On the macroscopic stability of freeway traffic

A simple model of traffic flow is used to analyze the spatio-temporal distribution of flow and density on closed-loop homogeneous freeways with many ramps, which produce inflows and allow outflows. As we would expect, if the on-ramp demand is space-independent then this distribution tends toward uniformity in space if the freeway is either: (i) uncongested; or (ii) congested with queues on its on-ramps and enough inflow to cause the average freeway density to increase with time. In all other cases, however, including any recovery phase of a rush hour where the freeway’s average density declines, the distribution of flow and density quickly becomes uneven. This happens even under conditions of perfect symmetry, where the percentage of vehicles exiting at every off ramp is the same. The flow-density deviations from the average are shown to grow exponentially in time and propagate backwards in space with a fixed wave speed. A consequence of this type of instability is that, during recovery, gaps of uncongested traffic will quickly appear in the unevenly congested stream, reducing average flow. This extends the duration of recovery and invariably creates clockwise hysteresis loops on scatter-plots of average system flow vs. density during any rush hour that oversaturates the freeway. All these effects are quantified with formulas and verified with simulations. Some have been observed in real networks. In a more practical vein, it is also shown that the negative effects of instability diminish (i.e., freeway flows increase) if (a) some drivers choose to exit the freeway prematurely when it is too congested and/or (b) freeway access is regulated in a certain traffic-responsive way. These two findings could be used to improve the algorithms behind VMS displays for driver guidance (finding a), and on-ramp metering rates (finding b).     

Average time gaps in congested freeway flow

Characteristics of time gaps (that is, the time separation between the rear of the lead vehicle and the front of the following vehicle) in congested freeway flow provide an important link between microscopic and macroscopic traffic flow. Although individual time gaps are a microscopic phenomenon, average time gaps can easily be determined from commonly collected macroscopic traffic flow data. Data from San Diego freeways and the Queen Elizabeth Way in Ontario, Canada are analyzed to show that average time gaps in congested flow are essentially constant with respect to speed; that they vary considerably between lanes at a single location and, for the same lane, from site to site; that they display considerable scatter; and that at some sites there is a distinct increase in average time gaps in the median lane in the transition to congested flow but at others there is no change or a slight reduction. The variability of average time gaps is not easily explained, although differences in driver populations may partly explain differences among different sites. Hysteresis due to acceleration and deceleration does not appear to be an explanation for the high degree of scatter in average time gaps, since no positive correlation was found between speed changes and average time gaps.     

A kinematic wave approach to traffic statics and dynamics in a double-ring network

Recently there has been much interest in understanding macroscopic fundamental diagrams of stationary road networks. However, there lacks a systematic method to define and solve stationary states in a road network with complex junctions. In this study we propose a kinematic wave approach to defining, analyzing, and simulating static and dynamic traffic characteristics in a network of two ring roads connected by a 2 × 2 junction, which can be either an uninterrupted interchange or a signalized intersection. This study is enabled by recently developed macroscopic junction models of general junctions. With a junction model based on fair merging and first-in-first-out diverging rules, we first define and solve stationary states and then derive the macroscopic fundamental diagram (MFD) of a stationary uninterrupted network. We conclude that the flow-density relationship of the uninterrupted double-ring network is not unique for high average network densities (i.e., when one ring becomes congested) and unveil the existence of infinitely many stationary states that can arise with a zero-speed shockwave. From simulation results with a corresponding Cell Transmission Model, we verify that all stationary states in the MFD are stable and can be reached, but show that randomness in the retaining ratio of each ring drives the network to more symmetric traffic patterns and higher flow-rates. Furthermore we model a signalized intersection as two alternate diverge junctions and demonstrate that the signalized double-ring network can reach asymptotically periodic traffic patterns, which are therefore defined as “stationary” states in signalized networks. With simulations we show that the flow-density relation is well defined in such “stationary” states, and asymptotic traffic patterns can be impacted by signal cycle lengths and retaining ratios. But compared with uninterrupted interchanges, signalized intersections lead to more asymmetric traffic patterns, lower flow-rates, and even gridlocks when the average density is higher than half of the jam density. The results are consistent between this study and existing studies, but the network kinematic wave model, with appropriate junction models, is mathematically tractable and physically meaningful. It has offered a more complete picture regarding the number and type of stationary states, their stability, and MFD in freeway and signalized networks.     

Closed-form multiclass cell transmission model enhanced with overtaking,lane-changing,and first-in first-out properties

A novel multiclass macroscopic model is proposed in this article. In order to enhance first-in, first-out property (FIFO) and transmission function in the multiclass traffic modeling, a new multiclass cell transmission model with FIFO property (herein called FM-CTM) is extended from its prior multiclass cell transmission model (M-CTM). Also, to enhance its analytical compactness and resultant computational convenience, FM-CTM is formulated in this paper as a set of closed-form matrix equations. The objective is to improve the accuracy of traffic state estimation by enforcing FIFO property when a fast vehicle cannot overtake a slow vehicle due to a limitation of a single-lane road. Moreover, the proposed model takes into account a different priority for vehicles of each class to move forward through congested road conditions, and that makes the flow calculation independent from their free-flow speeds. Some hypothetical and real-world freeway networks with a constant or varying number of lanes are selected to verify FM-CTM by comparing with M-CTM and the conventional CTM. Observed densities of VISSIM and real-world dataset of I-80 are selected to compare with the simulated densities from the three CTMs. The numerical results show that FM-CTM outperforms the other two models by 15% of accuracy measures in most cases. Therefore, the proposed model is expected to be well applicable to the road network with a mixed traffic and varying number of lanes.     

Continuous formulations and analytical properties of the link transmission model

The link transmission model (LTM) has great potential for simulating traffic flow in large-scale networks since it is much more efficient and accurate than the Cell Transmission Model (CTM). However, there lack general continuous formulations of LTM, and there has been no systematic study on its analytical properties such as stationary states and stability of network traffic flow. In this study we attempt to fill the gaps. First we apply the Hopf–Lax formula to derive Newell’s simplified kinematic wave model with given boundary cumulative flows and the triangular fundamental diagram. We then apply the Hopf–Lax formula to define link demand and supply functions, as well as link queue and vacancy functions, and present two continuous formulations of LTM, by incorporating boundary demands and supplies as well as invariant macroscopic junction models. With continuous LTM, we define and solve the stationary states in a road network. We also apply LTM to directly derive a Poincaré map to analyze the stability of stationary states in a diverge-merge network. Finally we present an example to show that LTM is not well-defined with non-invariant junction models. We can see that Newell’s model and continuous LTM complement each other and provide an alternative formulation of the network kinematic wave theory. This study paves the way for further extensions, analyses, and applications of LTM in the future.     

On the fundamental diagram for freeway traffic: A novel calibration approach for single-regime models

The speed-density or flow-density relationship has been considered as the foundation of traffic flow theory. Existing single-regime models calibrated by the least square method (LSM) could not fit the empirical data consistently well both in light-traffic/free-flow conditions and congested/jam conditions. In this paper, first, we point out that the inaccuracy of single-regime models is not caused solely by their functional forms, but also by the sample selection bias. Second, we apply a weighted least square method (WLSM) that addresses the sample selection bias problem. The calibration results for six well-known single-regime models using the WLSM fit the empirical data reasonably well both in light-traffic/free-flow conditions and congested/jam conditions. Third, we conduct a theoretical investigation that reveals the deficiency associated with the LSM is because the expected value of speed (or a function of it) is nonlinear with regard to the density (or a function of it).     

The characteristics of congested flow on a freeway across lanes,space, and time

For the most part, previous studies of freeway flow kinematics and dynamics (especially relating to schock wave propagation and to the fundamental diagram) have looked only at flow within a single lane. However, the perturbations in flow which make the dynamics interesting—and of practical importance—normally arise in multiple lane settings. This study examines flow-occupancy dynamics at the onset of congestion by taking into consideration the flows across all the lanes, individually. The results show that just prior to the onset of congestion, flow rates in the shoulder lane are only about 50% of the flows in the median and middle lanes. As the congestion moves upstream through a data collection station, flow rates in the two fast lanes decrease, but flow rates in the shoulder lane invariably increase. After the onset of congested operations, all three tend toward the same average occupancy and speed. These results provide support for an earlier suggestion that discontinuous flow-concentration functions are not necessary, and also help to resolve some of the questions raised by that earlier suggestion.     

Dual influences on vehicle speed in special-use lanes and critique of US regulation

We verify that slow speeds in a special-use lane, such as a carpool or bus lane, can be due to both, high demand for that lane and slow speeds in the adjacent regular-use lane. These dual influences are confirmed from months of data collected from all freeway carpool facilities in the San Francisco Bay Area. Additional data indicate that both influences hold: for other types of special-use lanes, including bus lanes; and for other parts of the world.The findings do not bode well for a new US regulation stipulating that most classes of Low-Emitting Vehicles, or LEVs, are to vacate slow-moving carpool lanes. These LEVs invariably constitute small percentages of traffic; e.g. they are only about 1% of the freeway traffic demand in the San Francisco Bay Area. Yet, we show: that relegating some or all of these vehicles to regular-use lanes can significantly add to regular-lane congestion; and that this, in turn, can also be damaging to vehicles that continue to use the carpool lanes. Counterproductive outcomes of this kind are predicted first by applying kinematic wave analysis to a real Bay Area freeway. Its measured data indicate that the site selected for this analysis stands to suffer less from the regulation than will others in the region. Yet, we predict: that the regulation will cause the site’s people-hours and vehicle-hours traveled during the rush to each increase by more than 10%; and that carpool-lane traffic will share in the damages. Real data from the site support these predictions. Further parametric analysis of a hypothetical, but more generic freeway system indicates that these kinds of negative outcomes will be widespread. Constructive ways to amend the new regulation are discussed, as are promising strategies to increase the vehicle speeds in carpool lanes by improving the travel conditions in regular lanes.     

Eco-system optimal time-dependent flow assignment in a congested network

This research addresses the eco-system optimal dynamic traffic assignment (ESODTA) problem which aims to find system optimal eco-routing or green routing flows that minimize total vehicular emission in a congested network. We propose a generic agent-based ESODTA model and a simplified queueing model (SQM) that is able to clearly distinguish vehicles’ speed in free-flow and congested conditions for multi-scale emission analysis, and facilitates analyzing the relationship between link emission and delay. Based on the SQM, an expanded space-time network is constructed to formulate the ESODTA with constant bottleneck discharge capacities. The resulting integer linear model of the ESODTA is solved by a Lagrangian relaxation-based algorithm. For the simulation-based ESODTA, we present the column-generation-based heuristic, which requires link and path marginal emissions in the embedded time-dependent least-cost path algorithm and the gradient-projection-based descent direction method. We derive a formula of marginal emission which encompasses the marginal travel time as a special case, and develop an algorithm for evaluating path marginal emissions in a congested network. Numerical experiments are conducted to demonstrate that the proposed algorithm is able to effectively obtain coordinated route flows that minimize the system-wide vehicular emission for large-scale networks.     

Bicycle lane priority: Promoting bicycle as a green mode even in congested urban area

The main obstacles to boosting the bicycle as a mode of transport are safety concerns due to interactions with motorized traffic. One option is to separate cyclists from motorists through exclusive bicycle priority lanes. This practice is easily implemented in uncongested traffic. Enforcing bicycle lanes on congested roads may degenerate the network, making the idea very hard to sell both to the public and the traffic authorities. Inspired by Braess Paradox, we take an unorthodox approach to seeking latent misutilized capacity in the congested networks to be dedicated to exclusive bicycle lanes. The aim of this study is to tailor an efficient and practical method to large size urban networks. Hence, this paper appeals to policy makers in their quest to scientifically convince stakeholder that bicycle is not a secondary mode, rather, it can be greatly accommodated along with other modes even in the heart of the congested cities. In conjunction with the bicycle lane priority, other policy measures such as shared bicycle scheme, electric-bike, integration of public transport and bicycle are also discussed in this article. As for the mathematical methodology, we articulated it as a discrete bilevel mathematical programing. In order to handle the real networks, we developed a phased methodology based on Branch-and-Bound (as a solution algorithm), structured in a less intensive RAM manner. The methodology was tested on real size network of city of Winnipeg, Canada, for which the total of 30 road segments – equivalent to 2.77 km bicycle lanes – in the CBD were found.     

The smoothing effect of carpool lanes on freeway bottlenecks

Real data show that reserving a lane for carpools on congested freeways induces a smoothing effect that is characterized by significantly higher bottleneck discharge flows (capacities) in adjacent lanes. The effect is reproducible across days and freeway sites: it was observed, without exception, in all cases tested. Predicted by an earlier theory, the effect arises because disruptive vehicle lane changing diminishes in the presence of a carpool lane. We therefore conjecture that smoothing can also be induced by other means that would reduce lane changing.The benefits can be large. Queueing analysis shows that the smoothing effect greatly reduces the times spent by people and vehicles in queues. For example, by ignoring the smoothing effect at one of the sites we analyzed one would predict that its carpool lane increased both the people-hours and the vehicle-hours traveled by well over 300%. In reality, the carpool lane reduced both measures due to smoothing. The effect is so significant that even a severely underused carpool lane can in some instances increase a freeway bottleneck’s total discharge flow. This happens for the site we analyzed when carpool demand is as low as 1200 vph.     

Speed-spacing dependency on relative speed from the adjacent lane: New insights for car following models

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.     

Modeling cooperative and autonomous adaptive cruise control dynamic responses using experimental data

Vehicle longitudinal control systems such as (commercially available) autonomous Adaptive Cruise Control (ACC) and its more sophisticated variant Cooperative ACC (CACC) could potentially have significant impacts on traffic flow. Accurate models of the dynamic responses of both of these systems are needed to produce realistic predictions of their effects on highway capacity and traffic flow dynamics. This paper describes the development of models of both ACC and CACC control systems that are based on real experimental data. To this end, four production vehicles were equipped with a commercial ACC system and a newly developed CACC controller. The Intelligent Driver Model (IDM) that has been widely used for ACC car-following modeling was also implemented on the production vehicles. These controllers were tested in different traffic situations in order to measure the actual responses of the vehicles. Test results indicate that: (1) the IDM controller when implemented in our experimental test vehicles does not perceptibly follow the speed changes of the preceding vehicle; (2) strings of consecutive ACC vehicles are unstable, amplifying the speed variations of preceding vehicles; and (3) strings of consecutive CACC vehicles overcome these limitations, providing smooth and stable car following responses. Simple but accurate models of the ACC and CACC vehicle following dynamics were derived from the actual measured responses of the vehicles and applied to simulations of some simple multi-vehicle car following scenarios.     

Modelling heavy vehicle car‐following behaviour in congested traffic conditions

This study develops a car‐following model in which heavy vehicle behaviour is predicted separately from passenger car. Heavy vehicles have different characteristics and manoeuvrability compared with passenger cars. These differences could create problems in freeway operations and safety under congested traffic conditions (level of service E and F) particularly when there is high proportion of heavy vehicles. With increasing numbers of heavy vehicles in the traffic stream, model estimates of the traffic flow could be degrades because existing car‐following models do not differentiate between these vehicles and passenger cars. This study highlighted some of the differences in car‐following behaviour of heavy vehicle and passenger drivers and developed a model considering heavy vehicles. In this model, the local linear model tree approach was used to incorporate human perceptual imperfections into a car‐following model. Three different real world data sets from a stretch of freeway in USA were used in this study. Two of them were used for the training and testing of the model, and one of them was used for evaluation purpose. The performance of the model was compared with a number of existing car‐following models. The results showed that the model, which considers the heavy vehicle type, could predict car‐following behaviour of drivers better than the existing models. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal deployment of charging lanes for electric vehicles in transportation networks

Given the rapid development of charging-while-driving technology, we envision that charging lanes for electric vehicles can be deployed in regional or even urban road networks in the future and thus attempt to optimize their deployment in this paper. We first develop a new user equilibrium model to describe the equilibrium flow distribution across a road network where charging lanes are deployed. Drivers of electric vehicles, when traveling between their origins and destinations, are assumed to select routes and decide battery recharging plans to minimize their trip times while ensuring to complete their trips without running out of charge. The battery recharging plan will dictate which charging lane to use, how long to charge and at what speed to operate an electric vehicle. The speed will affect the amount of energy recharged as well as travel time. With the established user equilibrium conditions, we further formulate the deployment of charging lanes as a mathematical program with complementarity constraints. Both the network equilibrium and design models are solved by effective solution algorithms and demonstrated with numerical examples.     

Modelling of sub-micrometer particle concentrations in free-flowing freeway traffic,Brisbane, Australia: some empirical results

As road networks become increasingly more congested, environmental concerns relating to emissions from motor vehicles assume a higher significance. This study found that road side concentrations of particles produced by freeway traffic in Brisbane, Australia, is primarily dependent upon traffic flow differentiated into fuel type, and wind speed. The analysis differentiates between diesel and petrol vehicles, and finds that particle concentration is very sensitive to the proportion of diesel-fuelled vehicles. A 20% increase in diesel vehicles can produce an 18% increase in particle concentrations compared with a 2% particle increase for the same number of additional petrol vehicles.     

Properties of a well-defined macroscopic fundamental diagram for urban traffic

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.     

Empirical flow-density and speed-spacing relationships: Evidence of vehicle length dependency

Traffic flow theory has come to a point where conventional, fixed time averaged data are limiting our insight into critical behavior both at the macroscopic and microscopic scales. This paper develops a methodology to measure relationships of density and vehicle spacing on freeways. These relationships are central to most traffic flow theories but have historically been difficult to measure empirically. The work leads to macroscopic flow-density and microscopic speed-spacing relationships in the congested regime derived entirely from dual loop detector data and then verified against the NGSIM data set. The methodology eliminates the need to seek out stationary conditions and yields clean relationships that do not depend on prior assumptions of the curve shape before fitting the data. Upon review of the clean empirical relationships a key finding of this work is the fact that many of the critical parameters of the macroscopic flow-density and microscopic speed-spacing relationships depend on vehicle length, e.g., upstream moving waves should travel through long vehicles faster than through short vehicles. Thus, the commonly used assumption of a homogeneous vehicle fleet likely obscures these important phenomena. More broadly, if waves travel faster or slower depending on the length of the vehicles through which the waves pass, then the way traffic is modeled should be updated to explicitly account for inhomogeneous vehicle lengths.     

Methods of dropping auxiliary lanes at freeway weaving segments

Auxiliary lanes connecting freeway entrance and exit ramps provide additional space for entering and exiting vehicles to change lanes. The method of dropping auxiliary lanes is critical in the design of freeway auxiliary lanes. This study investigates the performance of different methods of dropping auxiliary lanes. Case studies were conducted at two selected freeway segments with successive entrance or exit ramps in the City of Houston. Traffic simulation analysis results of these two case studies show that additional operational benefits can be achieved by extending an auxiliary lane beyond the freeway weaving segment. The study also found that if the weaving segment is followed by an entrance/exit ramp and this ramp has high traffic volume, it can be less operationally favorable to extend and terminate the auxiliary lane at this entrance/exit ramp location. Instead, dropping the auxiliary lane before this entrance/exit ramp represents a more operationally effective option.