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.     

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.     

A novel approach for assessing the LOS for two‐lane intercity highways under heterogeneous traffic conditions

Performance of two‐lane intercity highways has been evaluated in terms of level of service (LOS) by different researchers. Different follower‐related performance measures, namely, the number of followers (NF), percent followers (PF), follower density (FD) and the number of followers as a proportion of capacity (NFPC) are examined in the present study to define LOS. Data are collected from five sites located in different parts of India. While almost all the past studies used 3‐s headway rule to identify followers suggested by US Highway Capacity Manual, a new methodology is proposed in the current study to identify the followers by analysing speed difference (SD) and the gap between two consecutive vehicles. It is observed that vehicles travel in non‐following condition after a critical gap threshold value of 10 s. By using a SD limit of ?4 km/h to +10 km/h and a gap value of 10 s, followers are identified across all the study sites. Thereafter, different critical gap values ranging from 1.9 s to 4.3 s are observed at the study sites beyond which the probability of not following would increase. Variation in two‐way traffic volume is found to be the main contributory factor which affects the critical gap values. Among all of the performance measures, NFPC shows a strong correlation with two‐way traffic volume followed by FD under heterogeneous traffic condition. Finally, different threshold values of LOS ranges for two‐lane intercity highways are provided by carrying out cluster analysis with the help of NFPC and FD. Copyright © 2017 John Wiley & Sons, Ltd.     

Developing passenger car equivalents for heavy vehicles on freeways during queue discharge flow

This paper investigates the hypothesis that the effect of heavy vehicles on traffic is greater during congestion than during undersaturated conditions. A new approach was developed to quantify this effect by deriving passenger car equivalents (PCEs) using queue discharge flow (QDF) capacity as the equivalency criterion. This approach is based on the premise that QDF capacity observations can be expected to show minimal variation if traffic stream was uniform and consisted of passenger cars only. Two sites in Ontario, Canada were used for this research. The first is located at an entrance ramp merge area and the second at a long-term freeway reconstruction zone. Nonlinear programming was utilized to perform optimizations on a number of data sets at each site. Results strongly suggest that the research hypothesis is true and that the approach developed by this research is both plausible and feasible. The mean PCE factor at the first site was 2.36 versus 1.5 in the Highway Capacity Manual (HCM) 2000. At the second site, the mean PCE factors in the two directions of travel were 3.21 and 2.7 versus 2.0 in the HCM 2000. Results also showed that the PCE factor developed from the optimization runs behaves as a random variable that generally follows the normal distribution. Furthermore, the PCE factor was neither a function of weather conditions nor of roadside maintenance work.     

Evacuation traffic dynamics

Historically, evacuation models have relied on values of road capacity that are estimated based on Highway Capacity Manual methods or those observed during routine non-emergency conditions. The critical assumption in these models is that capacity values and traffic dynamics do not differ between emergency and non-emergency conditions. This study utilized data collected during Hurricanes Ivan (2004), Katrina (2005) and Gustav (2008) to compare traffic characteristics during mass evacuations with those observed during routine non-emergency operations. From these comparisons it was found that there exists a consistent and fundamental difference between traffic dynamics under evacuation conditions and those under routine non-emergency periods. Based on the analysis, two quantities are introduced: “maximum evacuation flow rates” (MEFR) and “maximum sustainable evacuation flow rates” (MSEFR). Based on observation, the flow rates during evacuations were found to reach a maximum value of MEFR followed by a drop in flow rate to a MSEFR that was able to be sustained over several hours, or until demand dropped below that necessary to completely saturate the section. It is suggested that MEFR represents the true measure of the “capacity”. These findings are important to a number of key policy-shaping factors that are critical to evacuation planning. Most important among these is the strong suggestion of policy changes that would shift away from the use of traditional capacity estimation techniques and toward values based on direct observation of traffic under evacuation conditions.     

Model for the capacity of the urban signal intersection with work zone

Work zones exist widely on urban arterials in the cities that are undergoing road construction or maintenance. However, the existing studies on arterial work zones are very limited, especially on the work zones at urban intersections, although they have a severe negative impact on the urban traffic system. For the first time, this study focuses on how work zones reduce intersection capacity. A type of widely observed work zone, the straddling work zone that straddles on a road segment and an intersection, is studied. A linear regression model and a multiplicative model suggested by Highway Capacity Manual are proposed respectively to determine the saturation flow rate of the signal intersection with the straddling work zone. The data of 22 straddling work zones are collected and used to evaluate the performances of the proposed models. The results display that the linear regression model outperforms the multiplicative model suggested by Highway Capacity Manual. The study also reveals that reducing approach (or exit) lanes and the mixture of motor vehicles and non‐motor vehicles (and pedestrians) can significantly decrease the capacity of the intersection with straddling work zone. Therefore, in setting a straddling work zone, workers should try to ensure that the intersection approach and exit are unobstructed and set a separation for non‐motors and pedestrians to avoid mixed traffic flow. Copyright © 2016 John Wiley & Sons, Ltd.     

Modification of the Highway Capacity Manual two‐lane highway analysis procedure for Spanish conditions

The US Highway Capacity Manual (HCM) methodology is used in Spain to evaluate traffic operation and quality of service. The effect of passing manoeuvre on two‐lane highway operational performance is considered through adjustment factors to average travel speeds and percent time spent following. The procedure is largely based on simulations in TWOPAS and passing behaviours observed during US calibrations in the 1970s. It is not clear whether US driving behaviour and vehicles' performance are comparable with Spanish conditions. The objective of this research is to adapt the HCM 2010 methodology to Spanish driver behaviour, for base conditions (i.e. no passing restrictions). To do so, TWOPAS was calibrated and validated based on current Spanish passing field data. The calibration used a genetic algorithm. The case study included an ideal two‐lane highway with varying directional traffic flow rate, directional split and percentage of trucks. The updated methodology for base conditions is simpler than the current HCM 2010 and does not rely on interpolation from tables. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison of fuzzy logic and artificial neural networks approaches in vehicle delay modeling

Modeling vehicle delay has been an interesting subject for traffic engineers and urban planners. Determination of vehicle delay is a complex task and the delay is influenced by many variables that have uncertainties and vagueness, especially for non-uniform or over-saturated conditions. In this study, vehicle delay is modeled using new approaches such as Fuzzy Logic (FL) and Artificial Neural Networks (ANN) to deal with all conditions. The Neuro Fuzzy Delay Estimation (NFDE) model and Artificial Neural Networks Delay Estimation (ANNDE) model are developed. The overall delay data required for the model were collected from ten signalized intersections in Turkey. The results of the developed models are compared with the Highway Capacity Manual (HCM), Akçelik’s methods and the delay data collected from intersections. The results showed that delay estimations by the ANNDE and NFDE model are promising. It is also inferred that the NFDE model results are the best fitted. The Average Relative Error (ARE) rates of NFDE model are determined as 7% for under-saturated and 5% for over-saturated conditions. The results reflect the fact that the neuro-fuzzy approach may be used as a promising method in vehicle delay estimation.     

Identification of freeway crash-prone traffic conditions for traffic flow at different levels of service

The primary objective of this study was to evaluate the risks of crashes associated with the freeway traffic flow operating at various levels of service (LOS) and to identify crash-prone traffic conditions for each LOS. The results showed that the traffic flow operating at LOS E had the highest crash potential, followed by LOS F and D. The traffic flow operating at LOS B and A had the lowest crash potential. For LOS A and B, the vehicle platoon and abrupt change in vehicle speeds were major contributing factors to crash occurrences. For LOS C, crash risks were correlated with lane-change maneuvers, speed variation, and small headways in traffic. For LOS D, crash risks increased with an increase in the temporal change in traffic flow variables and the frequency of lane-change maneuvers. For LOS E, crash risks were mainly affected by high traffic volumes and oscillating traffic conditions. For LOS F, crash risks increased with an increase in the standard deviation of flow rate and the frequency of lane-change maneuvers. The findings suggested that the mechanism of crashes were quite different across various LOS. A Bayesian random-parameters logistic regression model was developed to identify crash-prone traffic conditions for various LOS. The proposed model significantly improved the prediction performance as compared to the conventional logistic regression model.     

Development of a delay model for unsignalized intersections applicable to traffic assignment

Abstract

This paper develops a model for estimating unsignalized intersection delays which can be applied to traffic assignment (TA) models. Current unsignalized intersection delay models have been developed mostly for operational purposes, and demand detailed geometric data and complicated procedures to estimate delay. These difficulties result in unsignalized intersection delays being ignored or assumed as a constant in TA models.

Video and vehicle license plate number recognition methods are used to collect traffic volume data and to measure delays during peak and off-peak traffic periods at four unsignalized intersections in the city of Tehran, Iran. Data on geometric design elements are measured through field surveys. An empirical approach is used to develop a delay model as a function of influencing factors based on 5- and 15-min time intervals. The proposed model estimates delays on each approach based on total traffic volumes, rights-of-way of the subject approach and the intersection friction factor. The effect of conflicting traffic flows is considered implicitly by using the intersection friction factor. As a result, the developed delay model guarantees the convergence of TA solution methods.

A comparison between delay models performed using different time intervals shows that the coefficients of determination, R ², increases from 43.2% to 63.1% as the time interval increases from 5- to 15-min. The US Highway Capacity Manual (HCM) delay model (which is widely used in Iran) is validated using the field data and it is found that it overestimates delay, especially in the high delay ranges.     

Methodology for the qualitative evaluation of pedestrian crossings at road junctions with traffic lights

The aim of this work is to test the application of a method for making a qualitative evaluation of pedestrian crossings, based on the methodology of Khisty (Transportation Research Record 1438:45–50, 1994). The study identifies the Performance Measures (Comfort, Safety, System Continuity), with their respective attributes (waiting time, space available while waiting to cross, number of pedestrians, one-way or two-way street, state of the road surface, road width, vehicle speed, visibility, lighting conditions, guardrails, absence of obstacles in vicinity, state of sidewalks, lowered kerb, pedestrian signals, central island), which may be utilized in the evaluation. The first step was to ascertain the relative importance, from the point of view of the pedestrian, of the Performance Measures employed. Then the level-of-service (LOS), as perceived by the users, was determined for each of the pedestrian crossings in the survey, on the basis of the users’ level of satisfaction with each attribute. Khisty’s methodology makes it possible to relate the overall level of satisfaction with a qualitative LOS for the pedestrian facility under analysis. The chosen methodology was adapted to the Brazilian context, in a case study carried out in the city of São Paulo (Brazil), in collaboration with the local Traffic Engineering Corporation (Companhia de Engenharia de Tráfego, CET-SP). To this end, four pedestrian crossings at road junctions with traffic lights were analysed. The qualitative LOS obtained were compared to the quantitative LOS, calculated according to the Highway Capacity Manual (TRB 2000).     

A simulation-based approach in determining permitted left-turn capacities

A fundamental objective of traffic signal operations is the development of phasing plans that reduce delays while maintaining a high level of safety. One issue of concern is the treatment of left-turn phasing, which can operate as a protected movement, a permitted movement yielding to conflicting traffic, a combination protected–permitted movement or as a split-phase intersection. While protected-only movements can improve safety for the turning movement, they can also increase delays and congestion at the intersection. Most states maintain independent guidance for determining left-turn phasing; however, the most common identified guidance for protected left-turn phases is using a threshold based on the cross product of the left-turn volume and opposing through movements. The use of the cross product has been questioned recently as an indicator for determining phase selection. Based on simulation analysis within this research, the cross product is shown to be a poor indicator of left-turn capacity and congestion at the intersection.This research proposes a simplified single variable exponential model to determine left-turn capacity based on opposing volume and percent green time to determine left-turn capacity thresholds for protected left-turn phasing. The model is developed based on observed capacity from 450 VISSIM microsimulation scenarios which evaluated varying opposing volume, opposing number of lanes, cycle lengths and green time splits. Validation of the model based on complex Highway Capacity Manual procedures, indicates that the proposed model provides similar correlation to observed capacities. Finally, a nomograph is developed which presents the model in a simple form for interpretation and application by practicing traffic engineers, when required to determine left-turn phasing options. This procedure allows simple determination based on minimum input data needs similar to the cross product determination, without the need for complex hand calculations or computing requirements of the Highway Capacity Manual.     

An exact modelling of the uniform control traffic delay in undersaturated signalized intersections

The average delay experienced by vehicles at a signalized intersection defines the level of service (LOS) at which the intersection operates. A major challenge in this regard is the ability to accurately estimate all the components underlying the overall control delay, including the uniform, incremental and initial queue delays. This paper tackles this challenging task by proposing a novel exact model of the uniform control delay component with a view to enhancing the accuracy of the existing approximate models, notably, the one reported in the Highway Capacity Manual 2010. Both graphical and analytical proofs are employed to derive exact closed‐form expressions for the uniform control delay at undersaturated signalized intersections. The high degree of accuracy of the proposed models is analysed through extensive simulations to demonstrate their abilities to exactly characterize the performance of real‐life intersections in terms of the resulting vehicle delay. Unlike the existing widely adopted uniform delay models, which tend to overestimate the LOS of real‐life intersections, the delay models introduced in this paper have the merit of exactly capturing such a LOS. Copyright © 2016 John Wiley & Sons, Ltd.     

Path flow estimator for planning applications in small communities

This paper presents an alternative planning framework to model and forecast network traffic for planning applications in small communities, where limited resources debilitate the development and applications of the conventional four-step travel demand forecasting model. The core idea is to use the Path Flow Estimator (PFE) to estimate current and forecast future traffic demand while taking into account of various field and planning data as modeling constraints. Specifically, two versions of PFE are developed: a base year PFE for estimating the current network traffic conditions using field data and planning data, if available, and a future year PFE for predicting future network traffic conditions using forecast planning data and the estimated base year origin–destination trip table as constraints. In the absence of travel survey data, the proposed method uses similar data (traffic counts and land use data) as a four-step model for model development and calibration. Since the Institute of Transportation Engineers (ITE) trip generation rates and Highway Capacity Manual (HCM) are both utilized in the modeling process, the analysis scope and results are consistent with those of common traffic impact studies and other short-range, localized transportation improvement programs. Solution algorithms are also developed to solve the two PFE models and integrated into a GIS-based software called Visual PFE. For proof of concept, two case studies in northern California are performed to demonstrate how the tool can be used in practice. The first case study is a small community of St. Helena, where the city’s planning department has neither an existing travel demand model nor the budget for developing a full four-step model. The second case study is in the city of Eureka, where there is a four-step model developed for the Humboldt County that can be used for comparison. The results show that the proposed approach is applicable for small communities with limited resources.     

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).     

Modeling the effects of traveler information on freeway origin–destination demand prediction

The primary focus of this research is to develop an approach to capture the effect of travel time information on travelers’ route switching behavior in real-time, based on on-line traffic surveillance data. It also presents a freeway Origin–Destination demand prediction algorithm using an adaptive Kalman Filtering technique, where the effect of travel time information on users’ route diversion behavior has been explicitly modeled using a dynamic, aggregate, route diversion model. The inherent dynamic nature of the traffic flow characteristics is captured using a Kalman Filter modeling framework. Changes in drivers’ perceptions, as well as other randomness in the route diversion behavior, have been modeled using an adaptive, aggregate, dynamic linear model where the model parameters are updated on-line using a Bayesian updating approach. The impact of route diversion on freeway Origin–Destination demands has been integrated in the estimation framework. The proposed methodology is evaluated using data obtained from a microscopic traffic simulator, INTEGRATION. Experimental results on a freeway corridor in northwest Indiana establish that significant improvement in Origin–Destination demand prediction can be achieved by explicitly accounting for route diversion behavior.     

An observed traffic pattern in long freeway queues

A simple exercise in data analysis showed that, in queued traffic, a well-defined relation exists between the flow on a homogeneous freeway segment and the segment’s vehicle accumulation. The exercise consisted of constructing cumulative vehicle arrival curves to measure the flows and densities on multiple segments of a queued freeway. At this particular site, each interchange enveloped by the queue exhibited a higher on-ramp flow than off-ramp flow and as a consequence, motorists encountered a steady improvement in traffic conditions (e.g., reduced densities and increased speeds) as they traveled from the tail of the queue to the bottleneck. This finding has practical implications for freeway traffic planning and management. Perhaps most notably, it suggests that the first-order hydrodynamic theory of traffic is adequate for describing some of the more relevant features of queue evolution. This and other practical issues are discussed in some detail.     

Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment

The paper proposes a first-order macroscopic stochastic dynamic traffic model, namely the stochastic cell transmission model (SCTM), to model traffic flow density on freeway segments with stochastic demand and supply. The SCTM consists of five operational modes corresponding to different congestion levels of the freeway segment. Each mode is formulated as a discrete time bilinear stochastic system. A set of probabilistic conditions is proposed to characterize the probability of occurrence of each mode. The overall effect of the five modes is estimated by the joint traffic density which is derived from the theory of finite mixture distribution. The SCTM captures not only the mean and standard deviation (SD) of density of the traffic flow, but also the propagation of SD over time and space. The SCTM is tested with a hypothetical freeway corridor simulation and an empirical study. The simulation results are compared against the means and SDs of traffic densities obtained from the Monte Carlo Simulation (MCS) of the modified cell transmission model (MCTM). An approximately two-miles freeway segment of Interstate 210 West (I-210W) in Los Ageles, Southern California, is chosen for the empirical study. Traffic data is obtained from the Performance Measurement System (PeMS). The stochastic parameters of the SCTM are calibrated against the flow-density empirical data of I-210W. Both the SCTM and the MCS of the MCTM are tested. A discussion of the computational efficiency and the accuracy issues of the two methods is provided based on the empirical results. Both the numerical simulation results and the empirical results confirm that the SCTM is capable of accurately estimating the means and SDs of the freeway densities as compared to the MCS.     

Extensions of theoretical capacity models to account for special conditions

The computational procedures used to analyze two-way stop-controlled intersections were extended in the National Cooperative Highway Research Project 3-46 to account for a number of effects commonly observed at actual unsignalized intersections. This paper presents theoretical extensions that can account for commonly observed phenomena, such as two-stage gap acceptance when median storage is available; right-turn “sneakers” at flared minor-street approaches; non-random arrivals caused by upstream signals; impedance due to pedestrian crossings; and delay to major-street through vehicles using shared left-turn and through lanes. The individual effects are then combined into an analytical framework suitable for inclusion in the Unsignalized Intersections procedures of the 1997 “Highway Capacity Manual”. ©