Real-time freeway traffic state estimation based on extended Kalman filter: Adaptive capabilities and real data testing

This paper reports on real data testing of a real-time freeway traffic state estimator, with a particular focus on its adaptive capabilities. The pursued general approach to the real-time adaptive estimation of complete traffic state in freeway stretches or networks is based on stochastic macroscopic traffic flow modeling and extended Kalman filtering. One major innovative feature of the traffic state estimator is the online joint estimation of important model parameters (free speed, critical density, and capacity) and traffic flow variables (flows, mean speeds, and densities), which leads to three significant advantages of the estimator: (1) avoidance of prior model calibration; (2) automatic adaptation to changing external conditions (e.g. weather and lighting conditions, traffic composition, control measures); (3) enabling of incident alarms. These three advantages are demonstrated via suitable real data testing. The achieved testing results are satisfactory and promising for subsequent applications.     

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.     

RENAISSANCE – A unified macroscopic model-based approach to real-time freeway network traffic surveillance

The paper presents a unified macroscopic model-based approach to real-time freeway network traffic surveillance as well as a software tool RENAISSANCE that has been recently developed to implement this approach for field applications. RENAISSANCE is designed on the basis of stochastic macroscopic freeway network traffic flow modeling, extended Kalman filtering, and a number of traffic surveillance algorithms. Fed with a limited amount of real-time traffic measurements, RENAISSANCE enables a number of freeway network traffic surveillance tasks, including traffic state estimation and short-term traffic state prediction, travel time estimation and prediction, queue tail/head/length estimation and prediction, and incident alarm. The traffic state estimation and prediction lay the operating foundation of RENAISSANCE since RENAISSANCE bases the other traffic surveillance tasks on its traffic state estimation or prediction results. The paper first introduces the utilized stochastic macroscopic freeway network traffic flow model and a real-time traffic measurement model, upon which the complete dynamic system model of RENAISSANCE is established with special attention to the handling of some important model parameters. The algorithms for the various traffic surveillance tasks addressed are described along with the functional architecture of the tool. A simulation test was conducted via application of RENAISSANCE to a hypothetical freeway network example with a sparse detector configuration, and the testing results are presented in some detail. Final conclusions and future work are outlined.     

Traffic state estimation and uncertainty quantification based on heterogeneous data sources: A three detector approach

This study focuses on how to use multiple data sources, including loop detector counts, AVI Bluetooth travel time readings and GPS location samples, to estimate macroscopic traffic states on a homogeneous freeway segment. With a generalized least square estimation framework, this research constructs a number of linear equations that map the traffic measurements as functions of cumulative vehicle counts on both ends of a traffic segment. We extend Newell’s method to solve a stochastic three-detector problem, where the mean and variance estimates of cell-based density and flow can be analytically derived through a multinomial probit model and an innovative use of Clark’s approximation method. An information measure is further introduced to quantify the value of heterogeneous traffic measurements for improving traffic state estimation on a freeway segment.     

Estimating median velocity instead of mean velocity at single loop detectors

Loop detectors are the preeminent vehicle detector for freeway traffic surveillance. Although single loops have been used for decades, debate continues on how to interpret the measurements. Many researchers have sought better estimates of velocity from single loops. The preceding work has emphasized techniques that use many samples of aggregate flow and occupancy to reduce the estimation error. Although rarely noted, these techniques effectively seek to reduce the bias due to long vehicles in measured occupancy. This paper presents a different approach, using a new aggregation methodology to estimate velocity and reduce the impact of long vehicles in the original traffic measurements. In contrast to conventional practice, the new estimate significantly reduces velocity estimation errors when it is not possible to control for a wide range of vehicle lengths.     

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).     

Recognition and tracking of spatial–temporal congested traffic patterns on freeways

The two models FOTO (Forecasting of Traffic Objects) and ASDA (Automatische Staudynamikanalyse: Automatic Tracking of Moving Traffic Jams) for the automatic recognition and tracking of congested spatial–temporal traffic flow patterns on freeways are presented. The models are based on a spatial–temporal traffic phase classification made in the three-phase traffic theory by Kerner. In this traffic theory, in congested traffic two different phases are distinguished: “wide moving jam” and “synchronized flow”. The model FOTO is devoted to the identification of traffic phases and to the tracking of synchronized flow. The model ASDA is devoted to the tracking of the propagation of moving jams. The general approach and the different extensions of the models FOTO and ASDA are explained in detail. It is stressed that the models FOTO and ASDA perform without any validation of model parameters in different environmental and traffic conditions. Results of the online application of the models FOTO and ASDA at the TCC (Traffic Control Center) of Hessen near Frankfurt (Germany) are presented and evaluated.     

Some observed details of freeway traffic evolution

Certain details of traffic evolution were studied along a 2 km, homogenous freeway segment located upstream of a bottleneck. By comparing (transformed) cumulative curves constructed from the vehicle counts measured at neighboring loop detectors, it was found that waves propagated through queued traffic like a random walk with predictable statistical variation. There was no observed dependency of wave speed on flow. As such, these waves neither focused nor fanned outward and shocks arose only at the interfaces between free-flowing traffic and the back of queues. Although these traffic features may have long been suspected, actual observations of this kind have hitherto not been documented. Also of note, the shocks separating queued and unqueued traffic sometimes exhibited unexpectedly long transitions between these two states. Finally, some observations presented here corroborate earlier reports that, in unqueued traffic, vehicle velocity is insensitive to flows and that forward-moving changes in traffic states therefore travel with vehicles. Taken together, these findings suggest that certain rather simple models suffice for describing traffic on homogeneous freeway segments; brief discussion of this is offered in Section 5.     

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.     

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.     

Data mining using regularized adaptive B‐splines regression with penalization for multi‐regime traffic stream models

This paper presents a new data mining method that integrates adaptive B‐spline regression and traffic flow theory to develop multi‐regime traffic stream models (TSMs). Parameter estimation is implemented adaptively and optimally through a constrained bi‐level programming method. The slave programming determines positions of knots and coefficients of the B‐spline by minimizing the error of B‐spline regression. The master programming model determines the number of knots through a regularized function, which balances model accuracy and model complexity. This bi‐level programming method produces the best fitting to speed–density observations under specific order of splines and possesses great flexibility to accommodate the exhibited nonlinearity in speed–density relationships. Jam density can be estimated naturally using spline TSM, which is sometimes hardly obtainable in many other TSM. Derivative continuity up to one order lower than the highest spline degree can be preserved, a desirable property in some application. A five‐regime B‐spline model is found to exist for generalized speed–density relationships to accommodate five traffic operating conditions: free flow, transition, synchronized flow, stop and go traffic, and jam condition. A typical two‐regime B‐spline form is also explicitly given, depending only on free‐flow speed, optimal speed, optimal density, and jam density. Copyright © 2013 John Wiley & Sons, Ltd.     

Validation of an extended discrete first-order model with variable speed limits

This paper validates the prediction model embedded in a model predictive controller (MPC) of variable speed limits (VSLs). The MPC controller was designed based on an extended discrete first-order model with a triangular fundamental diagram. In our previous work, the extended discrete first-order model was designed to reproduce the capacity drop and the propagation of jam waves, and it was validated with reasonable accuracy without the presence of VSLs. As VSLs influence traffic dynamics, the dynamics including VSLs needs to be validated, before it can be applied as a prediction model in MPC. For conceptual illustrations, we use two synthetic examples to show how the model reproduces the key mechanisms of VSLs that are applied by existing VSL control approaches. Furthermore, the model is calibrated by use of real traffic data from Dutch freeway A12, where the field test of a speed limit control algorithm (SPECIALIST) was conducted. In the calibration, the original model is extended by using a quadrangular fundamental diagram which keeps the linear feature of the model and represents traffic states at the under-critical branch more accurately. The resulting model is validated using various traffic data sets. The accuracy of the model is compared with a second-order traffic flow model. The performance of two models is comparable: both models reproduce accurate results matching with real data. Flow errors of the calibration and validation are around 10%. The extended discrete first-order model-based MPC controller has been demonstrated to resolve freeway jam waves efficiently by synthetic cases. It has a higher computation speed comparing to the second-order model-based MPC.     

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.     

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.     

A new approach to time-of-day control based on a dynamic freeway traffic model

This paper presents a new approach to time-of-day control. While time-of-day control strategies presented up-to-now are only optimal under steady-state conditions, the control algorithm derived in this paper takes into account the evolution of traffic flow according to the time delay between a volume change at a ramp and its subsequent disturbance at a freeway point downstream. The new control strategy is based on the solution of a linear programming optimization problem and makes freeway volume hold the capacity constraints for the total time of control operation. In order to reduce the computational effort a simplified version of the new algorithm is also discussed. Simulation results obtained by use of two different traffic flow models show that control derived through the new algorithm can avoid congestion and ensure operation with peak performance even if a steady-state condition is never attained.     

Effects of low speed limits on freeway traffic flow

Recent years have seen a renewed interest in Variable Speed Limit (VSL) strategies. New opportunities for VSL as a freeway metering mechanism or a homogenization scheme to reduce speed differences and lane changing maneuvers are being explored. This paper examines both the macroscopic and microscopic effects of different speed limits on a traffic stream, especially when adopting low speed limits. To that end, data from a VSL experiment carried out on a freeway in Spain are used. Data include vehicle counts, speeds and occupancy per lane, as well as lane changing rates for three days, each with a different fixed speed limit (80 km/h, 60 km/h, and 40 km/h). Results reveal some of the mechanisms through which VSL affects traffic performance, specifically the flow and speed distribution across lanes, as well as the ensuing lane changing maneuvers. It is confirmed that the lower the speed limit, the higher the occupancy to achieve a given flow. This result has been observed even for relatively high flows and low speed limits. For instance, a stable flow of 1942 veh/h/lane has been measured with the 40 km/h speed limit in force. The corresponding occupancy was 33%, doubling the typical occupancy for this flow in the absence of speed limits. This means that VSL strategies aiming to restrict the mainline flow on a freeway by using low speed limits will need to be applied carefully, avoiding conditions as the ones presented here, where speed limits have a reduced ability to limit flows. On the other hand, VSL strategies trying to get the most from the increased vehicle storage capacity of freeways under low speed limits might be rather promising. Additionally, results show that lower speed limits increase the speed differences across lanes for moderate demands. This, in turn, also increases the lane changing rate. This means that VSL strategies aiming to homogenize traffic and reduce lane changing activity might not be successful when adopting such low speed limits. In contrast, lower speed limits widen the range of flows under uniform lane flow distributions, so that, even for moderate to low demands, the under-utilization of any lane is avoided. These findings are useful for the development of better traffic models that are able to emulate these effects. Moreover, they are crucial for the implementation and assessment of VSL strategies and other traffic control algorithms.     

A recursive, cell processing model for predicting freeway travel times

Travel time information influences driver behaviour and can contribute to reducing congestion and improving network efficiency. Consequently many road authorities disseminate travel time information on road side signs, web sites and radio traffic broadcasts. Operational systems commonly rely on speed data obtained from inductive loop detectors and estimate travel times using simple algorithms that are known to provide poor predictions particularly on either side of the peak period. This paper presents a new macroscopic model for predicting freeway travel times which overcomes the limitations of operational ‘instantaneous’ speed models by drawing on queuing theory to model the processing of vehicles in sections or cells of the freeway. The model draws on real-time speed, flow and occupancy data and is formulated to accommodate varying geometric conditions, the relative distribution of vehicles along the freeway, variations in speed limits, the impact of ramp flows and fixed or transient bottlenecks. Field validation of the new algorithm was undertaken using data from two operational freeways in Melbourne, Australia. Consistent with the results of simulation testing, the validation confirmed that the recursive model provided a substantial improvement in travel time predictions when compared to the model currently used to provide real-time travel time information to motorists in Melbourne.     

Understanding the variability of speed distributions under mixed traffic conditions caused by holiday traffic

Understanding the variability of speed patterns and congestion characteristics of interstate freeway systems caused by holiday traffic is beneficial because appropriate countermeasures for safety improvement and congestion mitigation can be prepared and drivers can avoid traffic congestion and change their holiday travel schedules. This study evaluated the traffic congestion patterns during the Thanksgiving holiday period in 2006 using a Gaussian mixture speed distribution estimated by the Expectation–Maximization (EM) algorithm. This mathematical approach showed the potential of improving freeway operational performance evaluation schemes for holiday periods (even non-holiday periods). This study suggested that a Gaussian mixture model using the EM algorithm could be used to properly characterize the severity and the variability of congestion on certain interstate roadway systems. However, this study also pointed out that the fundamental limitations of the mixture model and the statistical significance test about the mixture components should be well understood and need to be further investigated. In addition, because this study investigated the changing patterns of speed distributions with only one interstate freeway system, I-95 northbound, other freeway systems with both directions need to be evaluated so that a more broad and confident analysis on holiday traffic can be achieved.     

Some observed queue discharge features at a freeway bottleneck downstream of a merge

Details of traffic evolution were studied upstream and downstream of a freeway bottleneck located near a busy on-ramp. It is shown that on certain days the bottleneck became active upon dissipation of a queue emanating from somewhere further downstream. On such occasions, the bottleneck occurred at a fixed location, approximately one kilometer downstream of the merge. Notably, even after the dissipation of a downstream queue, the discharge flows in the active bottleneck were nearly constant, since the cumulative counts never deviated much from a linear trend. The average bottleneck discharge flows were also reproducible from day to day. The diagnostic tools used in this study were curves of cumulative vehicle arrival number versus time and cumulative occupancy versus time constructed from data measured at neighboring freeway loop detectors. Once suitably transformed, these cumulative curves provided the measurement resolution necessary to observe the transitions between freely flowing and queued conditions and to identify some important traffic features.     

Hysteresis phenomena of a Macroscopic Fundamental Diagram in freeway networks

Observations of traffic pairs of flow vs. density or occupancy for individual locations in freeways or arterials are usually scattered about an underlying curve. Recent observations from empirical data in arterial networks showed that in some cases by aggregating the highly scattered plots of flow vs. density from individual loop detectors, the scatter almost disappears and well-defined macroscopic relations exist between space-mean network flow and network density. Despite these findings for the existence of well-defined relations with low scatter, these curves should not be universal. In this paper we investigate if well-defined macroscopic relations exist for freeway network systems, by analyzing real data from Minnesota’s freeways. We show that freeway network systems not only have curves with high scatter, but they also exhibit hysteresis phenomena, where higher network flows are observed for the same average network density in the onset and lower in the offset of congestion. The mechanisms of traffic hysteresis phenomena at the network level are analyzed in this paper and they have dissimilarities to the causes of the hysteresis phenomena at the micro/meso level. The explanation of the phenomenon is dual. The first reason is that there are different spatial and temporal distributions of congestion for the same level of average density. Another reason is the synchronized occurrence of transitions from individual detectors during the offset of the peak period, with points remain beneath the equilibrium curve. Both the hysteresis phenomenon and its causes are consistently observed for different spatial aggregations of the network.