Continuum theory for pedestrian traffic flow: Local route choice modelling and its implications

This contribution puts forward a novel multi-class continuum model that captures some of the key dynamic features of pedestrian flows. It considers route choice behaviour on both the strategic (pre-trip) and tactical (en-route) level. To achieve this, we put forward a class-specific equilibrium direction relation of the pedestrians, which is governed by two parts: one part describing the global route choice, which is pre-determined based on the expectations of the pedestrians, and one part describing the local route choice, which is a density-gradient dependent term that reflects local adaptations based on prevailing flow conditions.Including the local route choice term in the multi-class model causes first of all dispersion of the flow: pedestrians will move away from high density areas in order to reduce their overall walking costs. Second of all, for the crossing flow and bi-directional flow cases, local route choice causes well known self-organised patterns to emerge (i.e. diagonal stripes and bi-directional lanes). We study under which demand conditions self-organisation occurs and fails, as well as what the impact is of the choices of the different model parameters. In particular, the differences in the weights reflecting the impact of the own and the other classes appear to have a very strong impact on the self-organisation process.     

A pedestrian flow model considering the impact of local density: Voronoi diagram based heuristics approach

Local density, which is an indicator for comfortable moving of a pedestrian, is rarely considered in traditional force based and heuristics based pedestrian flow models. However, comfortable moving is surely a demand of pedestrian in normal situations. Recently, Voronoi diagram had been successfully adopted to obtain the local density of a pedestrian in empirical studies. In this paper, Voronoi diagram is introduced into the heuristics based pedestrian flow model. It provides not only local density but also other information for determining moving velocity and direction. Those information include personal space, safe distance, neighbors, and three elementary characteristics directions. Several typical scenarios are set up to verify the proposed model. The simulation results show that the velocity-density relations and capacities of bottleneck are consistent with the empirical data, and many self-organization phenomena, i.e., arching phenomenon and lane formation, are also reproduced. The pedestrians are likely to be homogeneously distributed when they are sensitive to local density, otherwise pedestrians are non-uniformly distributed and the stop-and-go waves are likely to be reproduced. Such results indicate that the Voronoi diagram is a promising tool in modeling pedestrian dynamics.     

Characterization and comparison of traffic flow on reversible roadways

Reversible traffic operations have become an increasingly popular strategy for mitigating traffic congestion associated with the directionally unbalanced traffic flows that are a routine part of peak commute periods, planned special events, and emergency evacuations. It is interesting that despite its widespread and long‐term use, relatively little is known about the operational characteristics of this form of operation. For example, the capacity of a reversed lane has been estimated by some to be equal to that of a normal lane while others have theorized it to be half of this value. Without accurate estimates of reversible lane performance it is not possible to confidently gauge the benefits of reversible roadways or model them using traffic simulation. This paper presents the results of a study to measure and evaluate the speed and flow characteristics of reverse‐flow traffic streams by comparing them under various operating conditions and locations. It was found that, contrary to some opinions, the flow characteristics of reverse‐flowing lanes were generally similar to normally flowing lanes under a variety of traffic volume, time‐of‐day, location, and type‐of‐use conditions. The study also revealed that drivers will readily use reversible lanes without diminished operating speeds, particularly as volumes increase. Copyright © 2010 John Wiley & Sons, Ltd.     

An anisotropic continuum model considering bi-directional information impact

In traffic flow with naturalistic driving only, stimulus information pre-dominantly comes from the preceding vehicles with drivers occasionally responding to the following vehicles through the inspection of rear-view mirrors. Such one-sided information propagation may potentially be altered in future connected vehicle environment. This brings new motivations of modeling vehicle dynamics under bi-directional information propagation. In this study, stemming from microscopic bi-directional car-following models, a continuum traffic flow model is put forward that incorporates the bi-directional information impact macroscopically but can still preserve the anisotropic characteristics of traffic flow and avoid non-physical phenomenon such as wrong-way travels. We then analyze the properties of the continuum model and respectively illustrate the condition that guarantees the anisotropy, eradicates the negative travel speed, preserves the traveling waves and keeps the linear stability. Through a series of numerical experiments, it is concluded that (1) under the bi-directional looking context only when the backward weight ratio belongs to an appropriate range then the anisotropic property can be maintained; (2) forward-propagating traffic density waves and standing waves emerge with the increasing consideration ratio for backward information; (3) the more aggressive driving behaviors for the forward direction can delay the backward-propagating and speed up the forward-propagating of traffic density waves; (4) positive holding effect and negative pushing effect of backward looking can also be observed under different backward weight ratios; and (5) traffic flow stability varies with different proportion of backward traffic information contribution and such stability impact is sensitive to the initial traffic density condition. This proposed continuum model may contribute to future development of traffic control and coordination in future connected vehicle environment.     

Effects of low speed limits on freeway traffic flow

Recent years have seen a renewed interest in Variable Speed Limit (VSL) strategies. New opportunities for VSL as a freeway metering mechanism or a homogenization scheme to reduce speed differences and lane changing maneuvers are being explored. This paper examines both the macroscopic and microscopic effects of different speed limits on a traffic stream, especially when adopting low speed limits. To that end, data from a VSL experiment carried out on a freeway in Spain are used. Data include vehicle counts, speeds and occupancy per lane, as well as lane changing rates for three days, each with a different fixed speed limit (80 km/h, 60 km/h, and 40 km/h). Results reveal some of the mechanisms through which VSL affects traffic performance, specifically the flow and speed distribution across lanes, as well as the ensuing lane changing maneuvers. It is confirmed that the lower the speed limit, the higher the occupancy to achieve a given flow. This result has been observed even for relatively high flows and low speed limits. For instance, a stable flow of 1942 veh/h/lane has been measured with the 40 km/h speed limit in force. The corresponding occupancy was 33%, doubling the typical occupancy for this flow in the absence of speed limits. This means that VSL strategies aiming to restrict the mainline flow on a freeway by using low speed limits will need to be applied carefully, avoiding conditions as the ones presented here, where speed limits have a reduced ability to limit flows. On the other hand, VSL strategies trying to get the most from the increased vehicle storage capacity of freeways under low speed limits might be rather promising. Additionally, results show that lower speed limits increase the speed differences across lanes for moderate demands. This, in turn, also increases the lane changing rate. This means that VSL strategies aiming to homogenize traffic and reduce lane changing activity might not be successful when adopting such low speed limits. In contrast, lower speed limits widen the range of flows under uniform lane flow distributions, so that, even for moderate to low demands, the under-utilization of any lane is avoided. These findings are useful for the development of better traffic models that are able to emulate these effects. Moreover, they are crucial for the implementation and assessment of VSL strategies and other traffic control algorithms.     

Specification and calibration of a microscopic model for pedestrian dynamic simulation at signalized intersections: A hybrid approach

Macroscopic pedestrian models for bidirectional flow analysis encounter limitations in describing microscopic dynamics at crosswalks. Pedestrian behavior at crosswalks is typically characterized by the evasive effect with conflicting pedestrians and vehicles and the following effect with leading pedestrians. This study proposes a hybrid approach (i.e., route search and social force-based approach) for modeling of pedestrian movement at signalized crosswalks. The key influential factors, i.e., leading pedestrians, conflict with opposite pedestrians, collision avoidance with vehicles, and compromise with traffic lights, are considered. Aerial video data collected at one intersection in Beijing, China were recorded and extracted. A new calibration approach based on a genetic algorithm is proposed that enables optimization of the relative error of pedestrian trajectory in two dimensions, i.e., moving distance and angle. Model validation is conducted by comparison with the observed trajectories in five typical cases of pedestrian crossing with or without conflict between pedestrians and vehicles. The characteristics of pedestrian flow, speed, acceleration, pedestrian-vehicle conflict, and the lane formation phenomenon were compared with those from two competitive models, thus demonstrating the advantage of the proposed model.     

Survey of pedestrians' crossing time at non‐signalized mid‐block street crossing

At non‐signalized mid‐block street crossings in China's cities, pedestrians often weave between motor vehicle flows. This paper investigated the influence patterns of the gender and age of pedestrians, the presence of a pedestrian group, vehicles' interference and the crossing direction on the crossing time at non‐signalized mid‐block street crossings in Changsha, China. The results show that the crossing speed is approximately 1–1.1 m/s; the crossing time increases with increasing age, and the crossing speed of a pedestrian will be quicker when the time gap between the pedestrian and the oncoming vehicle is smaller if he/she decides to cross. This paper also analyzed the crossing time pattern when pedestrians cross lane by lane and found that pedestrians spend the most time crossing the first lane and the least time crossing the middle lane, regardless of whether they are crossing from the curb to the central island or from the central island to the curb. The crossing speed is an important input to the design of pedestrian facilities, so these findings can be applied to the assessment of pedestrian crossing safety in China's cities and can provide a basis for the design of pedestrian crossing facilities. Copyright © 2017 John Wiley & Sons, Ltd.     

A dynamic automated lane change maneuver based on vehicle-to-vehicle communication

Automated driving is gaining increasing amounts of attention from both industry and academic communities because it is regarded as the most promising technology for improving road safety in the future. The ability to make an automated lane change is one of the most important parts of automated driving. However, there has been little research into automated lane change maneuvers, and current research has not identified a way to avoid potential collisions during lane changes, which result from the state variations of the other vehicles. One important reason is that the lane change vehicle cannot acquire accurate information regarding the other vehicles, especially the vehicles in the adjacent lane. However, vehicle-to-vehicle communication has the advantage of providing more information, and this information is more accurate than that obtained from other sensors, such as radars and lasers. Therefore, we propose a dynamic automated lane change maneuver based on vehicle-to-vehicle communication to accomplish an automated lane change and eliminate potential collisions during the lane change process. The key technologies for this maneuver are trajectory planning and trajectory tracking. Trajectory planning calculates a reference trajectory satisfying the demands of safety, comfort and traffic efficiency and updates it to avoid potential collisions until the lane change is complete. The trajectory planning method converts the planning problem into a constrained optimization problem using the lane change time and distance. This method is capable of planning a reference trajectory for a normal lane change, an emergency lane change and a change back to the original lane. A trajectory-tracking controller based on sliding mode control calculates the control inputs to make the host vehicle travel along the reference trajectory. Finally, simulations and experiments using a driving simulator are conducted. They demonstrate that the proposed dynamic automated lane change maneuver can avoid potential collisions during the lane change process effectively.     

A generalised function for modeling bi-directional flow effects on indoor walkways in Hong Kong

This paper examines the relationships between walking speed and pedestrian flow under various bi-directional flow conditions at indoor walkways in Hong Kong. The effects of bi-directional pedestrian flows are investigated empirically with particular emphasis on their effects on walking time for different directions of flow at pedestrian walkways in Hong Kong. Flow measurements were conducted at selected indoor walkways in urban areas. A generalized walking time function that takes bi-directional flow distributions (or flow ratios) into account is proposed for these pedestrian facilities and calibrated for various flow conditions ranging from free-flow to congested-flow (at-capacity) situations. The bi-directional flow effects on free-flow walking speed, effective capacity and at-capacity walking speed are validated with observed data. It was found that the bi-directional flow ratios have significant impacts on both the at-capacity walking speeds and the maximum flow rates of the selected walkways but not on the free-flow walking speeds. The findings and study methodology provide better insight into the effects of bi-directional pedestrian flow characteristics and will assist engineers/planners in improving the design and operation of pedestrian facilities not only in Hong Kong, but also in other countries as well.     

A macroscopic traffic model for highway work zones: Formulations and numerical results

This study presents a multilane model for analyzing the dynamic traffic properties of a highway segment under a lane‐closure operation that often incurs complex interactions between mandatory lane‐changing vehicles and traffic at unblocked lanes. The proposed traffic flow formulations employ the hyperbolic model used in the non‐Newtonian fluid dynamics, and assume the lane‐changing intensity between neighboring lanes as a function of their difference in density. The results of extensive simulation experiments indicate that the proposed model is capable of realistically replicating the impacts of lane‐changing maneuvers from the blocked lanes on the overall traffic conditions, including the interrelations between the approaching flow density, the resulting congestion level, and the exiting flow rate from the lane‐closure zone. Our extensive experimental analyses also confirm that traffic conditions will deteriorate dramatically and evolve to the state of traffic jam if the density has exceeded its critical level that varies with the type of lane‐closure operations. This study also provides a convenient way for computing such a critical density under various lane‐closure conditions, and offers a theoretical basis for understanding the formation as well as dissipation of traffic jam.     

Optimal location of advance warning for mandatory lane change near a two-lane highway off-ramp

Improper mandatory lane change (MLC) maneuvers in the vicinity of highway off-ramp will jeopardize traffic efficiency and safety. Providing an advance warning for lane change necessity is one of the efficient methods to perform systematic lane change management, which encourages smooth MLC maneuvers occurring at proper locations to mitigate the negative effects of MLC maneuvers on traffic flow nearby off-ramp. However, the state of the art indicates the lack of rigorous methods to optimally locate this advance warning so that the maximum benefit can be obtained. This research is motivated to address this gap. Specifically, the proposed approach considers that the area downstream of the advance warning includes two zones: (i) the green zone whose traffic ensures safe and smooth lane changes without speed deceleration (S-MLC); the start point of the green zone corresponding to the location of the advance warning; (ii) the yellow zone whose traffic leads to rush lane change maneuvers with speed deceleration (D-MLC). An optimization model is proposed to search for the optimal green and yellow zones. Traffic flow theory such as Greenshield model and shock wave analysis are used to analyze the impacts of the S-MLC and D-MLC maneuvers on the traffic delay. A grid search algorithm is applied to solve the optimization model. Numerical experiments conducted on the simulation model developed in Paramics 6.9.3 indicate that the proposed optimization model can identify the optimal location to set the advance MLC warning nearby an off-ramp so that the traffic delay resulting from lane change maneuvers is minimized, and the corresponding capacity drop and traffic oscillation can be efficiently mitigated. Moreover, the experiments validated the consistency of the green and yellow zones obtained in the simulation traffic flow and from the optimization model for a given optimally located MLC advance warning under various traffic regimes. The proposed approach can be implemented by roadside mobile warning facility or on-board GPS for human-driven vehicles, or embedded into lane change aid systems to serve connected and automated vehicles. Thus it will greatly contribute to both literature and engineering practice in lane change management.     

On a mean field game approach modeling congestion and aversion in pedestrian crowds

In this paper we present a new class of pedestrian crowd models based on the mean field games theory introduced by Lasry and Lions in 2006. This macroscopic approach is based on a microscopic model, that considers smart pedestrians who rationally interact and anticipate the future. This leads to a forward-backward structure in time. We focus on two-population interactions and validate the modeling with simple examples. Two complementary classes of problems are addressed, namely the case of crowd aversion and the one of congestion. In both cases we describe the model and present numerical solvers (based on the optimization formulation and the partial differential equations respectively). Finally we present numerical tests involving anticipation phenomena and complex group behaviors such as lane formation.     

Experimental study and modeling of car-following behavior under high speed situation

To investigate the car-following behavior under high speed driving conditions, we performed a set of 11-car-platoon experiments on Hefei airport highway. The formation and growth of oscillations have been analyzed and compared with that in low speed situations. It was found that there is considerable heterogeneity for the same driver over different runs of the experiment. This intra-driver heterogeneity was quantitatively depicted by a new index and incorporated in an enhanced two-dimensional intelligent driver model. Using both the new high-speed and the previous low-speed experimental data, the new and three existing models were calibrated. Simulation results show that the enhanced model outperforms the three existing car-following models that do not take into account this intra-driver heterogeneity in reproducing the essential features of the traffic in the experiments.     

Modeling pedestrians’ road crossing behavior in traffic system micro-simulation in China

In many Chinese cities, pedestrian’s road crossing behavior is different from that of pedestrians in developed countries. This paper presents a pedestrian model for traffic system micro-simulation in China. Considering the high rate of signal non-compliance, we classify pedestrians into two types: law-obeying ones and opportunistic ones. Opportunistic ones decide whether to violate traffic signal during red man, depending on the states of some external factors (like policeman, vehicle flow and other pedestrians’ behaviors). Questionnaires were used to determine the proportions of these two types of pedestrians under different circumstances. In addition, a time gap distribution extracted from videotape were used to determine the criterion for pedestrians to decide whether to walk or wait when they conflict with vehicle flows. However, simulation results deviate from the data extracted from videotape in some degree. By adjusting the parameters on the basis of analyzing the occurrence of the deviations, the simulation results agree with the field results better. This model has represented the high rate of pedestrians’ red light running and the mixed characteristics of traffic flows in Chinese cities, and it may be applicable in the micro-simulation of traffic system in other developing cities.     

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.     

Experimental and empirical investigations of traffic flow instability

Traffic instability is an important but undesirable feature of traffic flow. This paper reports our experimental and empirical studies on traffic flow instability. We have carried out a large scale experiment to study the car-following behavior in a 51-car-platoon. The experiment has reproduced the phenomena and confirmed the findings in our previous 25-car-platoon experiment, i.e., standard deviation of vehicle speeds increases in a concave way along the platoon. Based on our experimental results, we argue that traffic speed rather than vehicle spacing (or density) might be a better indicator of traffic instability, because vehicles can have different spacing under the same speed. For these drivers, there exists a critical speed between 30 km/h and 40 km/h, above which the standard deviation of car velocity is almost saturated (flat) along the 51-car-platoon, indicating that the traffic flow is likely to be stable. In contrast, below this critical speed, traffic flow is unstable and can lead to the formation of traffic jams. Traffic data from the Nanjing Airport Highway support the experimental observation of existence of a critical speed. Based on these findings, we propose an alternative mechanism of traffic instability: the competition between stochastic factors and the so-called speed adaptation effect, which can better explain the concave growth of speed standard deviation in traffic flow.     

Simulating pedestrian movements at signalized crosswalks in Hong Kong

This paper presents a new pedestrian simulation (PS) model for signalized crosswalks in Hong Kong. This PS model is capable of estimating the variations of walking speed particularly on the effects of bi-directional pedestrian flows so as to determine the minimum required duration of pedestrian crossing time. Video records taken from the observational surveys at the selected crosswalk in urban area were used to extract the required data for model calibration. It was found that the design walking speed for signalized crosswalks should be varied by the effects of the bi-directional pedestrian flows. It was also interesting to note that the negative impact of the bi-directional flow effects (ranging from uni-directional to bi-directional pedestrian flows) on the chance of pedestrian crossing the crosswalk is increasing from free-flow to at-capacity flow conditions. The new PS model is also validated using an independent data set so as to examine the reliability of the simulation results. The validation results show that the new PS model can provide an accurate evaluation on the changes of walking speed and its standard deviation under different scenarios with particular emphasis on the effects of the bi-directional pedestrian flows. The advancement of this PS model can be applied to assess the effects of each improvement measure and to evaluate the benefits of each scenario in practice.