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).     

Considering various ALINEA ramp metering strategies for crash risk mitigation on freeways under congested regime

This study evaluates the expected benefits of using the ALINEA ramp metering algorithm as a method for real-time safety improvement on an urban freeway. The objective of this research is to use ramp metering to produce a significant decrease in the risk of crashes on the freeway while avoiding any significant adverse effects on operation. This is achieved by simulating the freeway during the congested period in micro-simulation and testing various ramp metering configurations to determine which provides the best results. Statistical measures developed for the same stretch of freeway using loop detector data are used to quantify the risk of crashes as well as the benefits in each of the alternative strategies. The study concludes that there are significant benefits in metering multiple ramps when the feedback ramp metering algorithm is implemented at multiple locations. It was found that increasing the number of metered on-ramps produces increasing safety benefits. Also, a shorter cycle length for each of the meters and a higher critical occupancy value leads to better results.     

Genetic algorithm-based simulation optimization of the ALINEA ramp metering system: a case study in Atlanta

ABSTRACT

This paper presents a case study of the optimal ALINEA ramp metering system model of a corridor of the metro Atlanta freeway. Based on real-world traffic data, this study estimates the origin-destination matrix for the corridor. Using a stochastic simulation-based optimization framework that combines a micro-simulation model and a genetic algorithm-based optimization module, we determine the optimal parameter values of a combined ALINEA ramp metering system with a queue flush system that minimizes total vehicle travel time. We found that the performance of ramp metering with optimized parameters, which is very sensitive possibly because bottlenecks are correlated, outperforms the no control model with its optimized parameters in terms of reducing total travel time.     

Observing freeway ramp merging phenomena in congested traffic

This work conducts a comprehensive investigation of traffic behavior and characteristics during freeway ramp merging under congested traffic conditions. On the Tokyo Metropolitan Expressway, traffic congestion frequently occurs at merging bottleneck sections, especially during heavy traffic demand. The Tokyo Metropolitan Expressway public corporation, generally applies different empirical strategies to increase the flow rate and decrease the accident rate at the merging sections. However, these strategies do not rely either on any behavioral characteristics of the merging traffic or on the geometric design of the merging segments. There have been only a few research publications concerned with traffic behavior and characteristics in these situations. Therefore, a three‐year study is undertaken to investigate traffic behavior and characteristics during the merging process under congested situations. Extensive traffic data capturing a wide range of traffic and geometric information were collected using detectors, videotaping, and surveys at eight interchanges in Tokyo Metropolitan Expressway. Maximum discharged flow rate from the head of the queue at merging sections in conjunction with traffic and geometric characteristics were analyzed. In addition, lane changing maneuver with respect to the freeway and ramp traffic behaviors were examined. It is believed that this study provides a thorough understanding of the freeway ramp merging dynamics. In addition, it forms a comprehensive database for the development and implementation of congestion management techniques at merging sections utilizing Intelligent Transportation System.     

Evaluation of forced flows on freeways with single‐loop detectors

This paper documents the development of a simple method for identifying and/or predicting freeway congestion using single loop detection systems. The proposed algorithm is simple and easy to incorporate into most freeway management systems. The Washington State Department of Transportation's Traffic Systems Management Center (TSMC) sponsored the original study. The investigation also led to a recommendation to replace the original TSMC definition of congestion or forced flow conditions with a more reliable indicator. Although, the TSMC has recently implemented a more advanced prediction system based on fuzzy set theory and neural networks to further identify patterns and rules for ramp metering strategies, the findings presented here continue to be constructive to freeway managers looking for quick and easy analyses that rely solely on single‐loop detection systems. The Seattle Area freeway study section used for the original study was the portion of mainline 1–5 northbound starting at the downtown Seattle Station 108 and ending at the Mountlake Terrace Station 193. Several days' worth of volume and lane‐occupancy data were collected for the afternoon time period from 2:30 p.m. to 6:30 p.m. Time intervals of 20 seconds were chosen for each data collection period. Important products of this research include the following:

• simple, and more reliable criterion for the definition of “bottleneck” or forced flow conditions than that originally used by the TSMC.
• simple, and reliable criterion for predicting impending “bottlenecks” or forced flow conditions.
• A proposed variable for improved selection of the appropriate metering rate. (Further analysis of the use of this variable for determining metering rates is recommended for future studies.

The proposed criteria are simple and easy to incorporate into current freeway management computer systems. Further investigation of freeway performance measurement using volume and occupancy data obtained from single‐loop systems is currently being performed.     

Stochasticity of freeway operational capacity and chance-constrained ramp metering

The notion of capacity is essential to the planning, design, and operations of freeway systems. However, in the practice freeway capacity is commonly referred as a theoretical/design value without consideration of operational characteristics of freeways. This is evident from the Highway Capacity Manual (HCM) 2000 in that no influence from downstream traffic is considered in the definition of freeway capacity. In contrast to this definition, in this paper, we consider the impact of downstream traffic and define freeway operational capacity as the maximum hourly rate at which vehicles can be expected to traverse a point or a uniform section of a roadway under prevailing traffic flow conditions. Therefore freeway operational capacity is not a single value with theoretical notion. Rather, it changes under different traffic flow conditions. Specifically, this concept addresses the capacity loss during congested traffic conditions. We further study the stochasticity of freeway operational capacity by examining loop detector data at three specifically selected detector stations in the Twin Cities’ area. It is found that values of freeway operational capacity under different traffic flow conditions generally fit normal distributions. In recognition of the stochastic nature of freeway capacity, we propose a new chance-constrained ramp metering strategy, in which, constant capacity value is replaced by a probabilistic one that changes dynamically depending on real-time traffic conditions and acceptable probability of risk determined by traffic engineers. We then improve the Minnesota ZONE metering algorithm by applying the stochastic chance constraints and test the improved algorithm through microscopic traffic simulation. The evaluation results demonstrate varying degrees of system improvement depending on the acceptable level of risk defined.     

Developing control strategies for freeway merging points under congested traffic situations using modeling and a simulation approach

This work focuses on developing a variety of strategies for alleviating congestion at freeway merging points as well as improving the safety of these points. On the Tokyo Metropolitan Expressway, traffic congestion frequently occurs at merging bottleneck sections, especially during heavy traffic demand. The Tokyo Metropolitan Expressway public corporation, generally applies different empirical strategies to increase the flow rate and decrease the accident rate at the merging sections. However, these strategies do not rely either on any behavioral characteristic of the merging traffic or on the geometric design of the merging segments. There have been only a few research publications concerned with traffic behavior and characteristics in these situations. Therefore, a three‐year extensive study has been undertaken to investigate traffic behavior and characteristics during the merging process under congested situations in order to design safer and less congested merging points as well as to apply more efficient control at these bottleneck sections. Two groups of strategies were investigated in this study. The First group was related to the traffic characteristics, and the second group to the geometric characteristics. In the first group, the control strategies related to closure of freeway and ramp lanes as well as lane‐changing maneuver restriction were investigated through a simulation program, detector data, and field experiment. In the second group, the angle of convergence of the ramp with the freeway in relation to merging capacity was analyzed using a simulation program. Results suggested the potential benefits of using proposed strategies developed in this work and can serve as initial guidance for the reduction of delay and improvement of safety under congested traffic conditions.     

Queue length estimation at metered freeway‐to‐freeway connectors

Freeway‐to‐freeway connector metering is a cost‐effective and proven freeway management strategy for relieving recurrent congestion. However, one of the critical challenges in design and operation of freeway‐to‐freeway connector metering is the lack of up‐to‐date queue storage length design guidance. In this study, it was found that ramp queue is dynamically related to the metering rate, on‐ramp demand, and traffic flow arrival pattern. Hence, simply using an average demand cannot provide accurate queue length estimation and is also not suitable for queue storage design where the maximum or a percentile queue length is generally used. A mesoscopic queue length simulation model was developed based on the input–output method for estimating queue lengths under various demand‐to‐capacity ratio scenarios. Simulation results indicate that for under‐saturated situations, the ramp queue may exist temporally due to the random short‐term surge of traffic arrivals, and the exponential function could best capture the relationship between queue length and demand‐to‐capacity ratio. For over‐saturated situations, the ramp queue tends to prolong linearly with the demand‐to‐capacity ratio. Based on the simulation, it was recommended that queue storage length be designed as 4.3% of on‐ramp demand when demand is lower than 1200 vph or 2.3% when demand is between 1200 and 2400 vph. Copyright © 2016 John Wiley & Sons, Ltd.     

Ramp meters on trial: Evidence from the Twin Cities metering holiday

Ramp meters in the Twin Cities have been the subject of a recent test of their effectiveness, involving turning them off for eight weeks. This paper analyzes the results with and without ramp metering for several representative freeways during the afternoon peak period. Seven performance measures: mobility, equity, productivity, consumers’ surplus, accessibility, travel time variation and travel demand responses are compared. It is found that ramp meters are particularly helpful for long trips relative to short trips. Ramp metering, while generally beneficial to freeway segments, may not improve trip travel times (including ramp delays). The reduction in travel time variation comprises another benefit from ramp meters. Non-work trips and work trips respond differently to ramp meters. The results are mixed, suggesting a more refined ramp control algorithm, which explicitly considers ramp delay, is in order.     

Evaluation of ramp control algorithms using microscopic traffic simulation

Ramp metering has emerged as an effective freeway control measure to ensure efficient freeway operations. A number of algorithms have been developed in recent years to ensure an effective use of ramp metering. As the performance of ramp metering depends on various factors (e.g. traffic volume, downstream traffic conditions, queue override policy etc), these algorithms should be evaluated under a wide range of traffic conditions to check their applicability and performance and to ensure their successful implementation. In view of the expenses of and confounding effects in field testing, simulation plays an important role in the evaluation of such algorithms. This paper presents an evaluation study of two ramp metering algorithms: ALINEA and FLOW. ALINEA is a local control algorithm and FLOW is an area wide coordinated algorithm. The purpose of the study is to use microscopic simulation to evaluate systematically how the level of traffic demand, queue spillback handling policy and downstream bottleneck conditions affect the performance of the algorithms. It is believed that these variables have complex interactions with ramp metering. MITSIM microscopic traffic simulator is used to perform the empirical study. The study consists of two stages. In the first stage, key input parameters for the algorithms were identified and calibrated. The calibrated parameters were then used for the second stage, where the performance of the algorithms were compared with respect to three traffic variables mentioned above using an orthogonal fraction of experiments. Regression analysis was used to identify the impacts of some of the interactions among experimental factors on the algorithms' performance, which is not otherwise possible with a tabular analysis. These results provide insights which may be helpful for design and calibration of more efficient ramp control algorithms.     

Efficiency and equity properties of freeway network-wide ramp metering with AMOC

The Advanced Motorway Optimal Control (AMOC) strategy for optimal freeway network-wide ramp metering is applied to the ring-road of Amsterdam, The Netherlands, in the aim of investigating some important and interesting problems arising in ubiquitous ramp metering systems. A number of suitably chosen scenarios along with a thorough analysis, interpretation, and suitable visualization of the obtained results provide a basis for the better understanding of some complex interrelationships of competing performance criteria. More precisely, the strategy’s efficiency and equity properties as well as their trade-off are studied and their partially competitive behaviour is discussed. This trade-off is implicitly addressed by the AMOC strategy through consideration of the available ramp storage space and may be used as a tool to establish a desired policy of the system’s efficiency versus equity.     

Congestion mechanism and demand adjustment strategies for double-cell system with bottlenecks

In this paper, ramp systems on the Beijing 3rd ring road are described as double-cell ramp systems with a bottleneck. By analyzing empirical data for the Beijing 3rd ring road, we found that the initial states have an important impact on the final convergence states of the ramp systems. Then, we studied the dynamic process of the ramp systems, determined the congestion mechanism, and then designed a ramp control method based on the obtained mechanism. Under a feasible demand, double-cell ramp systems exhibit two typical cases, including an upstream-bottleneck system (in which the bottleneck cell is upstream) and a downstream-bottleneck system (in which the bottleneck cell is downstream). Then, a cell transmission model is used to analyze the dynamic evolution processes, starting from different initial states, and determine the congestion mechanism for each case. It is proven that the two systems have different possible equilibrium sets and congestion mechanisms. In an upstream-bottleneck system, the downstream always converges to the uncongested equilibrium, while the upstream bottleneck cell may experience congestion under certain initial states. In a downstream-bottleneck system, the congestion starts downstream, and then gradually propagates upstream. Furthermore, based on the different congestion mechanisms, two demand adjustment strategies are proposed, which redistribute the stationary feasible demand. The simulation results indicate that both systems can converge to uncongested equilibriums after demand adjustment. The ramp demand adjustment methods provide a scientific basis for urban traffic system management.     

Will a higher free-flow speed lead us to a less congested freeway?

An approach based on cell transmission model (CTM) is proposed to estimate the impact of variable free-flow speeds (FFS) on the performance of a freeway system. Based on the basic CTM, four typical freeway control strategies consisting of non control, local ramp metering, coordinated ramp metering and global control are first formulated. Then the method of adjusting model parameters to the changed free-flow speeds is presented. Among the adjustments, an experimental function based on Fan and Seibold (2014) is proposed to change the jam density. Several useful measures are defined to estimate and compare the performances of different freeways. The following three main observations are obtained from numerical experiments. (a) With the gradually increasing FFS, the throughput of freeway will increase at the beginning and then change to decrease. (b) With the increasing FFS, the average delay of vehicles will decrease at the beginning and then change to increase. (c) A series of free-flow speeds associate with the best performance of freeway. These observations are theoretically analyzed through investigating the location and capacity of bottleneck. Study shows that in general the actual bottleneck capacity will increase at the beginning and then change to decrease with the continually increasing FFS. In view of the positive correlation between traffic delay and bottleneck capacity, the theoretical analysis confirms the numerical observations. The findings of this study can deepen the understanding of freeway systems and help management agents adopt proper measures to improve the performance of the whole system.     

Increasing the capacity of an isolated merge by metering its on-ramp

Measurements taken downstream of freeway/on-ramp merges have previously shown that discharge flow diminishes when a merge becomes an isolated bottleneck. By means of observation and experiment, we show here that metering an on-ramp can recover the higher discharge flow at a merge and thereby increase the merge capacity. Detailed observations were collected at a single merge using video. These data revealed that the reductions in discharge flow are triggered by a queue that forms near the merge in the freeway shoulder lane and then spreads laterally, as drivers change lanes to maneuver around slow traffic. Our experiments show that once restrictive metering mitigated this shoulder lane queue, high outflows often returned to the median lane. High merge outflows could be restored in all freeway lanes by then relaxing the metering rate so that inflows from the on-ramp increased. Although outflows recovered in this fashion were not sustained for periods greater than 13 min, the findings are the first real evidence that ramp metering can favorably affect the capacity of an isolated merge. Furthermore, these findings point to control strategies that might generate higher outflows for more prolonged periods and increase merge capacity even more. Finally, the findings uncover details of merge operation that are essential for developing realistic theories of merging traffic.     

Optimization of mainline traffic via an adaptive co-ordinated ramp-metering control model with dynamic OD estimation

Frequently implemented at freeway accesses to streamline traffic, ramp-metering control strategy is often implemented during rush hours in heavily congested areas. This paper presents a novel ramp-metering control model capable of optimizing mainline traffic by providing metering rates for accesses within the control segments. Based on Payne's continuum traffic stream model, a linear dynamic model with a quadratic objective function is constructed for integrated-responsive ramp-metering control. Incorporating on-line origin–destination (OD) estimation of co-ordinated interchanges into the proposed model increases efficiency of the control. In addition, an iterative algorithm is proposed to obtain the optimal solution. Simulation results demonstrate the robustness of the proposed model and its ability to streamline freeway traffic while avoiding traffic congestion.     

A Pareto-optimization approach for a fair ramp metering

This paper deals with a fair ramp metering problem which takes into account average travel delay distribution among on-ramps for an expressway system comprising expressways, on-ramps and off-ramps. A novel spatial equity index is defined to measure the evenness of travel delay distribution among on-ramps within the predefined on-ramp groups. An ideal fair ramp metering problem therefore aims to find an optimal dynamic ramp metering rate solution that not only minimizes the total system delay, but also maximizes the equity indexes associated to the groups. Some of these objectives, however, contradict with each other, and their Pareto-optimality is explored. The fair ramp metering problem proposed in this paper is formulated as a multiobjective optimization model incorporating a modified cell-transmission model (MCTM) that captures dynamic traffic flow pattern with ramp metering operations. The MCTM then is embedded in the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to solve the multiobjective optimization model. Finally, the Interstate I-210 W expressway-ramp network in the United States is adopted to assess the methodology proposed in this paper.     

Dynamic traffic assignment of cooperative adaptive cruise control

Advances in connected and automated vehicle technologies have resulted in new vehicle applications, such as cooperative adaptive cruise control (CACC). Microsimulation models have shown significant increases in capacity and stability due to CACC, but most previous work has relied on microsimulation. To study the effects of CACC on larger networks and with user equilibrium route choice, we incorporate CACC into the link transmission model (LTM) for dynamic network loading. First, we derive the flow-density relationship from the MIXIC car-following model of CACC (at 100% CACC market penetration). The flow-density relationship has an unusual shape; part of the congested regime has an infinite congested wave speed. However, we verify that the flow predictions match observations from MIXIC modeled in VISSIM. Then, we use the flow-density relationship from MIXIC in LTM. Although the independence of separate links restricts the maximum congested wave speed, for common freeway link lengths the congested wave speed is sufficiently high to fit the observed flows from MIXIC. Results on a freeway and regional networks (with CACC-exclusive lanes) indicate that CACC could reduce freeway congestion, but naïve deployment of CACC-exclusive lanes could cause an increase in total system travel time.     

The convergence of diagonalization algorithms for asymmetric network equilibrium problems

We provide a sufficient condition for the convergence of diagonalization algorithms for equilibrium traffic assignment problems with asymmetric Jacobian matrix B(v) of the link user cost mapping s(v) of the flow v. When

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, where D(v^*) > 0 is the diagonal of B(v^*) and v^* is the equilibrium flow, we demonstrate a local convergence theorem for nonlinear cost functions. The implication of this result for practical applications of the model are outlined.