Dynamics Of Traffic System Research Articles

Fractal dimensional analysis to reveal traffic flow dynamics as organic metabolism

As urban areas face rapid population and vehicle growth, understanding system dynamics is crucial for managing transportation congestion effectively. Utilizing fractal and metabolic concepts offers fresh perspectives on the behavior and efficiency of complex urban transportation systems. To understand the dynamics of congested traffic flows, we conducted fractal analysis on the traffic pattern in Seoul city with chronic congestion worldwide and investigated its potential for evaluating metabolic efficiency. Our rank and size fractal analysis revealed that Seoul's fractal dimension ranges from 6.7060 to 7.6801. The fractal dimension's curve, when plotted against traffic congestion, shows a peculiar symmetrical relationship. The linear correlation between fractal dimension and metabolic indicators suggests that fractal dimension could potentially serve as a novel metric for evaluating traffic flow efficiency. This study introduces new insights by integrating fractal and metabolic principles to understand traffic system dynamics, marking the first use of fractal analysis in traffic pattern evaluation.

Network-Wide Traffic Signal Control Using Bilinear System Modeling and Adaptive Optimization

This study proposes a new multi-input multi-output optimal bilinear signal control method in which a bilinear dynamic model approximation is used to capture the nonlinear dynamics of the urban traffic networks. With signal green time splits as the control input and traffic delay changes as the output for each intersections in the network, a bilinear system model was developed, which, on the basis of linear system modeling, takes interactions among traffic delays and signal timing splits into consideration. Based on the bilinear system modeling framework, we conducted two steps in each time interval to derive traffic control strategies: (1) we used the normalized least-squared algorithm to estimate system parameters; and (2) we solved an online optimization problem to obtain the updated traffic control inputs for the signal timing that minimizes future traffic delays. We evaluated the proposed method in a microscopic traffic simulation environment (VISSIM) with a 35-intersection network of Bellevue city in Washington. Two different traffic demand patterns: (1) normal traffic demands; and (2) time-varying traffic demands were simulated to compare the performance of different control strategies. Experimental results show that (1) the proposed bilinear system model can better describe traffic system dynamics than linear-model based methods, such as our previously developed linear-quadratic regulator control; and (2) the proposed method outperforms the state-of-the-art signal control strategies, namely the max-pressure and the self-organizing traffic light control methods. We have also shown that the proposed method is applicable to all other possible network layouts and signal controller phasing structures.

A meso-to-macro cross-resolution performance approach for connecting polynomial arrival queue model to volume-delay function with inflow demand-to-capacity ratio

• Cross-resolution modelling approach for understanding the dynamic relationship between demand and supply and the resulting congestion. • Describe oversaturated system dynamics with parsimonious macroscopic analytical formulations with consistent mesoscopic queue vehicular fluid model. • Unified integration of multi-scale models provides city planners with a valid analytical framework to analyze queue saturation evolution process. • Estimate key model parameters from real-world data sets on heavily congested corridors. Although the macroscopic volume-delay function (VDF) has been widely used in static traffic assignment for transportation planning, the planning community has long recognized its deficiencies as a static function in capturing traffic flow dynamics and queue evolution process. In the existing literature, many queueing-based and simulation-based dynamic traffic assignment (DTA) models involving various traffic flow parameters have been proposed to capture traffic system dynamics on different spatial scales; however, how to calibrate these DTA models could still be a challenging task in its own right, especially for real-world congested networks with complex traffic dynamics. By extending the fluid-based polynomial arrival queue (PAQ) model with quadratic inflow rates proposed by Newell (1982) and cubic inflow rates by Cheng et al. (2022), this paper attempts to propose a cross-resolution Queueing-based Volume-Delay Function (QVDF) to explicitly establish a coherent connection between (a) the macroscopic average travel delay performance function in a long-term planning horizon and (b) the mesoscopic dynamic queuing model during a single oversaturated period. By introducing two types of elasticity functional forms, this paper develops a relationship from the macroscopic inflow demand-to-capacity (D/C) ratio to the congestion duration of a bottleneck, from the congestion duration to the magnitude of speed reduction. The QVDF can be directly utilized to provide closed-form expressions for both average travel delay performance and the time-dependent speed profiles. The proposed cross-resolution QVDF provides a numerically reliable and theoretically rigorous performance function to characterize oversaturated bottlenecks at both macroscopic and mesoscopic scales.

A hierarchical MPC and sliding mode based two-level control for freeway traffic systems with partial demand information

In this paper a hierarchical two-level control scheme is proposed in order to solve a ramp metering problem in freeway traffic systems. The proposal combines a Model Predictive Control (MPC) based supervisor with decentralized low-level Sliding Mode Controllers (SMCs). The considered freeway METANET model describes the traffic system, which is naturally affected by uncertainties since the mainstream inflow, the traffic demands on the on-ramps, and the flows exiting the off-ramps are not a priori known. In the proposed scheme, two control loops are present. A centralized MPC computes the optimal control inputs by minimizing the total time spent by the vehicles in the traffic system on the basis of a nominal model of the considered freeway stretch. The computed optimal inputs are used to generate the corresponding density references for the low-level on-ramp controllers, which rely on a saturated version of the Suboptimal Second-Order Sliding Mode (SSOSM) control algorithm. SSOSM controllers allow to regulate the density error to zero in a finite time, thus reducing the mismatch between the controlled traffic system dynamics and the model used by the MPC supervisor during the optimization. A simulation study encompassing several realistic scenarios is reported to assess the validity of the proposed approach also in comparison with other classical traffic control strategies. As confirmed by simulation, in spite of the uncertainties, the proposed control scheme produces satisfactory performance in terms of both total time spent minimization and capacity drop alleviation.

Two-level hierarchical optimal control for urban traffic networks

A two-level hierarchical optimal control method is proposed in this paper. At the upper level, the reference signals (set-point) are optimized with a data-driven model-free adaptive control (MFAC) method. Traffic signals are regulated with the model predictive control (MPC) with the desired reference signals specified by the upper level. The main contribution is that the set-point optimization is addressed by using the MFAC method which does not need modeling of the traffic system dynamics. Moreover, through this scheme, the planning of vehicle distribution in a road network and the operation of traffic signal control can be executed simultaneously. The effectiveness of the proposed method is testified by an urban traffic network based on MATLAB and VISSIM 9.0 and is also demonstrated by the comparison results with the back-pressure traffic signal control and traditional MPC.

Effects of road network structure on the performance of urban traffic systems

Urban traffic system is important for the convenience and efficiency of people’s daily life. The understanding of inter-relations between urban street network and traffic flow can help the planning process of urban systems. Based on cellular automata modeling, this paper studies the influence of aspect ratio of a rectangular urban network on the dynamics of traffic system. The performance of road network is examined with the Macroscopic Fundamental Diagram (MFD). The maximal arrival rate and the critical density of congestion of MFD are investigated as two main indicators for system performance. Under the closed boundary condition, the square network shows the maximum arrival rate, but with a relatively lower critical density of congestion. With the increase of aspect ratio, the arrival rate decreases, while the critical congestion density increases. The phenomena can be explained by the vehicle distribution in the network, the left-turning and U-turning demand, and the average travel distance.

Bottom-up modeling approach and mesoscopic simulations in traffic system dynamics models

The application of system dynamics modeling in various domains enables its continuous development and improvement. Transportation systems are associated with a necessity to tame their complexity. Despite its potential, system dynamics as a specific methodological and modeling approach is implemented only occasionally and application to road transportation systems is sporadic. Existing studies focus mostly on a macroscopic level of modeling. Thus, this study demonstrates how system dynamics can develop and simulate models at the meso level. It is based on an unconventional bottom-up modeling approach grounded in the modeling of T-shaped, X-shaped, and roundabout crossroads as fundamental building blocks. Model modularity enables its extension to any type of road network with the required structure or complexity. Model applicability is verified by testing on a case study in real-life settings. Modeling issues associated with this modeling approach and application domain are explained and possible solutions proposed. By developing a bottom-up approach and mesoscopic simulations, this study brings uniqueness and a certain level of novelty into the realm of system dynamics and traffic transportation modeling and simulation.

Conformity and stability analysis of a modified spring–mass–damper system dynamics-based car-following model

Modeling the dynamics of a traffic system involves using the principles of both physical and social sciences since it is composed of vehicles as well as drivers. A novel car-following model is proposed in this paper by incorporating the socio-psychological aspects of drivers into the dynamics of a purely physics-based spring–mass–damper mechanical system to represent the driver–vehicle longitudinal movements in a traffic stream. The crux of this model is that a traffic system can be viewed as various masses interacting with each other by means of springs and dampers attached between them. While the spring and damping constants represent the driver behavioral parameters, the mass component represents the vehicle characteristics. The proposed model when tested for its ability to capture the traffic system dynamics both at micro, driver, and macro, stream, levels behaved pragmatically. The stability analysis carried out using perturbation method also revealed that the proposed model is both locally and asymptotically stable.

Recognizing Network Trip Patterns Using a Spatio-Temporal Vehicle Trajectory Clustering Algorithm

This paper presents a spatio-temporal trajectory clustering method for vehicle trajectories in transportation networks to identify heterogeneous trip patterns and explore underlying network assignment mechanisms. The proposed algorithm ST-TOPOSCAN is designed to consider both temporal and spatial information in trajectories. We adopt the time-dependent shortest-path distance measurement and take advantage of topological relations of a predefined network to discover the shared sub-paths among trajectories and construct the clusters. The proposed algorithm is implemented with a trajectory dataset obtained in the Chicago area. The results confirm the method’s ability to extract and generate spatio-temporal (sub-)trajectory clusters and identify trip patterns. Extensive numerical experiments verify the method’s performance and computational efficiency. Through spatio-temporal data mining, this paper contributes to exploring traffic system dynamics and advancing state-of-the-art spatio-temporal clustering for vehicle trajectories.

Dynamics in two-elevator traffic system with real-time information

Abstract We study the dynamics of traffic system with two elevators using a elevator choice scenario. The two-elevator traffic system with real-time information is similar to the two-route vehicular traffic system. The dynamics of two-elevator traffic system is described by the two-dimensional nonlinear map. An elevator runs a neck-and-neck race with another elevator. The motion of two elevators displays such a complex behavior as quasi-periodic one. The return map of two-dimensional map shows a piecewise map.

Performance Analysis of a Dynamic Bandwidth Allocation Algorithm for a Mixed Traffic TDMA Network

This paper considers a time-division multiple-access system that is designed for voice services and analyzes the effects of adding data services with a given bandwidth allocation protocol. This protocol stipulates priority for voice and movable traffic boundaries, and is unique in that it allocates slots at designated update-interval times. We develop a Markovian analytical model and use it to derive relevant system performance characteristics for voice and data traffic. In the analytical model, reserved and shared slots are separated, and therefore, frame compaction is not applied. We study the effects of reserved data slots on performance and determine the bandwidth available for the data, given a specified level of voice service. Additionally, we explore the optimum update interval that maximizes the data-capacity subject to the specified voice-traffic characteristics. Our analytical model provides a means for studying mixed traffic system dynamics, as well as the effects of different traffic types on the others' performance. It provides an approximation to the bandwidth allocation protocol that allows us to select system parameters without the need for lengthy simulation runs.

Technology, Human Interaction, and Complexity: Reflections on Vehicular Traffic Science

This paper is based on the second Philip McCord Morse Lecture given May 14, 1991, at the TIMS/ORSA Joint National Meeting in Nashville. It traces the author's involvement in the development of vehicular traffic science over the last 35 years. After some historical background, the paper discusses highlights of this work: developing and testing car-following theory, traffic theory for multilane highways, the behavior of traffic in towns, the relationship of trip decisions to traffic-system dynamics, and fuel consumption in urban areas. Throughout these discussions, particular attention is paid to the role of complexity and collective effects. The paper continues with comments on the importance of viewing traffic in the context of the overall infrastructure as well as its technology and environment. It concludes with some reflections on the state of the scientific enterprise in our society.