be a lack of robust control strategies for the problem. One major hurdle is of requirement on model linearization that is actually a basis of most existing results. The main objective of this paper is to explore a new robust perimeter control framework for dynamic traffic networks with parameter uncertainty (on the MFD) and exogenous disturbance induced by travel demand. The disturbance in question is in general time-varying and stochastic. Our main contribution focuses on developing a control-Lyapunov function (CLF) based approach to establishing a couple of universal control laws, one is almost smooth and the other is Bang-bang like, for different implementation scenarios. Moreover, it is indicated that the almost smooth control is more suited for road pricing while the Bang-bang like control for signal timing. In sharp contrast to existing methods, in which adjusting extensive design parameters are usually needed, the proposed methods can determine the control in an automatic manner. Furthermore, numerical results demonstrate that the control can drive the system dynamics towards a desired equilibrium under various scenarios with uncertain MFDs and travel demand. Both stability and robustness can be substantially observed. As a major consequence, the proposed methods achieve not only global asymptotic stability but also appealing robustness for the closed-loop traffic system. [ABSTRACT FROM AUTHOR]

Highlights • We examine morning commuters' departure time and route choices when a true distribution of travel time is unknown. • The departure time window is shifted earlier (later) for the risk-averse (risk-seeking) group than the risk-neutral group. • A large gap between the two classes' preferences may stagger the departure time choices and thereby relieve the congestion. • In the two-routes single-class (TRSC) problem, providing better information reduces the system cost for risk-averse commuters. • In the TRSC problem, providing better information also reduces the total expected congestion for risk-averse commuters. Abstract This paper examines commuters' departure time and route choices in the morning commute problem when a true distribution of travel time is unknown but belongs to a bounded distributional uncertainty set. The travel preferences towards risk and ambiguity are distinguished by adopting the criterion of ambiguity-aware Constant Absolute Risk Aversion (CARA) travel time. We first examine the dynamic user equilibrium for a single-route model with a homogeneous preference towards risk and ambiguity. Compared with risk-neutral commuters, we find that departure time window is shifted earlier for the risk-averse commuters and shifted later for the risk-seeking commuters. We also study the single bottleneck with a risk-averse class and a risk-seeking class. We show that with a larger gap between the two classes' preferences, the congestion pattern will change from one peak to two peaks. It implies that preference heterogeneity may stagger the departure time choices and thereby relieve the average congestion. Last, we examine a two-route problem with homogeneous preference. Commuters choose between a fast and risky route (highway) and a slow and safe route (local arterial). We prove the monotonicity of the traffic flow distribution between the two routes with respect to the maximum variation in travel time. Furthermore, we find that reducing the uncertainty on the highway by providing information will reduce the total system cost and the total expected congestion simultaneously for risk-averse commuters. However, it will reduce the total expected congestion but increase the total system cost for risk-seeking commuters. In the numerical section, the price of anarchy is analyzed by varying the risk preference and the ambiguity preference. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the equilibrium properties of the morning commute problem at the network level with heterogeneous trip lengths. Congestion is modeled with a Macroscopic Fundamental Diagram relating the space-mean speed of a network to the vehicular accumulation. It is shown for a large class of scheduling preferences that if users have continuously distributed characteristics, the network accumulation at equilibrium is a continuous function of time. With α − β − γ preferences and under certain conditions, a partial First-In, First-Out (FIFO) pattern emerges at equilibrium among early and late users. This FIFO pattern is strict only within families of users having heterogeneous trip lengths and identical preferences, or vice versa. Simulation results confirmed that an attracting steady-state exists for a wide range of demands and that the predicted patterns are indeed observed. [ABSTRACT FROM AUTHOR]

Abstract Traffic flow oscillations, including traffic waves, are a common yet incompletely understood feature of congested traffic. Possible mechanisms include traffic flow instabilities, indifference regions or finite human perception thresholds (action points), and external acceleration noise. However, the relative importance of these factors in a given situation remains unclear. We bring light into this question by adding external noise and action points to the Intelligent Driver Model and other car-following models thereby obtaining a minimal model containing all three oscillation mechanisms. We show analytically that even in the subcritical regime of linearly stable flow (order parameter ϵ < 0), external white noise leads to spatiotemporal speed correlations "anticipating" the waves of the linearly unstable regime. Sufficiently far away from the threshold, the amplitude scales with (− ϵ) − 0.5. By means of simulations and comparisons with experimental car platoons and bicycle traffic, we show that external noise and indifference regions with action points have essentially equivalent effects. Furthermore, flow instabilities dominate the oscillations on freeways while external noise or action points prevail at low desired speeds such as vehicular city or bicycle traffic. For bicycle traffic, noise can lead to fully developed waves even for single-file traffic in the subcritical regime. [ABSTRACT FROM AUTHOR]

Abstract This paper shows that severe congestion on streets controlled by traffic signals can be reduced by dynamically adapting the signal offsets to the prevailing density with a simple rule that keeps the signals' green-red ratios invariant. Invariant ratios reduce a control policy's impact on the crossing streets, so a policy can be optimized and evaluated by focusing on the street itself without the confounding factors present in networks. Designed for heavy traffic with spillovers, the proposed policies are adaptive and need little data – they only require average traffic density readings and no demand forecasts. A battery of numerical experiments simulating the dynamics of rush hour traffic on a congested, homogeneous circular street reveals that the proposed form of adaptation reduces the duration of the rush and overall congestion compared with pre-timed control strategies. Eighteen different adaptation policies were considered. All inspect the street densities periodically and simultaneously, and retime the signals immediately thereafter. The period is a fixed multiple of the cycle. The street is evenly divided into sections that contain a set number of consecutive blocks and signals. The offset is the same for all blocks in a section. Three inspection intervals and six section sizes were tested. The latter ranged from a single block/signal to the whole street. It was found that adaptation worked best when sections were large and adaptation frequent. The effects were considerable across all scenarios. For a short street with a short rush and high input flows the probabilistic incidence of gridlock was reduced from 10 to 0%, and the average duration of a trip from 216 to 181 s. For a long street with a long rush and high input flows the gridlock probability was reduced from 23 to 0% and the average trip duration from 2037 to 1143s. [ABSTRACT FROM AUTHOR]

Highlights • Network features are leveraged to study incident-induced impacts on road networks mobility. • Four network features are extracted to reflect the distinctive functionality of urban intersections. • Incidents impacts are measured in both temporal and spatial dimension. • Temporally, accident delay is significantly correlated with the Betweenness Centrality and K-shell. • Spatially, micro impact and macro impact are found to be strongly associated with the four network features. Abstract In this paper, we seek to investigate the spatiotemporal impacts of traffic incident on urban road networks. The theoretical lens of a complex network leads us to expect that incident impacts are associated with the functionality that an intersection acts in a network, and also, the location of incident sites. Incident impacts are measured in both temporal and spatial dimension through mining the large-scale traffic flow data in conjunction with the incident record. In the complex network context, the urban road network can be converted into a weighted direct graph with intersections as nodes and road segments as edges with their geographic information. Four network features, i.e., Betweenness Centrality, weighted PageRank, Hub, and K-shell are assigned to each intersection to measure its functionality. Temporally, we find out significant correlations between incident delay and two network features by applying hazard-based models. Spatially, the micro impact and the macro impact are found to be strongly associated with three network features through estimating a Bayesian Negative-binomial Conditional Autoregressive model and a generalized linear model, respectively. Our study provides the basis of leveraging urban road network context to evaluate incident impacts, with some explanations, insights and possible extensions that would assist traffic administrations to guide the post-incident resilience and emergency management. [ABSTRACT FROM AUTHOR]

Highlights • New generic multi-level microscopic traffic modelling and simulation framework. • Combines idealized (collision-free) models with HF mechanisms for perception and response. • Uses Endsley's three-level awareness model and Fullers risk allostasis theory. • Varying with perception errors and different response adaptions independently from chosen CF model. • Results in endogenous mechanisms for inter- and intra-driver differences in driving behavior. • Can generate multiple plausible HF mechanisms to explain the same observable traffic phenomena. Abstract Incorporation of more sophisticated human factors (HF) in mathematical models for driving behavior has become an increasingly popular and important research direction in the last few years. Such models enable us to simulate under which conditions perception errors and risk-taking lead to interactions that result in unsafe traffic conditions and ultimately accidents. In this paper, we present a generic multi-level microscopic traffic modelling and simulation framework that supports this important line of research. In this framework, the driving task is modeled in a multi-layered fashion. At the highest level, we have idealized (collision-free) models for car following and other driving tasks. These models typically contain HF parameters that exogenously "govern the human factor", such as reaction time, sensitivities to stimuli, desired speed, etc. At the lowest level, we define HF variables (task demand and capacity, awareness) with which we maintain what the information processing costs are of performing driving tasks as well as non-driving related tasks such as distractions. We model these costs using so-called fundamental diagrams of task demand. In between, we define functions that govern the dynamics of the high-level HF parameters with these HF variables as inputs. When total task demand increases beyond task capacity, first awareness may deteriorate, where we use Endsley's three-level awareness construct to differentiate between effects on perception, comprehension, anticipation and reaction time. Secondly, drivers may adapt their response in line with Fullers risk allostasis theory to reduce risk to acceptable levels. This framework can be viewed as a meta model, that provides the analyst possibilities to combine and mix a wide variety of microscopic models for driving behavior at different levels of sophistication, depending on which HF are studied, and which phenomena need to be reproduced. We illustrate the framework with a distraction (rubbernecking) case. Our results show that the framework results in endogenous mechanisms for inter- and intra-driver differences in driving behavior and can generate multiple plausible HF mechanisms to explain the same observable traffic phenomena and congestion patterns that arise due to the distraction. We believe our framework can serve as a valuable tool in testing hypotheses related to the effects of HF on traffic efficiency and traffic safety in a systematic way for both the traffic flow and HF community. [ABSTRACT FROM AUTHOR]

Bus headways are typically susceptible to external disturbances (e.g., due to traffic congestion, clustered passenger arrivals, and special passenger needs), which create gaps in the system that grow eventually into bunching. Although many control strategies, such as static and dynamic holding strategies, have been implemented to mitigate the effects of unreliable bus schedules, most of them would impose longer dwell times on the passengers. In this paper, we investigate the potential of an alternative bus substitution strategy that is currently implemented by some transit agencies in an ad-hoc manner. In this strategy, the agency deploys a fleet of standby buses to take over service from any early or late buses so as to contain deviations from schedule, and the intention is to impose minimum penalties on the onboard passengers. We develop a discrete-time infinite-horizon approximate dynamic programming approach to find the optimal policy to minimize the overall agency and passenger costs. It is shown through numerical examples that schedule deviations can be controlled by regularly inserting standby buses as substitutions. In some implementation scenarios, the proposed strategy holds the potential to achieve comparable performance with some of the most advanced strategies, and to outperform the conventional slack-based schedule control scheme. In light of the emerging opportunities associated with autonomous driving, the performance of the proposed strategy can become even stronger due to the reduction in costs for keeping the fleet of standby buses. [ABSTRACT FROM AUTHOR]

This paper proposes a novel breakdown probability model based on microscopic driver behavior for a freeway merge bottleneck. Extending Newell's car following model to describe the transition from free-flow to congested regimes, two elements of breakdown, trigger and propagation , are derived in terms of vehicle headway. Combining these elements, a general breakdown probability is derived in terms of various parameters related to driver behavior and traffic conditions – other than flow – that can be treated as constants or stochastic with probability distributions. The proposed model is validated with real data. It was found that the theoretical breakdown probability distribution accords well with the empirical counterpart within reasonable ranges of parameter values. Our model suggests that the breakdown probability (i) increases with flow (both mainline and merging) as expected, and the merging spacing, (ii) decreases with the merging speed and aggressive driver characteristics, and interestingly, (iii) increases with the deviation in headway. A proactive traffic control method to achieve uniform headway is developed considering low penetration rates of connected automated vehicle technologies. [ABSTRACT FROM AUTHOR]

Nowadays, traffic management has become a challenge for urban areas, which are covering larger geographic spaces and facing the generation of different kinds of traffic data. This article presents a robust traffic estimation framework for highways modeled by a system of Lighthill Whitham Richards equations that is able to assimilate different sensor data available. We first present an equivalent formulation of the problem using a Hamilton–Jacobi equation. Then, using a semi-analytic formula, we show that the model constraints resulting from the Hamilton–Jacobi equation are linear ones. We then pose the problem of estimating the traffic density given incomplete and inaccurate traffic data as a Mixed Integer Program. We then extend the density estimation framework to highway networks with any available data constraint and modeling junctions. Finally, we present a travel estimation application for a small network using real traffic measurements obtained obtained during Mobile Century traffic experiment, and comparing the results with ground truth data. [ABSTRACT FROM AUTHOR]

In this study, we focus on the discrete-time day-to-day dynamic congestion pricing scheme which varies the toll on a day-to-day basis and aims to drive the traffic system to a given objective traffic equilibrium state. As is well known, due to the asymmetric nature of the travel cost functions, multiple equilibria exist. In this case, without external force, the traffic system cannot converge to the traffic equilibrium state as desired by traffic management through a day-to-day adjustment process if the initial traffic state does not fall into its attraction domain (Bie and Lo, 2010). Therefore, it is imperative for traffic management to propose a traffic control measure to ensure the desired traffic state can be achieved regardless of the initial traffic state. Previous studies on the day-to-day dynamic congestion pricing, either worked on continues-time day-to-day pricing scheme, or took the form of discrete-time day-to-day pricing scheme but did not guarantee the convergence to the desired objective traffic state for the cases when multiple traffic equilibria exist. Both are undesirable. This study aims to develop a discrete-time day-to-day pricing scheme so as to direct the traffic evolution to reach the desired equilibrium from any initial traffic state when multiple traffic equilibria exist. Based on the very general formulation of day-to-day traffic dynamics model, we present a general formulation of such day-to-day pricing schemes and propose a method to obtain one specific road pricing scheme. Moreover, we present rigorous proofs and numerical tests to verify the proposed pricing scheme. [ABSTRACT FROM AUTHOR]

It is well known that traffic flows in road networks may vary not only within the day but also between days. Existing models including day-to-day variability usually represent all variability as unpredictable fluctuations. In reality, however, some of the differences in flows on a road may be predictable for transport planners with access to historical data. For example, flow profiles may be systematically different on Mondays compared to Fridays due to predictable differences in underlying activity patterns. By identifying days of the week or times of year where flows are predictably different, models can be developed or model inputs can be amended (in the case of day-to-day dynamical models) to test the robustness of proposed policies or to inform the development of policies which vary according to these predictably different day types. Such policies could include time-of-day varying congestion charges that themselves vary by day of the week or season, or targeting public transport provision so that timetables are more responsive to the day of the week and seasonal needs of travellers. A statistical approach is presented for identifying systematic variations in daily traffic flow profiles based on known explanatory factors such as the day of the week and the season. In order to examine day-to-day variability whilst also considering within-day dynamics, the distribution of flows throughout a day are analysed using Functional Linear Models. F-type tests for functional data are then used to compare alternative model specifications for the predictable variability. The output of the method is an average flow profile for each predictably different day type, which could include day of the week or time of year. An application to real-life traffic flow data for a two-year period is provided. The shape of the daily profile was found to be significantly different for each day of the week, including differences in the timing and width of peak flows and also the relationship between peak and inter-peak flows. Seasonal differences in flow profiles were also identified for each day of the week. [ABSTRACT FROM AUTHOR]

This article presents a study on freeway networks instrumented with coordinated ramp metering and the ability of such control systems to produce arbitrarily complex congestion patterns within the dynamical limits of the traffic system. The developed method is used to evaluate the potential for an adversary with access to control infrastructure to enact high-level attacks on the underlying freeway system. The attacks are executed using a predictive, coordinated ramp metering controller based on finite-horizon optimal control and multi-objective optimization techniques. The efficacy of the control schemes in carrying out the prescribed attacks is determined via simulations of traffic network models based on the cell transmission model with onramps modeled as queue buffers. Freeway attacks with high-level objectives are presented on two illustrative examples: congestion-on-demand, which aims to create precise, user-specified pockets of congestion, and catch-me-if-you-can, which attempts to aid a fleeing vehicle from pursuant vehicles. [ABSTRACT FROM AUTHOR]

This paper examines the profit maximizing behavior of a private firm which operates a toll road competing against a free alternative in presence of cars and trucks. Trucks differ from cars in value of time (VOT), congestion externality, pavement damage, and link travel time function. We find that the firm takes either a car-strategy or a truck-strategy for profit maximization. For a traffic mix with relatively large car volume and small truck volume, the car-strategy results in no trucks using the toll road, while the truck-strategy results in all trucks using the toll road. We derive the equilibrium flow pattern under any combination of car-toll and truck-toll, based on which we identify a profit-maximizing frontier and a strategy-switching frontier in the car-toll and truck-toll two-dimensional space. By geometrically comparing the two frontiers, we establish general conditions under which each strategy will be taken, which suggest that the truck-to-car VOT ratio, the total traffic demand, and the difference in travel distance between the two roads are critical in shaping the firm's strategy. [ABSTRACT FROM AUTHOR]

This paper examines the traffic dynamics underlying a recently observed phenomenon, the so called “sympathy of speeds” whereby a high occupancy vehicle (HOV) lane seemingly exhibits lower vehicular capacity and lower flow at speeds throughout the congested regime compared to the adjacent general purpose (GP) lanes. Unlike previous studies this paper examines a time-of-day HOV lane. During the non-HOV periods the study lane reverts to a GP lane, thereby providing a control condition for the specific lane and location. This work uses the single vehicle passage (svp) method to group vehicle passages before measuring the traffic state and extends the svp to bin vehicles in the study lane based on the relative speed to the adjacent lane. The extended svp method allows the work to also study the impacts during the non-HOV periods when the study lane serves GP vehicles. This work finds that: (1) during the non-HOV periods the study lane exhibited behavior indistinguishable from the adjacent GP lane. (2) The sympathy of speeds persists throughout the day, even when the study lane serves GP vehicles. (3) The relative speed to the adjacent lane provided a better predictor of behavior than whether or not the HOV restriction is active. In short, the car following behavior that gives rise to the sympathy of speeds is unrelated to the HOV restriction per se, persisting under GP operations as well. This dependency on the relative speed in the adjacent lane is an important finding given the fact that most existing car following models assume that the longitudinal acceleration of a following vehicle is strictly a function of the relationship to the leading vehicle in the same lane. Because drivers in general adopt a larger spacing when faced with a high differential in speed between lanes means that car following behavior also depends on the relative speed to the adjacent lane. This fact has likely gone unnoticed to date because generally the conditions that give rise to a differential in speeds between lanes are usually short lived, and thus, do not become apparent in conventional macroscopic data except under exceptional circumstances that include confounding factors like HOV operations. [ABSTRACT FROM AUTHOR]

In this paper, we consider repeated routing games with piecewise-constant congestion taxing in which a central planner sets and announces the congestion taxes for fixed windows of time in advance. Specifically, congestion taxes are calculated using marginal congestion pricing based on the flow of the vehicles on each road prior to the beginning of the taxing window (and, hence, there is a time-varying delay in setting the congestion taxes). We motivate the piecewise-constant taxing policy by that users or drivers may dislike fast-changing prices and that they also prefer prior knowledge of the prices. We prove for this model that the multiplicative update rule and the discretized replicator dynamics converge to a socially optimal flow when using vanishing step sizes. Considering that the algorithm cannot adapt itself to a changing environment when using vanishing step sizes, we propose adopting constant step sizes in this case. Then, however, we can only prove the convergence of the dynamics to a neighborhood of the socially optimal flow (with the size of the neighbourhood being of the order of the selected step size). The results are illustrated on a nonlinear version of Pigou’s famous routing game. [ABSTRACT FROM AUTHOR]

This study aims (i) to analyze theoretical properties of a recently proposed describing-function (DF) based approach (Li and Ouyang, 2011; Li et al., 2012) for traffic oscillation quantification, (ii) to adapt it for estimating fuel consumption and emission from traffic oscillation and (iii) to explore vehicle control strategies of smoothing traffic with advanced technologies. The DF approach was developed to predict traffic oscillation propagation across a platoon of vehicles following each other by a nonlinear car-following law with only the leading vehicle’s input. We first simplify the DF approach and prove a set of properties (e.g., existence and uniqueness of its solution) that assure its prediction is always consistent with observed traffic oscillation patterns. Then we integrate the DF approach with existing estimation models of fuel consumption and emission to analytically predict environmental impacts (i.e., unit-distance fuel consumption and emission) from traffic oscillation. The prediction results by the DF approach are validated with both computer simulation and field measurements. Further, we explore how to utilize advantageous features of emerging sensing, communication and control technologies, such as fast response and information sharing, to smooth traffic oscillation and reduce its environmental impacts. We extend the studied car-following law to incorporate these features and apply the DF approach to demonstrate how these features can help dampen the growth of oscillation and environmental impact measurements. For information sharing, we convert the corresponding extended car-following law into a new fixed point problem and propose a simple bisecting based algorithm to efficiently solve it. Numerical experiments show that these new car-following control strategies can effectively suppress development of oscillation amplitude and consequently mitigate fuel consumption and emission. [ABSTRACT FROM AUTHOR]

Urban traffic networks are inherently unstable when congested. This instability causes a natural tendency towards spatially inhomogeneous vehicle distributions and less consistent and reproducible relationships between urban traffic variables. It is important to find ways to mitigate this unstable behavior since well-defined relationships between average network flow and density – the MFD – are useful to aid network design and control. This paper examines the impacts of locally adaptive traffic signals – e.g., those that allocate green times proportionally to upstream approach densities – on network stability and the MFD. A family of adaptive signal control strategies is examined on two abstractions of an idealized grid network using an analytical model and an interactive simulation. The results suggest that locally adaptive traffic signals provide stability when the network is moderately congested, which increases average flows and decreases the likelihood of gridlock. These benefits increase with the overall adaptivity of the signals. However, adaptive signals appear to have little to no effect on network stability or the MFD in heavily congested networks as vehicle movement becomes more constrained by downstream congestion and queue spillbacks. Under these conditions, other strategies should be used to mitigate the instability, such as adaptively routing drivers to avoid locally congested regions. These behaviors are verified using more realistic micro-simulations and are consistent with other observations documented in the literature. [ABSTRACT FROM AUTHOR]

Highlights: [•] We developed two models which estimate values of travel time and travel time reliability in road networks. [•] The models developed in this study have the same structure as user equilibrium traffic assignment problem. [•] The values of travel time and travel time reliability increase as congestion level in network increases. [Copyright &y& Elsevier]

Highlights: [•] Investigated the morning commute problem with both bottleneck congestion and parking space constraints. [•] Examined the situation when some commuters have reserved parking spots while others have to compete for public ones. [•] Appropriate combination of reserved and unreserved parking spots can temporally relieve bottleneck congestion. [•] System performance is quantified in terms of the relative proportions of the two classes of commuters. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a dynamic user equilibrium for bus networks where recurrent overcrowding results in queues at stops. The route-choice model embedded in the dynamic assignment explicitly considers common lines and strategies with alternative routes. As such, the shortest hyperpath problem is extended to a dynamic scenario with capacity constraints where the diversion probabilities depend on the time at which the stop is reached and on the expected congestion level at that time. In order to reproduce congestion for all the lines sharing a stop, the Bottleneck Queue Model with time-varying exit capacity, introduced in Meschini et al. (2007), is extended. The above is applied to separate queues for each line in order to satisfy the First-In-First-Out principle within every attractive set, while allowing overtaking among passengers with different attractive sets but queuing single file. The application of the proposed model to a small example network clearly reproduces the formation and dispersion of passenger queues due to capacity constraints and thus motivates the implementation of the methodology on a real-size network case as the next step for future research. [Copyright &y& Elsevier]

Highlights: [•] Formulate the aggregated dynamics of urban multimodal networks with macroscopic fundamental diagrams. [•] Develop an optimization framework for distributing urban road space between different modes. [•] Integrate the dynamics of passenger flows at the macroscopic level with a mode choice model. [•] Investigate static and dynamic urban space distributions and congestion pricing strategies. [Copyright &y& Elsevier]

Highlights: [•] Tradable credits can be used to eliminate morning commute congestion. [•] Credit charge can be made equitable by suitably allocating the credits to the commuters. [•] A tradable credit system can make every commuter better off than without it. [ABSTRACT FROM AUTHOR]

Abstract: This paper Analyzes a new tradable credit scheme (TCS) for managing commuters’ travel choices, which seeks to persuade commuters to spread evenly within the rush hour and between primary and alternative routes so that excessive traffic congestion can be alleviated. The scheme defines a peak time window and charges those who use the primary route within that window in the form of mobility credits. Those who avoid the peak-time window, by either traveling outside the peak time window or switching to the alternative route, may be rewarded credits. A market is created such that those who need to pay credits can purchase them from those who acquire them from their rewarding travel choices. A general analytical framework is proposed for a system of two parallel routes. The framework (1) considers a variety of assumptions about commuters’ behavior in response to the discontinuous credit charge introduced at the boundary of the peak-time window, (2) allows modeling congestion effects (or demand elasticity) on the alternative route, and (3) enables both the design of system optimal TCS and the analysis of the efficiency of any given TCS. Our analyses indicate that the proposed TCS not only achieves up to 33% efficiency gains in the base scenario, but also distributes the benefits among all the commuters directly through the credit trading. The results also suggest that very simple TCS schemes could provide substantial efficiency gains for a wide range of scenarios. Such simplicity and robustness are important to practicability of the proposed scheme. Numerical experiments are conducted to examine the sensitivity of TCS designs to various system parameters. [Copyright &y& Elsevier]

Abstract: “Can a single car really absorb a traffic jam without making new jams?” In this paper, we focus on this frequently-discussed question, and have succeeded in making a theoretical framework of a driving technique how to absorb a traffic jam by using a minimal microscopic model. Jam-absorption driving comes from Beaty (Beaty, 1998; Beaty, 2013), and it is composed of a sequence of two actions termed the “slow-in” and “fast-out”. The “slow-in” is the action to avoid being captured by a jam and remove it by decelerating and taking a longer headway in advance. The “fast-out” is performed after the “slow-in”, and it is the action to follow the car in front without unnecessary time gaps by accelerating quickly. In our theoretical framework, we have represented the recipe of the actions such as the time–space points and the velocity. Moreover, we have clarified the condition of no secondary jams due to this driving, i.e., the condition that compression and expansion waves caused by this driving meet each other and disappear. Particularly, we have calculated how these waves propagates to the following cars and the point where and when they disappear. Besides, we have analyzed how this point moves in time–space diagrams by varying the timing to start the jam-absorption, and revealed that the pattern of this movement is not constant but changes greatly by the velocity-headway relationships. Furthermore, as a more realistic problem, we have formulated the driving for jam-absorption in two steps of deceleration, which brings rich patterns of collisions among compression and expansion waves. [Copyright &y& Elsevier]

Abstract: Diverging junctions are an important type of bottlenecks, which can reduce capacities and initiate and propagate traffic congestion in a road network. In this paper, we propose a kinematic wave theory for modeling dynamics of non-cooperative diverging traffic, in which traffic dynamics of vehicles to one direction are assumed to be independent of those to other directions instantaneously. During a short time interval, the kinematic wave model of diverging traffic is decoupled into a number of nonlinear resonant systems. From analytical solutions to the Riemann problem of a decoupled system, a new definition of partial traffic demand is introduced, so that diverging flows can be easily computed with the supply–demand method. Then a Cell Transmission Model is proposed to solve the kinematic wave model of diverging traffic by taking into account of the interactions among different traffic streams. Simulation results demonstrate that vehicles follow the First-In-First-Out principle in the long run, and the model converges when we decrease the cell and time-step sizes. In addition, it is shown that traffic streams to different directions segregate in a selfish manner, and the total throughput of a diverging junction is not maximized as in existing diverge models. In the future, more theoretical and empirical studies are needed for a better understanding of this and other diverge models. [Copyright &y& Elsevier]

Abstract: It has been recently shown that a macroscopic fundamental diagram (MFD) linking space-mean network flow, density and speed exists in the urban transportation networks under some conditions. An MFD is further well defined if the network is homogeneous with links of similar properties. This collective behavior concept can also be utilized to introduce simple control strategies to improve mobility in homogeneous city centers without the need for details in individual links. However many real urban transportation networks are heterogeneous with different levels of congestion. In order to study the existence of MFD and the feasibility of simple control strategies to improve network performance in heterogeneously congested networks, this paper focuses on the clustering of transportation networks based on the spatial features of congestion during a specific time period. Insights are provided on how to extend this framework in the dynamic case. The objectives of partitioning are to obtain (i) small variance of link densities within a cluster which increases the network flow for the same average density and (ii) spatial compactness of each cluster which makes feasible the application of perimeter control strategies. Therefore, a partitioning mechanism which consists of three consecutive algorithms, is designed to minimize the variance of link densities while maintaining the spatial compactness of the clusters. Firstly, an over segmenting of the network is provided by a sophisticated algorithm (Normalized Cut). Secondly, a merging algorithm is developed based on initial segmenting and a rough partitioning of the network is obtained. Finally, a boundary adjustment algorithm is designed to further improve the quality of partitioning by decreasing the variance of link densities while keeping the spatial compactness of the clusters. In addition, both density variance and shape smoothness metrics are introduced to identify the desired number of clusters and evaluate the partitioning results. These results show that both the objectives of small variance and spatial compactness can be achieved with this partitioning mechanism. A simulation in a real urban transportation network further demonstrates the superiority of the proposed method in effectiveness and robustness compared with other clustering algorithms. [Copyright &y& Elsevier]

Abstract: This paper studies traffic hysteresis arising in traffic oscillations from a behavioral perspective. It is found that the occurrence and type of traffic hysteresis is closely correlated with driver behavior when experiencing traffic oscillations and with the time driver reaction begins relative to the starting deceleration wave. Statistical results suggest that driver behavior is different depending on its position along the oscillation. This suggests that different car-following models should be used inside the different stages of an oscillation in order to replicate realistic congestion features. [Copyright &y& Elsevier]

Abstract: In this paper, stability analysis of traffic control for two-region urban cities is treated. It is known in control theory that optimality does not imply stability. If the optimal control is applied in a heavily congested system with high demand, traffic conditions might not change or the network might still lead to gridlock. A city partitioned in two regions with a Macroscopic Fundamental Diagram (MFD) for each of the regions is considered. Under the assumption of triangular MFDs, the two-region MFDs system is modeled as a piecewise second-order system. Necessary and sufficient conditions are derived for stable equilibrium accumulations in the undersaturated regimes for both MFDs. Moreover, the traffic perimeter control problem for the two-region MFDs system is formulated. Phase portraits and stability analysis are conducted, and a new algorithm is proposed to derive the boundaries of the stable and unstable regions. Based on these regions, a state-feedback control strategy is derived. Trapezoidal shape of MFDs are also addressed with numerical solutions. [Copyright &y& Elsevier]

Abstract: Extending a recent work () pertaining to a simple single-bottleneck model, this paper is the first of a two-part research wherein we undertake a mathematically rigorous study of the continuous-time dynamic user equilibrium (DUE) problem using the recently introduced mathematical paradigm of differential complementarity systems (DCSs) (). The first step in this comprehensive research is to gain a thorough understanding of some continuous-time point-queue models, which will be used as the building block of a computationally tractable model for the continuous-time DUE problem that we will study in detail in the accompanying paper (). Starting with the original point-queue model introduced by , we summarize some desirable properties that a continuous-time point-queue model should possess, and show that one of these properties—the nonnegativity of the queue lengths—is violated by Vickrey’s original model. As a remedy to this drawback of Vickrey’s model and with the goal of extending it to a continuous-time setting, we introduce two continuous-time point-queue models and show that they satisfy the properties we propose. Discretizations of the continuous-time models are discussed and construction of numerical trajectories is presented; convergence of such trajectories as the time step approaches zero is established; regularity of a solution to the continuous-time problem is clarified, and numerical results are presented. [Copyright &y& Elsevier]

Abstract: This paper analyzes a model of early morning traffic congestion, that is a special case of the model considered in . A fixed number of identical vehicles travel along a single-lane road of constant width from a common origin to a common destination, with LWR flow congestion and Greenshields’ Relation. Vehicles have a common work start time, late arrivals are not permitted, and trip cost is linear in travel time and time early. The paper explores traffic dynamics for the social optimum, in which total trip cost is minimized, and for the user optimum, in which no vehicle’s trip cost can be reduced by altering its departure time. Closed-form solutions for the social optimum and quasi-analytic solutions for the user optimum are presented, along with numerical examples, and it is shown that this model includes the bottleneck model (with no late arrivals) as a limit case where the length of the road shrinks to zero. [Copyright &y& Elsevier]

Abstract: The Newell–Daganzo merge model is not only very simple but also accurately reproduces experimental findings. However, the capacity downstream of the merge is an exogenous variable in the model. This is a serious limitation for merges that behave as active bottlenecks because their downstream capacity is a direct consequence of the merging behavior. This paper proposes an analytical model that extends the Newell–Daganzo model by incorporating, endogenously, the capacity drop related to the merging process. Two cases are investigated depending on the traffic states on the on-ramp. The model properties are analyzed and a sensitivity analysis is performed to quantify the relative contribution of the each parameter in the capacity drop. Finally, the extended Newell–Daganzo model is validated with experimental data coming from an active merge bottleneck on the M6 freeway in UK. [Copyright &y& Elsevier]

Abstract: An extended open system such as traffic flow is said to be convectively unstable if perturbations of the stationary state grow but propagate in only one direction, so they eventually leave the system. By means of data analysis, simulations, and analytical calculations, we give evidence that this concept is relevant for instabilities of congested traffic flow. We analyze detector data from several hundred traffic jams and propose estimates for the linear growth rate, the wavelength, the propagation velocity, and the severity of the associated bottleneck that can be evaluated semi-automatically. Scatter plots of these quantities reveal systematic dependencies. On the theoretical side, we derive, for a wide class of microscopic and macroscopic traffic models, analytical criteria for convective and absolute linear instabilities. Based on the relative positions of the stability limits in the fundamental diagram, we divide these models into five stability classes which uniquely determine the set of possible elementary spatiotemporal patterns in open systems with a bottleneck. Only two classes, both dominated by convective instabilities, are compatible with observations. By means of approximate solutions of convectively unstable systems with sustained localized noise, we show that the observed spatiotemporal phenomena can also be described analytically. The parameters of the analytical expressions can be inferred from observations, and also (analytically) derived from the model equations. [Copyright &y& Elsevier]

Abstract: A continuum model that describes a disordered, heterogeneous traffic stream is presented. Such systems are widely prevalent in developing countries where classical traffic models cannot be readily applied. The characteristics of such systems are unique since drivers of smaller vehicles exploit their maneuverability to move ahead through lateral gaps at lower speeds. At higher speeds, larger vehicles press their advantage of greater motive power. The traffic stream at the microscopic level is disordered and defines a porous medium. Each vehicle is considered to move through a series of pores defined by other vehicles. A speed-density relationship that explicitly considers the pore space distribution is presented. This captures the considerable dynamics between vehicle classes that are overlooked when all classes are converted to a reference class (usually Passenger Car Equivalents) as is traditionally done. Using a finite difference approximation scheme, traffic evolution for a two-class traffic stream is shown. [Copyright &y& Elsevier]

Abstract: We present a method of predicting pedestrian route choice behavior and physical congestion during the evacuation of indoor areas with internal obstacles. Under the proposed method, a network is first constructed by discretizing the space into regular hexagonal cells and giving these cells potentials before a modified cell transmission model is employed to predict the evolution of pedestrian flow in the network over time and space. Several properties of this cell transmission model are explored. The method can be used to predict the evolution of pedestrian flow over time and space in indoor areas with internal obstacles and to investigate the collection, spillback, and dissipation behavior of pedestrians passing through a bottleneck. The cell transmission model is further extended to imitate the movements of multiple flows of pedestrians with different destinations. An algorithm based on generalized cell potential is also developed to assign the pedestrian flow. [Copyright &y& Elsevier]

Abstract: A field experiment in Yokohama (Japan) revealed that a macroscopic fundamental diagram (MFD) linking space-mean flow, density and speed exists on a large urban area. It was observed that when the highly scattered plots of flow vs. density from individual fixed detectors were aggregated the scatter nearly disappeared and points grouped along a well defined curve. Despite these and other recent findings for the existence of well-defined MFDs for urban areas, these MFDs should not be universally expected. In this paper we investigate what are the properties that a network should satisfy, so that an MFD with low scatter exists. We show that the spatial distribution of vehicle density in the network is one of the key components that affect the scatter of an MFD and its shape. We also propose an analytical derivation of the spatial distribution of congestion that considers correlation between adjacent links. We investigate the scatter of an MFD in terms of errors in the probability density function of spatial link occupancy and errors of individual links’ fundamental diagram (FD). Later, using real data from detectors for an urban arterial and a freeway network we validate the proposed derivations and we show that an MFD is not well defined in freeway networks as hysteresis effects are present. The datasets in this paper consist of flow and occupancy measures from 500 fixed sensors in the Yokohama downtown area in Japan and 600 loop detectors in the Twin Cities Metropolitan Area Freeway network in Minnesota, USA. [Copyright &y& Elsevier]

Abstract: This paper presents new insights on the hysteresis phenomenon in congested freeway traffic. It is found that existing theories based on different driver behavior for acceleration and deceleration are incomplete. The data suggests that one needs to consider aggressive and timid driver behavior as well. These findings are based on an improved method for measuring traffic flow variables from trajectory data consistently with kinematic wave theory. [ABSTRACT FROM AUTHOR]

Abstract: We consider the problem of characterizing user equilibria and optimal solutions for routing in a given network. We extend the known models by considering users oblivious to congestion in the following sense: While in the typical user equilibrium setting the users follow a strategy that minimizes their individual cost by taking into account the (dynamic) congestion due to the current routing pattern, an oblivious user ignores congestion altogether; instead, he or she decides his routing on the basis of cheapest routes on a network without any flow whatsoever. These cheapest routes can be, for example, the shortest paths in the network without any flow. This model tries to capture the fact that a certain percentage of travelers base their route simply on the distances they observe on a map, without thinking (or knowing, or caring) about the delays experienced on this route due to their fellow travelers. In this work we study the effect of such users using as the measure of network performance its price of anarchy, i.e., the ratio of the total latency experienced by the users (oblivious or not) at equilibrium over the social optimum. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Despite the availability of large empirical data sets and the long history of traffic modeling, the theory of traffic congestion on freeways is still highly controversial. In this contribution, we compare Kerner’s three-phase traffic theory with the phase diagram approach for traffic models with a fundamental diagram. We discuss the inconsistent use of the term “traffic phase” and show that patterns demanded by three-phase traffic theory can be reproduced with simple two-phase models, if the model parameters are suitably specified and factors characteristic for real traffic flows are considered, such as effects of noise or heterogeneity or the actual freeway design (e.g. combinations of off- and on-ramps). Conversely, we demonstrate that models created to reproduce three-phase traffic theory create similar spatiotemporal traffic states and associated phase diagrams, no matter whether the parameters imply a fundamental diagram in equilibrium or non-unique flow-density relationships. In conclusion, there are different ways of reproducing the empirical stylized facts of spatiotemporal congestion patterns summarized in this contribution, and it appears possible to overcome the controversy by a more precise definition of the scientific terms and a more careful comparison of models and data, considering effects of the measurement process and the right level of detail in the traffic model used. [Copyright &y& Elsevier]

Abstract: This paper first presents a method to estimate Newell’s car-following model parameters in congestion at a microscopic scale. I-80 NGSim data analysis shows that at this scale driving behaviors vary from one vehicle to the another. Then, relations between stochastic Newell’s model with heterogeneous drivers and its associated macroscopic pattern are established. This proves that the mean jam spacing is the arithmetic mean of individual jam spacings whereas the mean wave speed is the harmonic mean of individual wave speeds. These new insights are valuable for (i) calibrating a macroscopic model from individual observations and (ii) establishing the equivalence between the stochastic and the well-calibrated deterministic versions of Newell’s model for a sufficiently large number of vehicles. [Copyright &y& Elsevier]

Abstract: This paper formulates the dynamic equilibrium conditions for a single bottleneck model with heterogeneous commuters as a linear complementarity problem. This novel formulation offers a formal framework for the rigorous study and solution of a single bottleneck model with general heterogeneity parameter assumptions, enabling the adoption of well established complementarity theory and methods to analyze the model, and providing a significant contribution to the existing literature that either lacks a rigorous formulation or solves the problem under a limited set of heterogeneity parameter assumptions. The paper presents theoretical proofs for solution existence and uniqueness, and numerical results and insights for different heterogeneity assumptions. [Copyright &y& Elsevier]

Abstract: Basic road network components, such as merging and diverging junctions, contribute much to formation and propagation of traffic congestion. However, in contrast to extensive studies of traffic dynamics on a road link, little is understood for those on a road network. In this study, we provide a comprehensive analysis of asymptotic traffic dynamics arising in diverge–merge networks with two intermediate links with first-order kinematic wave models. In addition, traffic demand at the origin and traffic demand at the destination are constant and maximum, and the proportion of vehicles choosing an intermediate link is constant. First, we examine all possible asymptotic stationary states and the sufficient and necessary conditions for their existence. With an example, we find that non-stationary states can include damped (DPO) and persistent periodic oscillations (PPO), and present an equivalent dynamical system that can be used to distinguish these two types of oscillations. This study can be a springboard for better understanding of traffic dynamics, especially formation and propagation of traffic congestion, on general road networks. [Copyright &y& Elsevier]