An improved cellular automata model for heterogeneous work zone traffic

This paper aims to develop an improved cellular automata (ICA) model for simulating heterogeneous traffic in work zone. The proposed ICA model includes the forwarding rules to update longitudinal speeds and positions of work zone vehicles. The randomization probability parameter used by the ICA is formulated as a function of the activity length, the transition length and the volumes of different types of vehicles traveling across work zone. Compared to the existing cellular automata models, the ICA model possesses a novel and realistic lateral speed and position updating rule so that the simulation of vehicle’s lateral movement in work zone is close to the reality. The ICA model is calibrated and validated microscopically and macroscopically by using the real work zone data. Comparisons of field data and ICA for trajectories, speed and speed–flow relationship in work zone show very close agreement. Finally, the proposed ICA model is applied to estimate traffic delay occurred in work zone.     

A high fidelity traffic simulation model based on cellular automata and car-following concepts

A high fidelity cell based traffic simulation model (CELLSIM) has been developed for simulation of high volume of traffic at the regional level. Straightforward algorithms and efficient use of computational resources make the model suitable for real time traffic simulation. The model formulation uses concepts of cellular automata (CA) and car-following (CF) models, but is more detailed than CA models and has realistic acceleration and deceleration models for vehicles. A simple dual-regime constant acceleration model has been used that requires minimal calculation compared to detailed acceleration models used in CF models. CELLSIM is simpler than most CF models; a simplified car-following logic has been developed using preferred time headway. Like CA models, integer values are used to make the model run faster. Space is discretized in small intervals and a new concept of percent space occupancy (SOC) is used to measure traffic congestion. CELLSIM performs well in congested and non-congested traffic conditions. It has been validated comprehensively at the macroscopic and microscopic levels using two sets of field data. Comparison of field data and CELLSIM for trajectories, average speed, density and volume show very close agreement. Statistical comparison of macroscopic parameters with other CF models indicates that CELLSIM performs as good as detailed CF models. Stability analyses conducted using mild and severe disturbances indicate that CELLSIM performs well under both conditions.     

Lane-harmonised passenger car equivalents for heterogeneous expressway traffic

In order to account for variations in traffic composition during traffic analysis, passenger car equivalent (PCE) factors are used to convert flow rates of various vehicle classes into flow rates in terms of passenger car units (PCUs). Earlier studies have developed various methods to estimate PCE values but only a few of them are based on uninterrupted traffic flow, particularly for flow regimes with heterogeneous traffic where differential (lower) speed limits are imposed on commercial vehicles. This paper proposes a lane-harmonisation approach, which leverages on the high variation in traffic composition across the lanes, to estimate PCE factors for urban expressways. Multiple linear regression is used and the PCE factors obtained for motorcycles, light goods vehicles, and heavy goods vehicles are 0.65, 1.53, and 2.75, respectively. The estimated capacity flow rate after the application of the obtained PCE factors is around 2200 PCUs per hour per lane.     

Empirical analysis of heterogeneous traffic flow and calibration of porous flow model

Heterogeneous traffic flow, characterized by a free inter-lane exchange, has become an important issue in addressing congestion in urban areas. It is of particular interest in many developing countries, that experience a strong increase in motorcycle use. New approaches to the heterogeneous non-lane-based flow have been proposed. However insufficient empirical verification has been made to estimate vehicle interaction, that is necessary for an accurate representation of mixed-flow conditions. In this paper, we focus on the porous flow approach to capture the complex interactions. The parameters from this approach are estimated from empirical observations. Video data was recorded and processed to capture vehicle interactions at a number of road sections in Surabaya City, Indonesia. The specific behavior of each vehicle in the traffic flow was captured by developing the pore size–density distributions, analyzing the class-specific critical pore sizes, and producing the class specific speed–density and flow–density diagrams. The results reveal how critical pore sizes are based on pore size–density distributions, the flow diagram for each vehicle class, and how traffic flow relationships for motorcyclists and the other vehicles exhibit significant differences. It is concluded that the proposed approach can represent the specific behavior of the motorcyclist in heterogeneous traffic flow, in both the situations of with- and without an exclusive lane for motorcycles, can clarify motorcyclist’s behavior in terms of passenger car unit of motorcycle, and can therefore support policy making on the improvement of urban transport.     

Inhomogeneous cellular automata modeling for mixed traffic with cars and motorcycles

This paper develops inhomogeneous cellular automata models to elucidate the interacting movements of cars and motorcycles in mixed traffic contexts. The car and motorcycle are represented by non‐identical particle sizes that respectively occupy 6×2 and 2×1 cell units, each of which is 1.25×1.25 meters. Based on the field survey, we establish deterministic cellular automata (CA) rules to govern the particle movements in a two‐dimensional space. The instantaneous positions and speeds for all particles are updated in parallel per second accordingly. The deterministic CA models have been validated by another set of field observed data. To account for the deviations of particles' maximum speeds, we further modify the models with stochastic CA rules. The relationships between flow, cell occupancy (a proxy of density) and speed under different traffic mixtures and road (lane) widths are then elaborated.     

Modelling a signal controlled traffic stream using cellular automata

Cellular automata models have formed the theory for the development of several transportation models to simulate various types of elements such as vehicles, pedestrians or even railway traffic. Furthermore, they have been applied to simulate several scenarios from very simple (freeway traffic) to rather complicated ones (lane reduction and signal optimisation). However, the properties of the model when used to simulate a signal controlled traffic stream have not been dealt with in great detail. This paper discusses several issues that arise while using the model for the simulation of traffic at signalised intersections. It also investigates the relationships between the randomisation parameter of the model, the model dynamics and the estimated saturation flow. For the deterministic version of the model, the formulas describing traffic quantities at the intersection are derived and are dependent on the desired speed – a parameter of the model. For the stochastic version, one can adopt several different approaches for the application of the randomisation rule, depending on the simulation needs.     

Estimating link travel time functions for heterogeneous traffic flows on freeways

Oversized vehicles, such as trucks, significantly contribute to traffic delays on freeways. Heterogeneous traffic populations, that is, those consisting of multiple vehicles types, can exhibit more complicated travel behaviors in the operating speed and performance, depending on the traffic volume as well as the proportions of vehicle types. In order to estimate the component travel time functions for heterogeneous traffic flows on a freeway, this study develops a microscopic traffic‐simulation based four‐step method. A piecewise continuous function is proposed for each vehicle type and its parameters are estimated using the traffic data generated by a microscopic traffic simulation model. The illustrated experiments based on VISSIM model indicate that (i) in addition to traffic volume, traffic composition has significant influence on the travel time of vehicles and (ii) the respective estimations for travel time of heterogeneous flows could greatly improve their estimation accuracy. Copyright © 2016 John Wiley & Sons, Ltd.     

A stochastic model for highway traffic

A nonlinear model for unidirectional flow of heavy traffic on a two-lane highway is considered. Features such as entrance, exit and lane transfer with time-dependent parameters are incorporated into the model, with the result that a number of previous models employed in the study of traffic flow become special cases of ours. Using the method of system-size expansion, an asymptotic analysis of the problem, including the time evolution of both deterministic and stochastic aspects of the traffic system, is carried out. In addition, a scheme for obtaining the moments of the probability distribution for systems of finite size is developed and a comparison is made with the exact results appropriate to a particular model. The agreement between the two sets of results turns out to be remarkably good.     

Effect of road width and traffic volume on vehicular interactions in heterogeneous traffic

Highway traffic flow phenomena involve several complex and stochastic variables with high interdependencies. The variations in roadway, traffic and environmental factors influence the traffic flow quality significantly. Capacity analysis of road sections under different traffic and geometric conditions need to quantify the vehicles of widely varying characteristics to a common and universally acceptable unit. Passenger car unit (PCU) is the universally adopted unit of traffic volume, keeping the passenger car as the ‘standard vehicle’ with reference to its static and dynamic characteristics; other vehicles are expressed to its equivalent number in terms of PCUs. The studies carried out in this aspect represent the dynamic nature of impedance caused by a vehicle while moving through a traffic stream. The PCU values recommended by the Highway Capacity Manual are widely applied in many countries; however, their applicability is highly under debate because of the variations in prevailing local traffic conditions. There are several factors that influence the PCU values such as traffic, roadway, vehicle, environmental and control conditions, etc. Apart from vehicular characteristics, the other two major factors that influence the PCU of vehicles are the following: (i) road width and (ii) traffic volume. In this study, estimation of PCU values for the different types of vehicles of a highly heterogeneous traffic on 7.5‐ and 11.0‐m‐wide roads, using micro‐simulation technique, has been dealt with. It has been found that the PCU value of a vehicle type varies significantly with variation in road width and traffic volume. The results of the study indicate that the PCU values are significantly influenced by the said two factors. Copyright © 2012 John Wiley & Sons, Ltd.     

Hierarchical perimeter control with guaranteed stability for dynamically coupled heterogeneous urban traffic

Perimeter control based on the Macroscopic Fundamental Diagram (MFD) is widely developed for alleviating or postponing congestion in a protected region. Recent studies reveal that traffic conditions might not be improved if the perimeter control strategies are applied to unstable systems where high demand generates heavy and heterogeneously distributed traffic congestion. Therefore, considering stability of the targeted traffic system is essential, for the sake of developing a feasible and then optimal control strategy. This paper sheds light on this direction. It integrates a stability characterization algorithm of MFD system equations into the Model Predictive Control (MPC) scheme, and features respectively an upper and a lower bound of the feasible control inputs, to guarantee system stability. Firstly, the dynamics of traffic heterogeneity and its effect on the MFD are analyzed, using real data from Guangzhou in China. Piecewise affine functions of average flow are proposed to capture traffic heterogeneity in both regional and subregional MFDs. Secondly, stability of a three-state two-region system is investigated via stable equilibrium and surface boundaries analysis. Finally, a three-layer hierarchical control strategy is introduced for the studied two-region heterogeneous urban networks. The first layer of the controller calculates the stable surface boundaries for the given traffic demands and then determines the bounds of control input (split rate). An MPC approach in the second layer is used to solve an optimization problem with two objectives of minimizing total network delay and maximizing network throughput. Heterogeneity among the subregions is minimized in the last layer by implementing simultaneously a subregional perimeter flow control and an internal flow control. The effectiveness and stability of the proposed control approach are verified by comparison with four existing perimeter control strategies.     

Modeling time mean speed and space mean speed for heterogeneous traffic conditions

This paper analyzes vehicular speeds at a micro level and studies the relationships between the important elements of speed, namely space mean speed (SMS) and time mean speed (TMS) under heterogeneous traffic conditions. Vehicular speed data were collected at selected road stretches around Delhi, India, in an attempt to understand and model the type of relationships between SMS and TMS under heterogeneous traffic conditions. To demonstrate the superiority of the proposed models, comparisons are made with existing traditional models. The results reveal that the proposed models are consistent in predicting speeds with high accuracy.     

Parameter estimation for the peak traffic model

In a previous article a model was developed for predicting the temporal distribution of peak traffic demand, and the model is sensitive to the determining cost parameters whose values were not known. These costs are the cost to late and early arrivals at work and the cost to delays in the system while travelling. In this paper, using the method of least squares, representative values for these cost parameters are estimated for both the Southbound and Northbound traffic using the Sydney Harbour Bridge during the morning peak period. The resulting estimates show that a traveller tends to attach much higher cost to delays than to earliness or lateness to work; although the relative cost he attaches to lateness is higher than he attaches to earliness.     

Quantifying traveler information provision in dynamic heterogeneous traffic networks

Information is effectively the same as a change in uncertainty perceived by an observer. This paper adopts the strict definition of information from Shannon’s Information Theory and provides procedures for quantifying effective provision of traveler information, considering it to be equivalent to the change of perceived uncertainty. The proposed method combines a cognitive grouping theory and an information learning scheme at an individual’s level to evaluate the dynamic information provision in the unit of a bit. Such numerical quantification can be meaningful in evaluating alternatives with more fine-grained information provision strategies and understanding their equity impact. Quantifying information in a manner consistent with Information Theory also provides a ‘shared language’ that facilitates more constructive discussion among stakeholders from different backgrounds. The case study is conducted on a heterogeneous dynamic traffic network near Downtown Los Angeles for evaluating different alternatives of a proposed dynamic message board in terms of its location and dynamic content.     

Train routing and timetabling problem for heterogeneous train traffic with switchable scheduling rules

This paper proposes a mathematical model for the train routing and timetabling problem that allows a train to occasionally switch to the opposite track when it is not occupied, which we define it as switchable scheduling rule. The layouts of stations are taken into account in the proposed mathematical model to avoid head-on and rear-end collisions in stations. In this paper, train timetable could be scheduled by three different scheduling rules, i.e., no switchable scheduling rule (No-SSR) which allows trains switching track neither at stations and segments, incomplete switchable scheduling rule (In-SSR) which allows trains switching track at stations but not at segments, and complete switchable scheduling rule (Co-SSR) which allows trains switching track both at stations and segments. Numerical experiments are carried out on a small-scale railway corridor and a large-scale railway corridor based on Beijing–Shanghai high-speed railway (HSR) corridor respectively. The results of case studies indicate that Co-SSR outperforms the other two scheduling rules. It is also found that the proposed model can improve train operational efficiency.     

Capacity-constrained traffic forecasting model

Projecting future traffic is an important stage in any traffic and transportation planning study. Accurate traffic forecasting is vital for transportation planning, highway safety evaluation, traffic operations analysis, and geometric and pavement design among others. In view of its importance, this paper introduces a regression-based traffic forecasting methodology for a one dimensional capacity-constrained highway. Five different prediction functions are tested; the best was selected according to the accuracy of projections against historical traffic data. The three-parameter logistic function produced more accurate projections compared to other functions tested when highway capacity constraints were taken into consideration. The R ² values at various test locations ranged from 88% to 98%, indicating good prediction capability. Using the Fisher's information matrix approach, the t-statistic test showed all parameters in the logistic function were highly statistically significant. To evaluate reliability of projections, predictive intervals were calculated at a 95% level of confidence. Predictions using the logistic function were also compared to those predicted using the compound growth rate and linear regression methods. The results show that the proposed methodology generates much more reasonable projections than current practices.     

Efficient dispatching rules on double tracks with heterogeneous train traffic

The most natural and popular dispatching rule for double-track segments is to dedicate one track for trains traveling in one direction. However, sometimes passenger trains have to share some portions of the railway with freight trains and passenger trains are traveling faster and faster nowadays. The major drawback of this dedicated rule is that a fast train can be caught behind a slow train and experience significant knock-on delay. In this paper, we propose a switchable dispatching policy for a double-track segment. The new dispatching rule enables the fast train to pass the slow train by using the track traveled by trains in the opposite direction if the track is empty. We use queueing theory techniques to derive the delay functions of this policy. The numerical experiments show that a switchable policy can reduce the fast train knock-on delay by as high as 30% compared to a dedicated policy. When there are crossovers at the middle of the double-track segment, our proposed switchable policy can reduce the delay of the fast trains by as high as 65%.     

Modeling the interactions between car and bicycle in heterogeneous traffic

In this paper, a new cellular automata model is proposed to simulate the car and bicycle heterogeneous traffic on urban road. To capture the complex interactions between these two types of vehicles, a novel occupancy rule is adopted in the proposed model to consider the variable lateral distances of mixed vehicular traffic. Based on massive simulations, microscopic fundamental diagrams under different bicycle densities are devised. With these, the bicycle's spilling behavior is then investigated and discussed. In order to reflect the interference of a bicycle on a car, the interference transformation from friction state to block state is modeled explicitly. Finally, different simulation results under different occupancy rules indicate that the constant and fixed occupancy rule adopted in the previous studies might lead to overestimation of car flux in the heterogeneous traffic flows with different bicycle densities. Copyright © 2013 John Wiley & Sons, Ltd.     

Real-time traffic state estimation in urban corridors from heterogeneous data

In recent years, rapid advances in information technology have led to various data collection systems which are enriching the sources of empirical data for use in transport systems. Currently, traffic data are collected through various sensors including loop detectors, probe vehicles, cell-phones, Bluetooth, video cameras, remote sensing and public transport smart cards. It has been argued that combining the complementary information from multiple sources will generally result in better accuracy, increased robustness and reduced ambiguity. Despite the fact that there have been substantial advances in data assimilation techniques to reconstruct and predict the traffic state from multiple data sources, such methods are generally data-driven and do not fully utilize the power of traffic models. Furthermore, the existing methods are still limited to freeway networks and are not yet applicable in the urban context due to the enhanced complexity of the flow behavior. The main traffic phenomena on urban links are generally caused by the boundary conditions at intersections, un-signalized or signalized, at which the switching of the traffic lights and the turning maneuvers of the road users lead to shock-wave phenomena that propagate upstream of the intersections. This paper develops a new model-based methodology to build up a real-time traffic prediction model for arterial corridors using data from multiple sources, particularly from loop detectors and partial observations from Bluetooth and GPS devices.     

Stochastic adaptive control model for traffic signal systems

An adaptive control model of a network of signalized intersections is proposed based on a discrete-time, stationary, Markov decision process. The model incorporates probabilistic forecasts of individual vehicle actuations at downstream inductance loop detectors that are derived from a macroscopic link transfer function. The model is tested both on a typical isolated traffic intersection and a simple network comprised of five four-legged signalized intersections, and compared to full-actuated control. Analyses of simulation results using this approach show significant improvement over traditional full-actuated control, especially for the case of high volume, but not saturated, traffic demand.     

Distributed model predictive control for railway traffic management

Every day small delays occur in almost all railway networks. Such small delays are often called “disturbances” in literature. In order to deal with disturbances dispatchers reschedule and reroute trains, or break connections. We call this the railway management problem. In this paper we describe how the railway management problem can be solved using centralized model predictive control (MPC) and we propose several distributed model predictive control (DMPC) methods to solve the railway management problem for entire (national) railway networks. Furthermore, we propose an optimization method to determine a good partitioning of the network in an arbitrary number of sub-networks that is used for the DMPC methods. The DMPC methods are extensively tested in a case study using a model of the Dutch railway network and the trains of the Nederlandse Spoorwegen. From the case study it is clear that the DMPC methods can solve the railway traffic management problem, with the same reduction in delays, much faster than the centralized MPC method.