Evaluation and Improvement of Consistency of Hybrid and Multi- Resolution Traffic Simulation Models

Transcription

1 Evaluation and Improvement of Consistency of Hybrid and Multi- Resolution Traffic Simulation Models James Tokishi Department of Civil Engineering and Engineering Mechanics, The University of Arizona, E nd St., Tucson, AZ 1, USA jtokishi@ .arizona.edu Yi-Chang Chiu, Ph.D. Department of Civil Engineering and Engineering Mechanics, The University of Arizona, E nd St., Tucson, AZ 1, USA chiu@ .arizona.edu Words:, Figures and Tables: 0=,00 Total Words:,1 1 Submitted Presentation and Publication at the th Annual Meeting of Transportation Research Board 1

2 Abstract In recent years, hybrid traffic models, which combine aspects of models with different time resolutions have been developed. These models, however, have additional consistency constraints, when compared with non-hybrid models, such as the need to maintain consistency across their components models. This consistency requirement takes two forms, model-based consistency, i.e. whether the model outputs and measures of effectiveness match under specific conditions; and process-based consistency, i.e. whether the models maintain consistency as demands or roadway conditions change. This paper is intended to provide insight into statistical measures that can be used to evaluate both kinds of consistency, and to demonstrate a process that can be used to increase the consistency of models. 1 Introduction The concept of hybrid modeling is rather common in many aspect of transportation engineering system modeling, ranging from automatic vehicle guidance (1), hybrid shortest path algorithms (, ), centralized-decentralized traffic routing and guidance (-), and real-time traffic prediction model (, ). The goal of hybridization is generally to retain/synergize the benefit of the respective component systems and to circumvent the shortcoming of the respective component systems. In recent years, as traffic simulation models have become widely accepted and used in practice, hybrid models, which combine aspects of models with different time resolutions have been developed. These hybrid models, which commonly combine macroscopic or mesoscopic models with microscopic models, allow for the modeling of large areas, such as entire cities or counties, while simultaneously maintaining detail in areas of interest. This allows for the development of model networks that can easily represent network-wide changes to local improvements. These hybrid traffic simulation models generally fall into two categories, on-line or runtime models, which directly integrate their component models and run them simultaneously on different sections of the network. In such a model a sub-area is typically created that run the microscopic simulation logic and rules while the rest of the network runs the with a mesoscopic traffic simulation rules. When a vehicle traverses the boundary the handshaking needs to take place to remove the vehicles object from the origin domain to the receiving domain. The

3 information that is passed to the receiving domain includes all the vehicles attributes as well as the route taken by the vehicles. Due to differing time resolution, simulation interval synchronization needs to be maintained and the vehicle departure distribution from meso to micro model and vice versa needs to be properly modeled (, ). There are several known runtime models, such as MiMe (1) (mesoscopic Mezzo, and microscopic Mitsim), InterMezzo (1), Aimsun (1) (Aimsun mesoscopic, microscopic models), and TransModeler (1), which directly integrate models of different time or vehicle flow resolutions, and model different sections of the network using the component models. Off-line or multi-resolution models (MRM), are those which convert desired subareas of a lower-resolution parent model into a high-resolution (often microscopic) model. Multiresolution models, such as SATURN/DRACULA-MARS (microscopic component of SATURN (Vilet 1), and macroscopic DRACULA-MARS (1, 1), VISUM (1)/VISSIM (1) integration (0), and the DynusT-VISSIM Conversion (1-) (mesoscopic DynusT) tool run their components independently, and feature methods to convert the network, demands, and routes from one model to another. In the DynusT-VISSIM MRM framework, a subarea is defined and cut from a calibrated large regional DynusT network. All vehicles traversing the sub-area have their trajectory properly trimmed and the sub-trajectories are converted to corresponding demand matrices, zones, and vehicle and path files. A scripting tool then reads those files and generates the corresponding network and vehicle elements and exports such information to VISSIM through VISSIM s COM interface API. All the vehicles and routes are simulated inside VISSIM as static routes, namely, no re-routing is permitted inside VISSIM (as the re-routing is performed by DynusT) (-). This MRM framework allows modelers to more easily develop a microscopic model for a desired subarea, which can be used to perform more detailed analyses using features not available in lower resolution models, such as incorporating transit stops or pedestrian volumes. While MRM models may bring forth great potential in synergizing models with different spatial and temporal resolutions and in potentially leading to an effective and efficient modeling paradigm, there are several issues relating to this type of approach that have not been extensively understood and researched in the literature.

4 One key issue is consistency. The notion of consistency is defined from two distinct contexts: (1) model-based consistency (MBC) and () process-based consistency (PBC). MBC is concerned with whether a model user has established a satisfactory level of similarity of traffic dynamic between micro and meso models before commencing a hybrid simulation run. The microscopic and mesoscopic component models used in hybrid simulation should produce similar and consistent traffic dynamics and simulation statistics in order for the hybrid simulation to be meaningful. Without maintaining a satisfactory level of consistency between the component models, a hybrid simulation may produce very different results every time a different subarea is defined even when the overall model inputs remain the same. This consistency issue could be addressed through the calibration process, in other words, calibrating both models against the same set of actual field data, or calibrating one model against the other (-). Field Data Microscopic Model Mesoscopic (DTA) Figure 1 Model-Based Consistency PBC is concerned with establishing the fixed point or equilibrium solution related to the interplay of the component models, when one of the component models is being updated significantly and the consistency between the component models has been disturbed. Without MBC, PBC does not exist. Even if MBC is attained, however, PBC could still be violated by modifying one of the component models. To this extent the re-establishment of PBC for the hybrid model a feedback iterative process in which the information is passed back-and-forth between the component models and an appropriately designed algorithm ensures that the PBC is properly re-established after a few iterations. The PBC is particularly relevant from the perspective of dynamic traffic assignment (DTA). One example of a case where PBC would need to be considered is when there is a significant change in volume on a link. A network for

5 which PBC is established would have a change in MoEs on that link similar to that which would be expected in reality; or, from the perspective of MRM, the parent and subarea networks should have similar MoEs. Another example is in the case where link capability is improved as part of an analysis scenario. In this case, the scenario would result in an improved level of service and may start to attract more motorists from other adjacent roadways. Within MRM, the network changes need to be fed back into the parent model, so that new demands can be created that reflect the roadway changes, and then re-exported to a new subarea network. This feedback process, as shown in Figure, continues until the route flows and MoE remain unchanged from one iteration to the next. Route Flow = F 1 (Micro Model MoE) Microscopic Model Mesoscopic (DTA) Micro Model MoE = F (Route Flow) Route Flow*=F 1 F (Route Flow*) Micro Mode MoE*=F F 1 (Micro Model MoE*) Figure : Process-Based Consistency Following the overall conceptual framework for MBC and PBC, this paper primarily focuses on presenting a method, based on calibration techniques, to evaluate whether the microscopic subarea of a MRM network is consistent with the larger mesoscopic network, and the calibration approach to improve the consistency of an inconsistent model. The PBC process is not discussed in detailed in this paper due to size limit.

6 The purpose of this research is to identify statistics and MoEs that can be used to evaluate consistency within a hybrid MRM framework, and to demonstrate a method through which a MRM subarea could be made more consistent with its parent model. The structure of this paper is as follows. Section discusses the relevant literature in hybrid model consistency, calibration statistics and standards. Section lays out the calibration approach and selected evaluation MoEs. Section provides an example of a MRM network analyzed and calibrated using this approach, and shows the improvements that can be examined using this approach. Finally, section concludes the paper. Relevant Literature.1 Consistency Criteria As with non-hybrid models, hybrid models need to be consistent with and be able to match field conditions. However, in the case of runtime hybrid models, they also need to maintain consistency between the models at the network boundaries, and maintain consistent logic across the entire network. Multi-resolution models also have additional criteria. First, the behavior of vehicles within the subarea should match both field conditions and the output from the larger modeled area so that the model starting conditions are the same. Second, the models used for the parent and subarea networks need to have consistent reactions to changes in demand. As part of the development of MiMe, Burghout () (, ) identified five general requirements which must be met in the formulation of a consistent hybrid model. These criteria were also used to evaluate the hybrid architecture of AIMSUN (0). 1 Consistency in route choice where vehicles make the same routing decisions in both the mesoscopic and microscopic networks Consistency in network representation Consistency of traffic dynamics at meso-micro boundaries, such as allowing queues to continue through the borders Consistency in traffic performance in the meso and micro submodels, where the two models have (ideally) identical vehicle dynamics under the same conditions Transparent communication and data exchanges, where the networks exchange a minimum amount of data.

7 In developing the DynusT-VISSIM Conversion (DVC) tool, Shelton et al. (1) also identified and addressed a number of specific consistency issues within the MRM technique used in this paper: 1 1 Vehicle loading, due to the difference in vehicle generation in DynusT (generation links) and VISSIM (loading at a defined point). Network geometry, due to VISSIM requiring more precision than DynusT or VISUM, and VISUM automatically adding features such as speed reduction zones. Time resolution, due to macroscopic models often having -hour resolutions, mesoscopic models having resolutions between several and tens of seconds ( seconds in DynusT), and microscopic models having resolutions measured in tenths of a second, which requires care when converting networks between models. Traffic dynamics, due to differences in vehicle behavior models (e.g. volume-delay, speed-density, car following) Calibration Model calibration is the crucial step which ensures that a base model network matches, to a reasonable degree, real-world conditions. This is usually an iterative procedure, where model parameters are adjusted based on feedback from the previous iteration until an acceptable result is found. Within the MRM framework, the calibration of the subarea network has two goals, matching the base conditions of the parent model to ensure that the initial conditions are consistent; and ensuring that the models have consistent reactions to variations in demand. Many papers (-) have been published addressing the statistical methods that can be applied toward model calibration. Many of these statistical techniques can be applied to either volume, or speed, where a perfect model would have equal values for all data points.

8 Measure Table 1 Sample model calibration statistics Equation Root Mean Squared Error (RMSE) Absolute Error (AE) Mean Error (ME) Percent Error (PE) [ ( ) ( )] ( ) ( ) or ( ) ( ) ( ) or ( ) ( ) ( ) ( ) ( ) ( ) or ( ) ( ) ( ) ( ) Mean Percent Error (MPE) or ( ) ( ) ( ) GEH Statistic ( ) Hypothesis testing (t-test) At an α significance level, reject H 0 if ( ) ( ) Hypothesis testing (Z-test) At an α significance level, reject H 0 if

9 Additionally, some state departments of transportation () and the FHWA (0) have developed model calibration criteria, such as those shown in Table. Some of these may also be applicable in evaluating the consistency of MRM models. Criteria and Measures Table WisDOT/FHWA model calibration targets Calibration Acceptance Targets Hourly Flows, Model Versus Observed Individual Link Flows Within 1%, for 00vph<Flow<00vph Within 0vph for Flow<00vph Within 00vph for Flow>00vph >% of cases > of cases >% of cases Sum of All Link Flows Within % GEH Statistic < for Individual Link Flows >% of cases GEH Statistic for Sum of All Link Flows < Travel Times, Model Versus Observed Journey Times, Network Within 1% (or 1 min, if higher) >% of cases Visual Audits Individual Link Speeds Visually Acceptable Speed-Flow Relationship To analyst s satisfaction Bottlenecks Visually Acceptable Queuing To analyst s satisfaction Research Methodology This project utilized the DynusT/VISSIM MRM framework, and assumes that a properly calibrated mesoscopic DTA network is already available. The procedure to improve the consistency of the MRM network focused mainly on the subarea network which was modeled in VISSIM.

10 .1 Number of Runs Using Corsim, Wiegand and Yang (1) found that model averages were unstable due to stochastic variation up to about -1 runs. Using that upper estimate, each step in the calibration process was run with 1 different random seeds, and averaged to get the desired MoEs.. Selected Metrics Based on the available existing standards and techniques, the following statistical measures were considered for use as measures of model consistency: hour adjusted GEH Percent of -minute periods that meet the percent or absolute error of link volume, based on Wisconsin DOT criteria Mean percent error of -minute link speeds over the entire simulated period Percentage of -minute intervals for which the error between models is equal to zero at a % confidence level using a Z-test for both speed and flow rate Network Cleanup During the network export process from VISUM to VISSIM, several design elements are automatically added. Zone connector links are added to load vehicles into the network, and conflict zones, stop signs, and reduced speed areas are added at locations where the conversion algorithm considers them necessary. In addition, all links are set to driver behavior settings which utilizes VISSIM s default driver behavior parameters. The first post-conversion step is network cleaning, which took six steps, through which unnecessary added features were removed, or necessary modifications were made to the network. The six steps in the network cleaning process are shown in Table.

11 1 1 Table Network cleanup procedure Step Change made 0 Baseline model (no edits) 1 Widen zone connectors to be equal to the immediate downstream link Remove unnecessary reduced speed zones Set freeway links to freeway driver behavior Remove unnecessary conflict zones Remove unnecessary stop signs. Network Calibration Following network cleaning, the VISSIM subarea network was calibrated against the parent DynusT network. VISSIM uses the Wiedemann and car following models() for urban and freeway driving, respectively. The Wiedemann model has a total of eleven adjustable parameters, shown in Table. Table VISSIM freeway driver behavior parameters Parameter Description Default Value CC0 Standstill distance. ft CC1 Headway time 0.0 s CC Following variation 1.1 ft CC Threshold for entering following -.00 CC Following threshold (negative) 0. CC Following threshold (positive) 0. CC Speed dependency of oscillation. CC Oscillation acceleration 0. ft/s CC Standstill acceleration. ft/s CC Acceleration at 0 km/h. ft/s Look-back distance Distance that a vehicle can see behind ft While much work has gone into devising calibration strategies for VISSIM networks (), Lownes and Machemehl (, ) examined these parameters to determine their effects on the capacity of VISSIM links, and found that CC0, CC1, CC, CC, CC, and CC had significant effects on roadway capacity.

12 In addition to the driver behavior parameters, VISSIM has seven parameters that govern lane changing behavior, shown in Table, below Table Default VISSIM freeway lane change parameters Parameter Default value Waiting time before diffusion (seconds) 0.0 Minimum headway (front/rear) (ft) 1. Safety distance reduction factor (unitless) 0.0 Maximum deceleration for cooperative braking (ft/s ) -. Maximum deceleration, used when approaching the emergency stop distance (ft/s ) Reduction rate to the maximum deceleration of -1 m/s per defined distance interval from the emergency stop distance (ft) -1.1 The calibration process was based on the parameters identified by Lownes and Machemehl and the lane change parameters. In this process, a single parameter in VISSIM s driver behavior or lane change settings was adjusted until an optimal value was determined, that parameter was fixed, and the process moved on to the next parameter, until a final calibrated model was developed. Case Study A DynusT network of the northwest side of Tucson around I-, was used to generate the subarea for consistency testing. From the larger network, a subarea section, was exported and converted to VISSIM for evaluation..1 Study network Link - in the Tucson DynusT network was chosen as the evaluation link. This link is a -lane wide segment between an upstream on-ramp and a downstream off-ramp, with a speed limit of mph. The model is based on hours of collected data, during which time vehicle flows range from about 00 vehicles per hour to 00 vehicles per hour. 00 1

13 Figure DynusT Network and Subarea Once the DynusT model had been fully calibrated, the selected link, and the stretch of freeway 1 mile upstream and downstream were converted into a VISSIM network using the DVC Tool and DynusT-VISSIM integration architecture. 1 Figure VISSIM Subarea Network. Evaluation of network In order to establish a consistent starting point for MBC, this base 0% demand network was evaluated first. Using the process decribed in Section, the model was cleaned to remoe unnecessary features or add required features, and was then calibrated, going through multiple 1

14 iterations for each parameter, until a final calibrated model was developed. The selected MoEs for the uncalibrated network, cleaned network, and the final iteration of calibration are shown in Table. All of the MoEs showed clear improvements across the calibration and consistency evaluation process, indicating that the network can be alibrated to improve consistency. Table Subarea network evaluation Uncalibrated Cleaned Network Final Iteration GEH Total percent error (Q) -.% -.% 0.% Percent meeting flow targets 1% 1% % Mean percent error (V) -% -% -% % Confidence Level (Q) % % 0% % Confidence Level (V) % % %. 1% demand Once MBC had been established, a second model was also developed to evaluate PBC, i.e. the ability of the VISSIM model to adequately reflect changes in demand, using the parameters from the final iteration of calibration. Using the same parent model with 1% demand, a new subarea was generated, and run through the same steps as the first model, except that instead of calibration following network cleaning, it was immediately set and run with the parameters from the final iteration of the first subarea. The selected MoEs are shown in Table. Table Increased demand network evaluation Uncalibrated Cleaned Network Calibrated Parameters GEH Total percent error (Q) -.% -.0% -0.% Percent meeting flow targets 0% 1% % Mean percent error (V) % -% -% % Confidence Level (Q) % 1% % % Confidence Level (V) % % % 1

15 While the MoEs in the final PBC model are generally worse than those in the initial MBC case, the model may still be able to be considered consistent. The volume-based metrics generally appear to be within acceptable ranges, as the MBC parameter network produces a GEH Statistic under.0, which is its lower bound for acceptance, the total volume error is likewise fairly low at -.%, and 1% of time periods have statistically zero error. The speed-based metrics are slightly poorer, with a mean percent error of 1%, and only % of time periods having statistically zero error, but they still indicate a general agreement between the two models. Concluding Remarks The purpose of this paper was to examine the existing literature to identify techniques that can be used to evaluate consistency within a hybrid MRM framework, and to demonstrate a method, based on the calibration techniques, through which a MRM subarea could be made more consistent with its parent model. The results of this analysis indicate that the models can be made consistent in both the MBC and PBC contexts. In establishing MBC, all of the evaluation MoEs greatly improved through an iterative calibration process, although the hypothesis testing on link speeds seems to indicate that there may still be some unresolved errors present. In establishing PBC, all of the evaluation MoEs similarly improved when the previously calibrated parameters were applied, but the discrepancy in meeting the flow targets may indicate unresolved errors. For example, it could indicate that the MBC parameters are a good match for the base conditions, but do not respond well to changes in demand, which may be resolved by combining the MBC and PBC procedures into a single calibration approach, where the model is calibrated against several different demand scenarios instead of just a single base scenario. Future research into this topic lies primarily in two areas. The first area is further examination of the network to identify issues and further improve evaluation MoEs, as well as testing of alternate links or different conditions to further test the evaluation process. The second area is developing standards, similar to the WisDOT and FHWA calibration criteria, which can be used to determine when models are sufficiently consistent. 1

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