Study of macroscopic fundamental diagram on Shanghai urban expressway network in China

The macroscopic fundamental diagram（ MFD） is studied to obtain the aggregate behavior of traffic in cities. This paper investigates the existence and the characteristics of different types of daily MFD for the Shanghai urban expressway network. The existence of MFD in the Shanghai urban expressway network is proved based on two weeks＇ data.Moreover, the hysteresis phenomena is present in most days and the network exhibits different hysteresis loops under different traffic situations. The relationship between the hysteresis phenomena and the inhomogeneity of traffic distribution is verified. The MFDs in the years of 2009 and 2012 are compared. The hysteresis loop still exists in 2012, which further verifies the existence of the hysteresis phenomenon. The direct relationship between the length of the hysteresis loop（ ΔO） and the congestion is proved based on sufficient data. The width of the hysteresis loop, i. e., the drop in network flow（ ΔQ） has no relationship with the congestion, and it varies from day to day under different traffic situations.

Perimeter traffic control strategy based on macroscopic fundamental diagrams

A perimeter traffic signal control strategy is proposed based on the macroscopic fundamental diagram theory(MFD)to solve the signal control problem in oversaturated states.First,the MFD of a specific regional network can be derived using VSS IM simulation software.Secondly,the maximum number of cumulative vehicles that the network can accommodate is determined based on the MFD.Then,through monitoring the influx flow,the number of vehicles existing in and exiting from the network,a perimeter traffic control model is proposed to optimize the signal timing of the boundary intersections.Finally,a virtual network simulation model is established and three different kinds o f traffic demand are loaded into the network.Simulation results show that a fer the strategy implementation,the number o f vehicles accumulating in the network can be kept near the optimal value,while the number o f both entering and exiting vehicles increases significantly and the road network can be maintained at a large capacity.Simultaneously,the queue length at the approach of the border intersections is reasonably controlled and vehicles entering and exiting the network can maintain a more efficient and stable speed.The network performance indices such as the average traffic delay and average number of stops can be improved to a certain degree,thus verifying the effectiveness and feasibility of the perimeter control strategy.

Vehicle emissions calculation for urban roads based on the Macroscopic Fundamental Diagram method and real-time traffic information

Vehicle emissions calculation methods mostly use ownership information or annual road monitoring data as the activity level to calculate air pollutant emissions,but it is hard to reflect either the emissions intensity under different conditions or the spatiotemporal characteristics in various sections based on such approaches.This paper presents a method based on the Macroscopic Fundamental Diagram and real-time traffic data to calculate vehicle emissions,which could reflect the operation conditions and emission characteristics of vehicles.Following the‘Technical Guide for the Compiling of Road Vehicle Air Pollutant Emissions Inventories’,the emissions of three roads with different lane numbers and road grades in Beijing were estimated and verified using this method.Compared with monitoring data,the average deviations of the traffic flow on the Fifth Expressway,Jingfu National Highway,and Jingzhou Provincial Highway were?25.5%,?26.5%,and?13.4%,respectively,and the average deviations of nitrogen oxides emissions were?27.7%,?12.9%,and?12%,respectively.This method showed good application potentials to construct the emissions inventory applied to the block-scale model and analyze the spatiotemporal distribution characteristics of motor vehicle emissions in urban areas.

An identification model of urban critical links with macroscopic fundamental diagram theory

How to identify the critical links of the urban road network for actual traffic management and intelligent trans- portation control is an urgent problem, especially in the con- gestion environment. Most previous methods focus on traf- fic static characteristics for traffic planning and design. How- ever, actual traffic management and intelligent control need to identify relevant sections by dynamic traffic information for solving the problems of variable transportation system. Therefore, a city-wide traffic model that consists of three re- lational algorithms, is proposed to identify significant links of the road network by using macroscopic fundamental diagram （MFD） as traffic dynamic characteristics. Firstly, weighted- traffic flow and density extraction algorithm is provided with simulation modeling and regression analysis methods, based on MFD theory. Secondly, critical links identification algo- rithm is designed on the first algorithm, under specified prin- ciples. Finally, threshold algorithm is developed by cluster analysis. In addition, the algorithms are analyzed and applied in the simulation experiment of the road network of the cen- tral district in Hefei city, China. The results show that the model has good maneuverability and improves the shortcom- ings of the threshold judged by human. It provides an ap- proach to identify critical links for actual traffic management and intelligent control, and also gives a new method for eval- uating the planning and design effect of the urban road net- work.

Fundamental diagrams for pedestrian flows in a channel via an extended social force model

In this paper, an extended social force model was applied to investigate fundamental diagrams of pedestrian flows. In the presented model, both the static floor field and the view field were taken into account. Then each pedestrian can determine his/her desired walking directions according to both global and local information. The fundamental diagrams were obtained numerically under periodic boundary condition. It was found that the fundamental diagrams show good agreement with the measured data in the case of unidirectional flow, especially in the medium density range. However, the fundamental diagram for the case of bidirectional flow gave larger values than the measured data. Furthermore, the bidirectional flux is larger than the tmidirectional flux in a certain density range. It is indicated that the bidirectional flow may be more efficient than the unidirectional flow in some cases. The process of lane formation is quite quick in the model. Typical flow patterns in three scenarios were given to show some realistic applications.

Model on empirically calibrating stochastic traffic flow fundamental diagram

This paper addresses two shortcomings of the data-driven stochastic fundamental diagram for freeway traffic.The first shortcoming is related to the least-squares methods which have been widely used in establishing traffic flow fundamental diagrams.We argue that these methods are not suitable to generate the percentile-based stochastic fundamental diagrams,because the results generated by least-squares methods represent weighted sample mean,rather than percentile.The second shortcoming is widespread use of independent modeling methodology for a family of percentile-based fundamental diagrams.Existing methods are inadequate to coordinate the fundamental diagrams in the same family,and consequently,are not in alignment with the basic rules in probability theory and statistics.To address these issues,this paper proposes a holistic modeling framework based on the concept of mean absolute error minimization.The established model is convex,but non-differentiable.To efficiently implement the proposed methodology,we further reformulate this model as a linear programming problem which could be solved by the state-of-the-art solvers.Experimental results using real-world traffic flow data validate the proposed method.

Bus frequency optimization in a large-scale multi-modal transportation system:integrating 3D-MFD and dynamic traffic assignment

A properly designed public transport system is expected to improve traffic efficiency.A high-frequency bus service would decrease the waiting time for passengers,but the interaction between buses and cars might result in more serious congestion.On the other hand,a low-frequency bus service would increase the waiting time for passengers and would not reduce the use of private cars.It is important to strike a balance between high and low frequencies in order to minimize the total delays for all road users.It is critical to formulate the impacts of bus frequency on congestion dynamics and mode choices.However,as far as the authors know,most proposed bus frequency optimization formulations are based on static demand and the Bureau of Public Roads function,and do not properly consider the congestion dynamics and their impacts on mode choices.To fill this gap,this paper proposes a bi-level optimization model.A three-dimensional Macroscopic Fundamental Diagram based modeling approach is developed to capture the bi-modal congestion dynamics.A variational inequality model for the user equilibrium in mode choices is presented and solved using a double projection algorithm.A surrogate model-based algorithm is used to solve the bi-level programming problem.

Cellular automaton model considering headway-distance effect

This paper presents a cellular automaton model for single-lane traffic flow. On the basis of the Nagel-Schreckenberg （NS） model, it further considers the effect of headway-distance between two successive cars on the randomization of the latter one. In numerical simulations, this model shows the following characteristics. （1） With a simple structure, this model succeeds in reproducing the hysteresis effect, which is absent in the NS model. （2） Compared with the slow-tostart models, this model exhibits a local fundamental diagram which is more consistent to empirical observations. （3） This model has much higher efficiency in dissolving congestions compared with the so-called NS model with velocitydependent randomization （VDR model）. （4） This model is more robust when facing traffic obstructions. It can resist much longer shock times and has much shorter relaxation times on the other hand. To summarize, compared with the existing models, this model is quite simple in structure, but has good characteristics.

The effect of ACC vehicles to mixed traffic flow consisting of manual and ACC vehicles

This paper studies the effect of adaptive cruise control （ACC） system on traffic flow by using simulations. The multiple headway and velocity difference （MHVD） model is used to depict the motion of ACC vehicles, and the simulation results are compared with the optimal velocity （OV） model which is used to depict the motion of manual vehicles. Compared the cases between the manual and the ACC vehicle flow, the fundamental diagram can be classified into four regions： I, II, III, IV. In low and high density the flux of the two models is the same; in region II the free flow region of the MHVD model is enlarged, and the flux of the MHVD model is larger than that of the OV model; in region III serious jams occur in the OV model while the ACC system suppresses the jams in the MHVD model and the traffic flow is in order, but the flux of the OV model is larger than that of the MHVD model. Similar phenomena also appeared in mixed traffic flow which consists of manual and ACC vehicles. The results indicate that ACC vehicles have significant effect on traffic flow. The improvement induced by ACC vehicles decreases with the increasing proportion of ACC vehicles.

Car Deceleration Considering Its Own Velocity in Cellular Automata Model

In this paper, we propose a new cellular automaton model, which is based on NaSch traffic model. In our method, when a car has a larger velocity, if the gap between the car and its leading car is not enough large, it will decrease. The aim is that the following car has a buffer space to decrease its velocity at the next time, and then avoid to decelerate too high. The simulation results show that using our model, the ear deceleration is realistic, and is closer to the field measure than that of NaSch model.

Simulation of bidirectional pedestrian flow in transfer station corridor based on multi forces

A good understanding of pedestrian movement in the transfer corridor is vital for the planning and design of the station,especially for efficiency and safety.A multi-force vector grid model was presented to simulate the movement of bidirectional pedestrian flow based on cellular automata and forces between pedestrians.The model improves rule-based characteristics of cellular automata,details forces between pedestrians and solves pedestrian collisions by a several-step updating method to simulate pedestrian movements.Two general scenarios in corridor were simulated.One is bidirectional pedestrian flow simulation with isolation facility,and the other is bidirectional pedestrian flow simulation without isolation facility,where there exists disturbance in the middle.Through simulation,some facts can be seen that pedestrians in the case with isolation facility have the largest speed and pedestrians in the case without isolation facility have the smallest speed; pedestrians in the case of unidirectional flow have the largest volume and pedestrians in the case of without isolation facility have the smallest volume.

One-Dimensional Traffic Model to Consider Priority of the Stochastic Deceleration

A one-dimensional cellular automaton model of traffic flow is proposed to introduce the different delay probabilities in the steps of rules and the stochastic deceleration prior to the deterministic one when the anticipation velocity of vehicle is larger than the headway. The fundamental diagram shows the capacity of road more approaches to the observed data compared with that by the NaSch model. Moreover, the model is able to reproduce the complicated behavior of the real traffic, such as the metastability state, the separation of different phases and the effect of hysteresis.It is concluded that the order arrangement of the stochastic deceleration and deterministic acceleration has indeed remarkable effect on traffic flow and the modification presented in this paper is reasonable and realistic.

Evacuation based on spatio-temporal resilience with variable traffic demand

The efficient evacuation of people from dangerous areas is a key objective of emergency management.However,many emergencies give little to no advanced warning,leading to spontaneous evacuation with no time for planning or management.For large emergencies,destinations become less certain,with traffic demand imbalanced and concentrated on a few oversaturated routes familiar to evacuees.Ultimately,this leads to rapid congestion and delay on some routes,while others remain barely used,extending clearance times with an accumulating population at risk.In this study we address these issues through incorporating spatio-temporal traffic resilience dynamics into a destination choice model utilizing the available capacity of the overall network.We validate our model through a post-concert egress event.The results suggest that our method can reduce total egress times and average travel time by 20%-43%over the no-guidance condition.Our method can be used to estimate and quantify emergency conditions to optimally guide destinations and routing choice for evacuees and/or autonomously moving vehicles during evacuations.

Steady-state solution of traffic flow on a simple road network

The steady-state traffic flow on a simply circled road network is analytically studied using the Lighthill-Witham-Richards(LWR)model.The network is typically composed of a diverging and a merging junction together with three connected road sections.At the diverging junction,traffic flow is assigned to satisfy the user-equilibrium condition.At the merging junction,queuing or shock structures due to the bottleneck effect is taken into account.We indicate that the solution depends on the total number of vehicles on the road network,and that the bottleneck effect gives rise to not only capacity drop but inefficient utilization of the two road sections upstream the merging junction.To further validate the derived steady-state solution,a first-order Godunov scheme of the LWR model is adopted for simulation of traffic flow in each road section and the demand-supply concept is applied to provide boundary values at the junctions for the scheme.By varying the total number of vehicles from zero to the maximum,the simulation shows that a randomly distributed state of traffic flow is bound to evolve into a steady state,which is completely in agreement with the analytical solution.

Location Specific Cell Transmission Model for Freeway Traffic

This paper describes a location specific cell transmission model of freeway traffic based on the observed variability of fundamental diagrams both along and across freeway segments. This model extends the original cell transmission model （CTM） mechanism by defining various shapes of fundamental diagrams to reproduce more complex traffic phenomena, including capacity drops, lane-by-lane variations, nonho- mogeneous wave propagation velocities, and temporal lags. A field test on a Canadian freeway was used to demonstrate the validity of the location specific CTM. The simulated spatio-temporal evolutions of traffic flow show that the model can be used to describe the traffic dynamics near bottlenecks more precisely than the original model.