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3. Existing Traffic Prediction/Estimation Models and Systems

This section identifies and reviews existing traffic prediction/estimation models and systems that can be used for both planning and real-time traffic management applications at the corridor and network levels.

Since the inception of ITS, traffic estimation and prediction have been considered a core enabling capability for advanced traveler information systems, as well as for advanced transportation management systems, and an integral part of the various architecture documents put forth for ITS through its various stages. However, deployments of traffic management systems (by associated traffic management centers) have proceeded largely without such capability. Similarly, traveler information systems and services with dynamic travel times and/or route recommendations have been very slow in coming to the market. Transportation agencies have generally been reticent to provide predicted travel times to users, partly concerned about public relations in the event of poor prediction or bad recommendations. In addition, for both traffic management and traveler information services, adjustment is still ongoing to use real-time information on prevailing states, and to try and leverage archived information. Hence the ability to make effective use of predictive travel times and traffic conditions often requires a big leap in capabilities and operational culture.

On the other hand, studies have continued to show the value of predictive information when compared to prevailing information-when supplied to travelers to help route choice (Mahmassani and Jayakrishnan 1991; Ben Akiva et al. 1996; Dong et al. 2006), or as a basis for setting prices dynamically (Dong et al. 2007). Systems for traffic estimation and prediction generally fall into two categories depending on the underlying methodology: (1) simulation-based, and (2) statistics-based. The latter uses statistical relations among directly measured quantities (e.g. time series of speeds and volumes) to produce short term predictions of traffic state descriptors for eventual travel time calculation. The former uses a representation of the traffic processes in the system and associated network interactions to project future traffic states. Simulation-based approaches can provide estimates of conditions on parts of the network where sensors are installed, whereas statistics-based approaches can only be applied to links where measurements exist, and does not deal adequately with disruptions in the temporal flow patterns. Hybrid methods that combine simulation-based approaches with advanced statistical techniques for data fusion try to combine the advantages of both approaches.

DYNASMART-P and DynaMIT were conceived as simulation-based approaches to overcome the limitations of "black box" statistical methods which had been used at the link level in the early literature. Both of these tools also incorporate logic that fuses statistical considerations with the structural representations.

While real-time estimation and prediction of traffic, and more important, development of anticipatory strategies have evolved significantly in the past decade, actual applications remain very limited as agencies have shied away from disseminating predictive information and using predictions in generating traffic controls. On the other hand, the past five years have seen the emergence of third parties providing some type of "real-time" traffic information, though most of it is not predictive, and is limited in geographic scope to major facilities with sensors. Often, the third parties are consolidators of information collected by government TMC's. However, a couple of private sector entities are now marketing real-time information that is claimed to be predictive, primarily for handheld GPS-based devices, though (1) the exact basis or method of prediction is not disclosed, though it is not simulation based, and is admittedly (for some) still preliminary; and (2) extensive validation has not been submitted for peer review. The most notable example is INRIX (courtesy of Microsoft corp.), which claims to use Bayesian statistical methods for state estimation. Another is Dash, Inc. a probe-based system where equipped vehicles that receive travel information also act as probes, sending information on their respective locations and times. While the eventual goal is to feature an integrated predictive system, the capabilities available to date are mostly ad hoc.

Because these new systems feature proprietary engines that have not been sufficiently validated within the traffic community, they will not be addressed further in his review. At their current stage of development, these models do not make special provision for weather effects. The discussion will therefore be limited to DYNASMART and DynaMIT as these reflect the state of the art in simulation-based prediction.

3.1 Overview of DYNASMART-X

This section presents an overview of DYNASMART-X, which provides state-of-the-art TrEPS functionality, as well as its applicability to support weather-related traffic management.

To place this discussion in context of available simulation-based DTA tools, it is useful to recall the difference between online and offline applications of DTA tools. Online applications are intended for real-time estimation and prediction of traffic conditions over the near-term (typically less than one hour), to be used in conjunction with traffic management activities such as information provision to motorists (via variable message signs or in-vehicle and other portable devices), traffic control via signals or ramp meters, and other traffic management functions such as incident response, traffic diversion and other congestion mitigation functions. DYNASMART-X is such an online traffic estimation and prediction system. On the other hand, offline applications are primarily intended for evaluation and operational planning activities, in conjunction with planned disruptions, scenario planning, contemplated future network and operational improvements, pricing schemes, and so on. DYNASMART-P is intended for such offline planning and evaluation applications.

As an online TrEPS, DYNASMART-X interacts continuously with multiple sources of real-time information, such as loop detectors, roadside sensors, and vehicle probes, which it integrates with its own model-based representation of the network traffic state. The system combines advanced network algorithms and models of trip-maker behavior in response to information in an assignment-simulation-based framework to provide: (1) estimates of current network traffic conditions; (2) predictions of network flow patterns over the near and medium terms, in response to various contemplated traffic control measures and information dissemination strategies; and (3) anticipatory traveler and routing information to guide trip-makers in their travel (Dong et al., 2006). The system includes several functional modules (for OD estimation, OD prediction, real-time network state simulation, consistency checking, updating and resetting functions, and network state prediction), integrated through a flexible distributed design that uses CORBA (Common Object Request Broker Architecture) standards, for real-time operation in a rolling horizon framework with multiple asynchronous horizons for the various modules (Mahmassani et al., 2004).

The functionality of DYNASMART-X is achieved through judicious selection of modeling features that achieve a balance between representational detail, computational efficiency and input data requirements. These features include (Mahmassani et al., 2004):

The TrEPS platform is comprised of four components: (1) the graphical user interface, or GUI, (2) the database, (3) the algorithmic modules that perform the DTA functional capabilities, and (4) the set of CORBA programs used to implement the scheduler and the data broker. The algorithmic component is the main entity in the system in terms of performing the TrEPS functions, and consists of the following modules: (a) state estimation, (b) state prediction, (c) OD estimation, (d) OD prediction, and (e) consistency checking and updating. The purpose of the state estimation module (RT-DYNA) is to estimate the current traffic state in the network. The state prediction module (P-DYNA) on the other hand provides future network traffic states for a pre-defined horizon. The OD estimation module (ODE) is responsible for estimating the coefficients of a time varying polynomial function that describes the OD demand in the current stage. The OD prediction module (ODP) utilizes these to calculate the demand that is generated from each origin to each destination at each departure time interval of the current and future stages. Finally, the consistency checking modules are responsible for minimizing the deviation or discrepancy between what is estimated by the system and what is occurring in the real world, in an effort to control error propagation.

Note that RT-DYNA and P-DYNA are essentially near-identical copies of the same simulation-assignment code, executed in a different manner and with different dynamic inputs. However, the core simulation logic is essentially identical, and is shared with the off-line DYNASMART-P DTA tool used primarily for analysis and evaluation to support operational planning decisions. Accordingly, modifications made in DYNASMART-P to capture the effect of adverse weather would then near-seamlessly be migrated to the on-line DYNASMART-X TrEPS. Hence, the modifications described in the next section are implemented initially in DYNASMART-P.

Capturing the effect of adverse weather on traffic patterns entails both supply side and demand side modifications to the model. As a decision support tool, DYNASMART-X could also help TMC design weather-related management strategies. Figure 3 1 depicts a high-level view of the DYNASMART-X system structure, the interrelationship among the components and modules, and the manner in which capturing weather impacts would affect these modules (Alfelor et al., 2009).

This figure depicts a high-level view of the DYNASMART-X system structure, the interrelationship among the components and modules, and the manner in which capturing weather impacts would affect these modules.
Figure 3-1. Incorporating Weather Impacts in DYNASMART-X Structure

3.2 Evaluation for Real-time Application of DYNASMART-X

3.2.1 Maryland CHART Test Bed

Data Sources

This section describes the data available for the Coordinated Highways Action Response Team (CHART) network in Maryland. It also discusses the data quality issues and the data conversion for application of DYNASMART-X to the CHART network. The data includes network geometry data, surveillance system attributes, signal timing data, real-time traffic data, planning data, and other related information. Because the calibration and evaluation plan described later relies on and makes extensive use of these data, it is important to develop a thorough understanding and appreciation of these data elements.

(1) Network geometry and system features

The CHART network was developed using a variety of data sources, including a GIS (geographic information system) file, maps, and field visits. The CHART GIS map file has been provided by the mapping center of the bureau of Transportation Statistics (http://www.bts.gov). Field visits and internet maps (from Mapquest website) were used to modify and fine-tune the network that was produced from the GIS file. In addition to geographic information, zoning and signal information are critical to the network development. The characteristics of the zones have been defined consistent with the traffic analysis zones (TAZs) provided in a transportation planning file from Maryland Department of Transportation (MDOT). The signal locations and signal timing plans were provided by the Maryland State Highway Administration (MDSHA).

The basic input files for DYNASMART include: network.dat, xy.dat, linkxy.dat, zone.dat, origin.dat, destination.dat. They were prepared using TransCAD and converted to DYNASMART using Dynabuilder (developed by the Maryland Transportation Initiative, the University of Maryland).

(2) Signal location and control logic

Information pertaining to signal locations and signal timing plans was provided by the Maryland SHA. The location data consists of a hard-copy inventory of signals by county and location (given by intersecting street names). In addition, signal timing information was provided for some arterials and corridors located in the CHART network. This information was provided in Sychro file format.

The above files are used to set up the input files (movement.dat, control.dat) in DYNASMART.

(3) Surveillance system

Real-time traffic data is available from sensors at various locations in the network. Detector information is obtainable from the University of Maryland Center for Advanced Transportation Technology (CATT), Maryland DOT and Maryland SHA. Information describing detector location, as well as detector data is available from the CATT laboratory webpage, http://www.cattlab.umd.edu/cf/index.cfm?js=enabled&bin=trafficData. The detector information is frequently invoked in processing and interpreting the real-time traffic data and the actuated signal data.

(4) Real-time traffic data

Real-time traffic data is available from Center for Advanced Transportation Technology (CATT), Maryland DOT and Maryland SHA. There are 18 detectors located in the network. Two detectors are located on arterials, the rest are on freeways.

Each detector data file contains timestamp information, detector location, traffic direction, vehicle counts, vehicles/hour, speeds, and percent occupancy. Sensors collect 24-hour data in 5 minute intervals. The percent occupancy refers to the percentage of time the detector was occupied during the 5 minute interval. The speed is the average speed recorded over the 5 minute interval. The vehicle count is the number of vehicles observed during the 5 minute interval.

(5) Planning data

There are 111 OD planning zones in the CHART network. Maryland DOT provided a TAZ (traffic analysis zone) file, describing the zonal characteristics of the study area. The OD files contain the static OD matrices for three time periods for the study area corresponding to the following modes: (1) SOV, (2) HOV2, (3) HOV3+, (4) Truck, and (5) Airport passengers. In addition, the three time periods are categorized as follows: (1) AM Peak, (2) PM Peak and (3) Off Peak.

The OD demand files required in DYNASMART include: demand.dat and demand_truck.dat. The demands were aggregated over all the modes. The static OD matrices can serve as initial values (or targets) when OD demand is calibrated offline or when OD demand estimation/prediction are performed in DYNASMART-X

(6) Other data

Some of the input files for DYNASMART-X are left either empty or with zeroes: LinkName.dat, vehicle.dat, incident.dat, workzone.dat, vms.dat, pricing.dat, bus.dat, path.dat, pricing.dat, SuperZone.dat. The information is either not applicable to the CHART network, or requires more effort to extract appropriately.

Some of the input files kept the default value provided by DYNASMART or offline calibration results: TrafficFlowModel.dat, leftcap.dat, yieldcap.dat, StopCap2Way.dat, StopCap4Way.dat, gradelengthPCE.dat, output_option.dat. Users of course have the opportunity to modify these values if other findings or preferences are available.

Other files such as system.dat and scenario.dat, as well as DYNASMART-X featured files modules.dat and scheduler.dat correspond to advanced settings. The corresponding setting guidance can be found in the DYNASMART-X User Guide.

Off-line Calibration

(1) Modified Greenshields model calibration

The traffic flow relations on freeways are specified by a modified Greenshields model in DYNASMART, which can be calibrated against the flow measurements along freeways to determine the possible parameter values at different congestion levels. Special emphasis could be given to freeway segments with on/off ramp weaving movements. Currently DYNASMART does not specifically model these detailed vehicle movements on freeways, but the parameters of the relations can be calibrated to adequately reflect such effects, as DYNASMART allows specification of different parameter values for different physical links. Because of the interruption of traffic flow due to signals, the surface arterials are expected to behave distinctly from freeways. Key parameters in the models, such as the jam density, saturation flow and the model's power parameters need to be estimated using data collected from the arterials of interest.

In the current version of DYNASMART, two types of the modified Greenshields model family are available. Type one model is a two-regime model in which constant free-flow speed is specified for the free-flow conditions and a Modified Greenshield model is specified for congested-flow conditions. The second model uses a single regime to model traffic relations for both free- and congested-flow conditions.

The two-regime model is generally applicable to freeways, whereas the single-regime model is applied to arterials. Because of their geometric design and controlled access characteristics, freeways can typically accommodate relatively large traffic flow rates (up to 1300vphpl) at near free-flow speeds, hence the applicability of the two-regime model form. Traffic on arterials, on the other hand, experiences greater interference and interaction, resulting in more immediate deterioration in prevailing speeds with increasing density. Therefore, traffic behavior on arterials is better represented using a single-regime model form.

These models can be estimated by conducting a linear regression analysis using time-varying link density and speed data. The parametric analysis procedure is also implemented to help for linear regression analysis. Alternative model forms require variants of this procedure, or the use of other statistical estimation methods.

(2) Time-dependent OD demand calibration

The available OD matrices for the CHART network are intended for planning applications and provide only static OD demand information. Archived real-time link traffic data is combined with the static OD information to perform an offline estimation of time-dependent OD demand. In addition to providing a representation of the structural characteristics of the dynamic OD demand in the CHART network, the resulting offline estimates also serve as a powerful basis and starting point for online OD demand estimation and prediction.

A bi-level optimization method has been developed to estimate the time-varying OD demand flows. In the upper level, the sum of squared deviations of the simulated link flows from the corresponding observed values is minimized; in the lower level a dynamic traffic assignment problem is solved. The process is iterated until convergence in the reduction of root mean square errors (RMSE) of the estimated link-flows is achieved.

In addition, a multi-objective bi-level optimization model is an extension to the iterative bi-level framework proposed above. Specifically, the upper-level problem is a constrained optimization problem, which is to estimate dynamic OD demand matrix, given link flow proportions and/or an initial target OD demand matrix, that will best reproduce the observed link flows. The link flow proportions are generated from the lower-level dynamic traffic network traffic assignment, namely DYNASMART. In this model, two objectives are considered. The first one is to minimize the discrepancy between observed and estimated link flows, and the second is to minimize the deviation between the target and estimated demand.

All entries in the time-dependent demand table, i.e. flows between all origin-destination pairs for all departure intervals during the study period, should be estimated. All other parameters of the procedure are determined internally, given the actual observations and a time-dependent assignment model like DYNASMART. The estimation will be done for a.m. peak hour of the day. The demand flow will be compared across days of the week.

The data required for the calibration is:

(3) Effectiveness of off-line calibration

After completion of the speed-density relation calibration and OD demand calibration, an evaluation is needed to assess the effectiveness of the calibration results. The effectiveness is analyzed by comparing the simulated link performance from the DYNASMART simulator with the observed link performance.

Link density and link volumes are outputted as simulation results and can be used for comparison with sensor data. The root mean-squared error (RMSE) is taken as the measure to assess the effectiveness of calibrated speed-density models and time-dependent OD demand matrices which are input to the DYNASMART simulator.

In general, the simulated link performance is less accurate in the peak time (6:00am-9:00am) than the off-peak time (4:00am-6:00am and 9:00am-10:00am). The simulated performance matches the observation data better for the freeway links than for arterial links. In addition, link density exhibits lower error than link volume. The RMSE measure for a certain link performance characteristic varies across links, which indicates that the simulation replicates the actual traffic states quite well for some of the links while for other links it is less accurate.

The discrepancy is likely the result of several sources. First, note that these results are only for an offline application of a priori calibrated models, and do not take advantage of the online calibration and consistency correction functions provide by DYNASMART-X. In fact, these results illustrate the need for an online estimation and prediction capability. One of the sources of discrepancy between simulated and observed data is that the traffic flow model in DYNASMART is currently based on the modified Greenshields model, which is static in nature. However, the collected sensor data reveals that the model does not always provide a very good fit to the observations. Considerable stochastic variation is evident in the field data. In such situations, although the model provides a "best" estimation of link performance under static assumptions, its effectiveness in matching sensor data naturally degrades somewhat vis-à-vis actual observations that might exhibit considerable fluctuation. So the more apparent randomness in the observation data, the worse the match is likely to be. Other sources of discrepancy might include the manner in which various traffic controls perform (e.g. fully actuated signal controllers). A third potential source might be that only the discrepancy of link densities is minimized in the objective function formulated in the calibration of OD demand matrices; this might explain the fact that link density exhibits closer match with observed data than the corresponding values of link volume or link speed. Other possible reasons could include limitation of the inherent route choice model, sensitivity of estimation on network configuration and limited quantity and quality of sensor data. Many of these sources suggest that an online approach to calibration, and to estimation and prediction, is likely to considerably improve operational performance of the models. In this case the time-dependent OD demand calibrated off-line can serve as a starting point. It is expected that the estimation errors would become smaller in on-line application since link performance will be updated quasi-continuously to be consistent with real world observations.

In summary, the calibrated speed-density relations and time-dependent OD demand matrices have been successfully implemented in the DYNASMART simulator, and generated reasonable estimation of traffic conditions which replicate actual observations fairly closely. The errors incurred by the simulation have been analyzed; the majority of these would be alleviated in on-line application or provide an important basis for future improvement of the research.

On-line Calibration

This section discusses the development of on-line traffic demand estimation and prediction modules, which provide time-dependent traffic demand matrices for dynamic traffic assignment and associated network traffic simulation.

Dynamic origin destination (OD) demand estimation and prediction is an important capability in its own right, and an essential support function for real-time dynamic traffic assignment (DTA) model systems for ITS applications. The dynamic OD demand estimation and prediction problem seeks to estimate time-dependent OD trip demand patterns at the current stage, and predict demand volumes over the near and medium terms in a general network, given historical demand information and real-world traffic measurements from various surveillance devices (e.g. occupancy and volume observations from loop detectors on specific links).

To provide accurate and robust demand estimation and prediction for real-time dynamic traffic assignment in operational settings, the following primary functional requirements need to be satisfied: (1) incorporate regular demand information into the real-time demand prediction process; and (2) recognize and capture possible structural changes in demand patterns under various conditions.

A recursive real-time OD demand estimation and prediction framework (shown in Figure 3 2) is briefly described as follows (Zhou and Mahmassani, 2007).

Step 1: Receive real-time traffic measurements from surveillance system.
Step 2: Fetch link proportion data from the DTA simulator.
Step 3: (OD estimation) Estimate time-varying OD demand matrices involved in the current estimation stage using the Kalman filtering method.
Step 4: (OD prediction) Predict OD demand over next future horizon.
Step 5: Advance estimation stage forward, and then go back to Step 1.

Illustration of recursive estimation-prediction implementation.
Figure 3-2. Illustration of Recursive Estimation-Prediction Implementation

j = index for origin-destination pairs, j =1,..., Nod

τ = index for aggregated departure time intervals, τ = 1, 2, ...

k = index for stage period, k = 1, 2, 3, ...

υj, τ = structural demand deviation of from a priori estimate for OD pair j with departure time τ

Evaluation and Applications

(1) Evaluation of estimation capability

The offline calibrated link-specific speed-density relations are used as traffic flow models for the network. The calibrated time-dependent OD demand matrices are used as the historical demand matrices, which constitute essential input to the on-line OD estimation and prediction. With the adjustments induced by analyzing sensor data using Kalman filter technology, the demand level for each OD pair is estimated. The estimated demand incorporates the historical information and at the same time recognizes the real-time information implied by the incoming sensor data to accommodate the day-to-day changes in traffic demand. It is the estimated demand matrices that load vehicles to the network in traffic estimation.

The RMSEs of density, volume and speed for each of the observed links for different estimation time periods are calculated. Link density and link volume are processed at 5-minute intervals and link volume is obtained from traffic flows mid-block on links instead of link outflows, in order to have meaningful volume values. Compared to the off-line calibration results, the RMSEs for the online estimation are in general lower than those obtained with offline estimation alone, which means that link density and volume could be estimated better in online applications. Whereas the offline simulation would simply load predetermined OD demand tables, the online estimation keeps receiving real-time data, which it uses to update quasi-continuously the internal representation of the system state by means of consistency checking and OD estimation/ prediction.

(2) Evaluation of prediction capability

The traffic prediction in DYNASMART-X is implemented based on a rolling horizon approach. In this framework, the planning horizon is subdivided into several overlapping stages. The consecutive stages overlap at fixed intervals, the length of each is referred to as the roll period. The stage length (or horizon) is denoted by h and the roll period is denoted by l. In the experiment, h is set to 20 minutes and l is set to 5 minutes. The roll period l is the short-term future duration for which the available forecasts of OD desires are considered to be reliable. In the remaining time of the stage, (h-l), forecasts of OD data are expected to be less reliable. Therefore, the short term prediction should be more reliable and precise than the long term prediction. For a duration A, the traffic status is predicted first time at Stage m, second time at Stage m+1, third time at Stage m+2, and fourth time at Stage m+3. It is expected that the prediction is less accurate in Stage m than Stage m+3.

This image represents the rolling horizon procedure.
Figure 3-3. Rolling Horizon Procedure

To compare the accuracy of predictions, the link performance (density, speed, or volume) is considered through four groups which correspond to prediction obtained at four different times (corresponding to consecutive stages). In other words, the first time prediction indicates the result from the remotest prediction horizon, whereas the fourth time prediction is obtained from the nearest prediction horizon; and so on. The results indicate that the discrepancy of the first time prediction is in general larger than the second, third and fourth times. The fourth time prediction is closest to the actual observed value. This verifies that the short-term predictions in the present rolling horizon procedure are more reliable than the longer-term predictions due to the greater reliability of more recent information.

(3) Travel time information

Pre-trip as well as en-route travel information is an Advanced Traveler Information System (ATIS) user service. Its objective is to inform travelers of traffic and transit conditions, so they can best assess travel options before selecting a route, mode, time-of-day, or deciding whether to make a trip. DYNASMART-X can provide estimations and predictions of network flow patterns and travel times in response to various contemplated traffic control measures and information dissemination strategies.

Based on the predicted OD demand and dynamic assignment simulation result from PDyna, time-dependent link travel times and turning penalties over the prediction horizon can be obtained. If users specified a path, the predictive travel times for different departure time intervals within the prediction horizon are displayed to assist users in making route choice and departure time choice. If users are interested in the travel times between an OD pair, the time-dependent point-to-point travel times as well as the associated shortest paths between the OD pair will be provided.

3.3 Overview and Applications of DynaMIT

This section discusses field applications of DynaMIT (Ben-Akiva et al., 2002; Balakrishna et al., 2006), a real time computer system designed to effectively support the operation of Advance Traveler Information Systems (ATIS) and Advanced Traffic Management Systems (ATMS) at a Traffic Management Center (TMC). The framework of the system is shown in Figure 3 4. The field implementations made in Hampton Roads, VA and Los Angeles, CA studies are discussed. Note that the DynaMIT networks can be easily converted to DYNASMART and hence be considered in the evaluation of the weather-responsive traffic response models.

Flow diagram shows the progression of information in the DynaMIT framwork.
Figure 3-4. DynaMIT Framework

3.3.1 Hampton Roads, VA

The University of Virginia (UVA) team evaluated the performance of the DynaMIT-R program in off-line traffic estimation and prediction (Phase I, 2004) and online estimation and prediction capabilities (Phase II, 2006) in Hampton Roads, Virginia (Park et al., 2004; Park et al., 2006).

Network of Phase I and II

The Hampton Roads network is composed of three freeways segments: I-64 between Bay Avenue and the Virginia Beach-Chesapeake City Limits, I-64 forming the outer loop, I-564 between Terminal Boulevard and I-64, I-264 between Broad Creek and Rosemont Road, and entire I-664. The same network was used for Phase II.

Phase I Traffic Data Sources

Two sets of databases were used for DynaMIT supply parameter calibration and OD demand flow estimation. The first dataset was used for OD estimation and calibration of DynaMIT and the second dataset for both calibration and validation of DynaMIT. For each of years 2001 and 2003 data, two datasets were prepared for supply parameter calibration and historical OD estimation. The dataset for the supply parameter calibration was composed of 10-minute aggregated double-loop detector data with the accuracy of speed and volume data. The dataset for historical OD estimation dealt with volume data from all Smart Travel Laboratory (STL) detectors and Traffic Management System (TMS) stations.

Datasets of Phase II

Traffic counts and speed data were obtained from the traffic sensor stations. For the case of supply parameter calibration, only data from the stations configured with double loop detectors was used to ensure accurate speed measures for supply parameter calibration. In addition, traffic data including travel times were used in order to measure the performance of DynaMIT.

Since there existed stations with some missing detector data and inflated by the total number of detectors, and a number of sections where the right most lane or the auxiliary lane carries very low volumes or very high volumes depending on the distance to adjacent interchange and flow characteristics, lane utilization factors were introduced for computing traffic counts of detectors with missing data that could be highly overestimated or underestimated on the basis of equal lane distribution assumption. In the calibration of supply parameters, it was found that they were slightly revised to better represent field traffic conditions by incorporating the lane utilization factors.

Calibration and Validation of Supply Parameters (Phase I and II)

The major steps of supply parameter calibration include segment classification, determination of three key parameters (i.e., capacity, free flow speed and maximum density under free flow speed) and curve fittings. First, the segments in the test network were categorized into several homogenous groups according to their characteristics such as corridors and roadway geometric characteristics and number of lanes. A preliminary analysis through the visual inspection of flow and speed data plots was performed to justify the segment classification; and final segment groups were defined with field data availability. Capacity and free flow speed of each segment groups was determined on the basis of field data and recommendations from the Highway Capacity Manual (HCM). The capacities under inclement weather conditions were estimated to be 95% of those under normal conditions and free flow speed was reduced by 2 mph from normal conditions. Maximum densities under free flow conditions were determined using HCM level of service A and B densities.

Since speeds and flows are relatively accurate compared with densities less reliable mainly because they are estimated from occupancies, the UVA team calibrated this two regime flow-speed function instead of speed-density function. Hence, the supply parameters were estimated with traffic sensor data from the first dataset, the estimated parameters were validated with the second dataset. Using the sensor data of double loop detectors from the second dataset, the quality of the supply parameters was visually verified and it was found that the supply parameters fit well.

Demand Calibration (Phase I and II)

The objective of demand calibration is to estimate the historical OD flows and the variance-covariance matrix (varcov) for the study network. For the purpose of demand calibration, the planning version of DynaMIT (i.e., DynaMIT-P) was used to compute the assignment matrices during the OD optimization. The historical OD estimations were done for two periods: off-peak (10:30 AM to 12:30 AM) and peak (4:30 PM to 6:30 PM) periods with normal days for the estimation of stable historical OD flows at relatively quick convergence.

Initial OD matrix was obtained by a double-constrained gravity model since the Hampton Roads network is a well-bounded freeway system where the total trips in entering and exiting the freeway system with on ramps as origins and off ramps as destinations should be close. Since the relative reliability of traffic sensor and OD pair demands were not known, calibration process was started by providing higher weights to the OD pairs having low counts and use of the data quality for the stations. Three normal days were used for demand calibration. The following points summarize the procedure followed in the demand calibration process for both Phase I and Phase II.

  1. DynaMIT-P program was run with traffic counts from a normal day using the initial OD matrix obtained from a gravity model. Once newly estimated assignment matrices from DynaMIT-P were obtained, the estimated OD matrix was externally optimized via MATLAB software to ensure its convergence.
  2. By replacing the initial OD with the OD obtained at the end of step 1, DynaMIT-P was run for the same day again. The estimated OD from DynaMIT-P was again externally optimized via MATLAB.
  3. Using the new OD matrix after step 2, DynaMIT-P was run with a second day by following the same procedure as in the above tow steps. An updated OD was obtained.
  4. At the end of the second day, varcov matrix was estimated.
  5. Using the updated OD matrix obtained at step 3 and varcov matrix at step 4, DynaMIT-P was run for a third day.
  6. At the end of third day, the obtained estimated OD was used as historical OD and varcov matrix was computed again.

Both calibration results for off-peak and peak periods showed that the Root Mean Square Normalized (RMSN) errors were decreasing consistently for the last three runs and then showing similar values for the last two runs. Also, high correlation between the simulated and actual sensor counts was observed to show the comparison of counts for the last day of the calibration for both periods. Hence, OD was converged for the off-peak and peak conditions and considered as a reliable historical OD matrix. The same was true to the results of Phase II.

Evaluation of DynaMIT-R Off-line Performance

In Phase I, DynaMIT-R (real time version) was implemented with the five different scenarios consisting of two off-peak and two peak periods, and a VMS case. For each of non-peak and peak periods, five normal days were evaluated for the performance of DynaMIT-R under normal conditions, and a mix of normal, bad weather, and incident days were evaluated for such mixed conditions. The VMS scenario evaluated the impact of diversion due to the implementation of VMS display of incident conditions. As a result, it can be concluded that DynaMIT-R fairly well predicts traffic conditions for all the scenarios studied and is also capable of giving guidance to the users of the surface transportation system with the use of VMS functionality.

Online Evaluation (Phase II)

Online evaluation for three days was conducted with all required data provided in real-time by various sources such as traffic sensors (e.g., loop detectors), CCTV cameras, Hampton Roads Smart Traffic Center (HRSTC) operators, etc. Through the sources, traffic counts, speed and incident information were fed into the DynaMIT program during online evaluation. In addition, a probe vehicle was employed to obtain field travel times on a few key routes. The other key element was to achieve faster computation on given estimation and prediction intervals. This would help DynaMIT operator have more time to implement various strategies, especially under incident conditions.

With the newly estimated 24-hour historical OD and supply parameters, online evaluation of DynaMIT was implemented. Traffic sensor counts were aggregated into five minute counts and fed into the DynaMIT. The incident management interface provided an incident alert as soon as a new incident is being identified and recorded. With the incident alert and the use of traffic surveillance camera, an operator can assess the condition of incident and enter the incident information to the DynaMIT using the enhanced Java Road Network Editor (jRNE) incident input interface. Since the implementation of DynaMIT was an online-open loop evaluation, there was no feedback from DynaMIT to the field. The performance measures of RMSN errors for volume counts, absolute values of speeds and travel times were considered for comparing the simulated results from DynaMIT with the actual field conditions.

From the online evaluation, the MATLAB enabled DynaMIT, which enhanced OD estimation procedure, significantly improved its computation runtime. Average runtime and maximum runtime were reduced by 44% and 25%, respectively. This would certainly provide more time for an operator at a TMC to better estimate DynaMIT parameters, especially during incidents, and to better evaluate various strategies for proactive control of traffic.

DynaMIT showed good performance with the RMSN errors of 0.15 ~ 0.25 in the estimation of traffic sensor counts, while those of predicted traffic sensor counts ranged from 0.25 and 0.4. These errors were fairly consistent regardless of network congestion levels. The prediction errors were a bit worse than those obtained at the off-line evaluation during the Phase I study. The performance of traffic counts estimation during incidents was as good as those shown during normal conditions, except for a case with sever incident condition where the estimation of incident parameters was not done accurately. As such, it was found that DynaMIT can adequately model incident conditions as long as incident parameters are properly determined.

When speeds and travel times were used in the evaluation of DynaMIT's estimation and prediction capabilities during online evaluation, it was observed that both estimation and prediction show some discrepancies during congested conditions even though traffic counts matched quite well. This clearly indicates traffic count is not a very sensitive measure in the evaluation of DynaMIT's estimation and prediction capabilities. In addition, it suggests that supply parameters may not be optimal for all the segments. Obviously, this was not a limitation of DynaMIT, but it was due to lack of actual field traffic data. Therefore, more efforts in the calibration of supply parameters should be given wherever possible. As traffic data is not available for each segment of the network, supply parameters of those segments were obtained from similar segments.

Challenges Encountered (Phase I and II)

The following section includes the challenges that the project teams encountered through both studies and their discussions related with OD estimation and update of varcov matrix.

Phase I:

Phase II:

3.3.2 South Park region of Downtown Los Angeles, CA

The study network in South Park region of downtown Los Angeles consists of two major freeways (I-10 and I-110) and a dense network of arterial streets. It is represented in DynaMIT by a set of 243 nodes and interconnected 606 directed links, which are subdivided into 740 segments to model changing section geometry within a link. Half of more than 200 arterial intersections in the network consist of signalized intersections. Signals along the major arterial segments are synchronized (Wen et al., 2006).

Demand Calibration

There was ground work before the demand calibration as follows:

The path generation process attempted to capture all reasonable and feasible paths for each OD pair. To this end, a suitable path set was obtained using 20 random draws to complement link-elimination based shortest paths from every link on the network to every destination node. In the course of this process, a path with a higher freeway percentage among two paths with same travel time was preferred and all paths longer than the shortest path by more than 20% were eliminated between each OD pair to eliminate many redundant and unreasonable paths. Manual inspection of various OD pairs confirmed that nearly all practical paths were included in the path choice set, which finally contained total of 44,224 OD paths for 3745 OD pairs.

Since DynaMIT would be deployed for real-time traffic estimation and prediction-based guidance generation on the site, the period of off-line calibration encompasses entire 24 hour, excluding 3 hours from midnight to 3:00 AM when arterial data was not available. The 21 hour calibration period was divided into 84 intervals of 15 minutes each, which was decided considering computational efficiency and the fact that sensor counts do not exhibit significantly large variations for shorter interval.

Several simplifying assumptions were made in order to accommodate practical considerations and data availability. The covariance matrices of error between the estimated and a-priori OD flows (Wh) and error between simulated sensor counts and observed counts (Vh) were assumed to possess a diagonal structure implying that the sensor measurement errors and direct OD measurement errors are uncorrelated. The auto-regressive factors were also assumed to be diagonal suggesting that deviation of OD pair from its historical values depends only on the deviation of same OD pair from its historical values in previous intervals.

Since it was observed that availability of many alternative paths between a freeway-to-freeway OD pair were forcing an unreasonably high proportion of drivers to use part-arterial-based path, path-size logit model was applied to calculated the probabilities of selecting various routes with utility of given path. To resolve this issue, optimal route choice parameters were found.

OD estimation, Calibration, and Validation

Five days were selected spanning one entire month and all days of week (Monday-Friday) to carry out the sequential calibration process (Figure 3-5). Generalized Least Square Estimation was used to estimate OD matrix interval by interval. Very high weights were applied to sensor counts and very small weights to seed OD flows so that they could extract all possible information from sensor counts instead of meaningless estimate of seed OD flows for the first day of calibration. Once first day was completely estimated, error covariance matrices were obtained. Calibration procedure for the second day was exactly similar to the first day, except the calculated error covariance matrix used in GLS formulation. This approach was repeated in the third day, fourth day and fifth day, every time recalculating the error covariance matrix and updating historical OD matrices and experienced travel times. The performance of calibration was verified with the estimated error statistics and graphical comparisons of simulated and observed counts for the same periods.

Diagram shows the elements of the sequential callibration process over a five-day period.
Figure 3-5. Within-Day and Day-to-Day Process

After calibration was done for five days, auto-regressive (AR) factors were calculated for DynaMIT's prediction capabilities. The calibrated AR factors were obtained by regressing the deviations of estimated OD flows for all five days with corresponding historical OD flows with auto-regressive factor equation introduced in the report and presented by the group of OD pairs classified by their size.

Validation were employed to assess whether the calibrated set of historical OD matrices, historical travel times, and variance-covariance matrices continues to perform satisfactorily when supplied with fresh input, as would be the case in an on-site application. For the validation for its estimation and prediction performance, another day of new data which was not used in calibration process was selected. It was observed that errors during validation runs were comparable to those obtained during calibration process within acceptable limit in the validation of its estimation performance.

Prediction tests for calibrated AR parameters were started by estimating OD flows for selected time intervals for both days. Five intervals were picked uniformly during the day to test the effectiveness of the calibrated AR factors. Then, deviations in the OD flows for next fifteen minute period (one-step prediction) were predicted using estimated OD flows for each time period. Similarly, prediction for next fifteen minute (two-step prediction) were performed using a set of estimated OD flows from past intervals, and just predicted OD flow for previous interval was calculated. In the same manner, further step predictions up to next one hour were carried out. It was observed that errors during validation runs were comparable to those obtained during calibration process, and were within acceptable limit. Therefore, it was validated that the historical (calibrated) parameters were able to replicate weekday data. Several variations of the OD prediction method were tested, and one based on moving averages was found to yield the most consistent patterns.

Off-line Calibration of Speed-density Relationships

Link performance functions in much of the literature are calibrated by fitting a curve to the observed traffic data. In the previous approaches, the calibration variables were limited to the speed-density function parameters. However, the optimization depends on several other DTA inputs such as OD flows and route choice model parameters. The values selected for these other inputs and parameters thus impact the outcome of the supply calibration. One may thus iterate between demand and supply calibration steps until convergence (as defined by the modeler) is reached. This iterative procedure can be time-consuming and inefficient, as only a subset of the available data is used in either calibration.

Balakrishna et al. (2007) presented a calibration framework that allows the simultaneous calibration of all supply and demand parameters and unknown inputs typical to DTA models (e.g. OD flows, route choice parameters, capacities, speed-density parameters) using any available data (e.g. counts, speeds, densities, queue lengths). Thus all significant DTA inputs and parameters may be estimated simultaneously, providing the most efficient result. The problem is solved with the SPSA algorithm.

This calibration approach provides a unique advantage. Since the parameters of the speed-density functions for all segments are estimated simultaneously, the function parameters for each segment can be calibrated to better fit the traffic data at the network level.

The above method has been applied to the Los Angeles network (Balakrishna et al., 2008), an area of heavy traffic throughout the year owing to commuters and the regularity of sporting and convention special events. The numerical results show that the estimator, denoting supply calibration using count data, results in a significant improvement in replicating the counts and traffic dynamics (speeds) in the area. Further, the increased accuracy is reflected on both freeway and arterial links. In the base case, the speed-density parameters were fitted at individual sensor locations and attributed to all segments in the respective groups.

On-line Calibration of Speed-density Relationships

In the current DTA framework, only the OD flows are calibrated on-line. In most cases, the approach to the problem of calibration of the other parameters has been to calibrate the simulation models off-line using a database of historic information. The calibrated parameter values are then used in the on-line simulations. The calibrated model parameters, therefore, represent average conditions over the period represented in the data. Models that were calibrated this way may produce satisfactory results in off-line evaluation studies, which are concerned with the expected performance of various traffic management strategies. However, this may not be the case in real-time applications, which are concerned with the system performance on the given day. If the model that was calibrated off-line is used without adjustment, the system is not sensitive to the variability of the traffic conditions between days, which are the result of variations in the parameters of the system, such as weather and surface conditions. Such variations may cause traffic conditions to differ significantly from the average values. Thus, the predictive power of the simulation model may be reduced. To overcome this problem, real-time data can be used to recalibrate and adjust the model parameters on-line so that prevailing traffic conditions can be captured more accurately. The wealth of information included in the off-line values can be incorporated into this process by using them as a priori estimates.

Tavana and Mahmassani (2000) use transfer function methods (bivariate time-series models) to estimate dynamic speed-density relations from typical detector data. Huynh et al. (2002) extend the work of Tavana and Mahmassani (2000) by incorporating the transfer function model into a simulation-based DTA framework. Qin and Mahmassani (2004) evaluate the same model with actual sensor data from several links of the Irvine, CA network.

Antoniou et al. (2007) formulate the problem of on-line calibration of a DTA model as a nonlinear state-space model that allows for the simultaneous calibration of all model parameters and inputs. The methodology is generic and flexible and does not make any assumptions on the underlying model structure, the parameters to be calibrated or the type of available measurements. Because of its nonlinear nature, the resulting model cannot be solved by the Kalman filter, and therefore, nonlinear extensions are considered: the extended Kalman filter (EKF); the limiting EKF (LimEKF); and the unscented Kalman filter. The solution algorithms are applied to the on-line calibration of the state-of-the-art DynaMIT DTA model, and their use is demonstrated in a freeway network in Southampton, U.K. The LimEKF shows accuracy that is comparable to that of the best algorithm but with vastly superior computational performance. Antoniou et al. (2007) present an application of their on-line DTA calibration methodology using data from a freeway network in Southampton, UK. The study demonstrates the performance gains that can be obtained through the dynamic, simultaneous calibration of the speed-density relationships and other supply-side parameters.

On-line Evaluation

For the on-line evaluation, DynaMIT was run in on-line, real-time mode, and the sensor files are used to simulate the surveillance interface setup at LADOT. Through the preliminary studies, a few promising results were achieved. Firstly, estimated counts generally stay close to the actual counts for the entire day. Secondly, predicted counts also follow the same trends and most of them are reasonably accurate. This indicates that estimates reported by DynaMIT through its traffic simulation are likely to reflect the real traffic condition, and the predictions of DynaMIT are likely to foresee the evolving traffic condition. The preliminary evaluation also illustrated that one-step prediction (obtained just one interval ahead of the real-time) is in general better than two-step prediction. It indicated that the accuracy of prediction will deteriorate over time.

Other than the areas introduced above, there are more areas that DynaMIT was tested and applied as a decision-aid tool for traffic diversion particularly in Switzerland. The scope of its application was the development of diversion strategies with a VMS-based system.

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