COMPARATIVE ANALYSIS OF CAR-FOLLOWING MODELS FOR EMISSION ESTIMATION

Transcription

1 COMPARATIVE ANALYSIS OF CAR-FOLLOWING MODELS FOR EMISSION ESTIMATION by Guohua Song, Ph.D., Associate Professor MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University Shangyuan Cun, Haidian District, Beijing, P.R. China Tel: --, Fax: --, Lei Yu, Ph.D., P.E. Professor of Texas Southern University Yangtze River Scholar of Beijing Jiaotong University College of Science and Technology, Texas Southern University Cleburne Avenue, Houston, Texas Tel: --, Fax: --, and Long Xu, Traffic Engineer Beijing Tranportation Research Center Liuliqiao Road, Fengtai District. Beijing, P.R. China Tel: --, Fax: --, Submitted for Presentation at the nd Transportation Research Board Annual Meeting and Publication in the Transportation Research Record Washington D.C., January, Date of Submission: July, Word Count: (Text) + * (Tables) + * (Figures) = TRB Annual Meeting

2 Song, Yu, and Xu ABSTRACT Recent studies indicated that the accuracy of the emission estimation in a traffic simulation model can hardly be improved by using the traditional model calibration approaches. Instead, its internal mechanism in depicting the second-by-second vehicle activities needs to be investigated. Since the car-following model is the core component of a traffic simulation model, this paper attempts to conduct a comparative study of car-following models on their effects on the explanatory parameter of vehicle emissions - vehicle specific power (VSP) distribution. OVM, GFM, FVDM, Wiedemann, and Fritzsche car-following models are selected for the analysis. Massive filed car-following trajectories are collected and a numerical simulation method is designed for each car-following model to generate its vehicle trajectories and the speed-specific VSP distributions. By comparing VSP distributions collected from the field and generated by car-following models, it is found that OVM and GFM models generate unrealistic VSP distributions, which will lead to significant emission estimation errors. By adding the variable of positive velocity difference, The FVDM molde can improve the accrucy of the VSP distribution and emission estimation effectively. The VSP distribution of Wiedemann model differs largely from the field data, which overestimates the peak VSP fraction and the fractions in aggressive driving modes. The Fritzsche model produces consistent VSP distributions with the field ones. It is also found that the speed-specific VSP distribution is highly correlated with the acceleration distribution. Therefore, improving the accuracy of speed-specific acceleration distribution is an effective measure to improve the accuracy of the VSP distribution, thus the emission estimation of the car-following models. Keywords: Car-Following Model; VSP Distribution; Traffic Simulation; Vehicle Emissions; TRB Annual Meeting

3 Song, Yu, and Xu ITRODUCTION Traffic management strategies have been widely accepted as an important measure to improve vehicle operating conditions, thus reduce vehicle emissions of road traffic. In order to evaluate the effects of traffic management strategies on vehicle emissions, issues associated with the integration of traffic micro-simulation models and vehicle emission models have been extensively studied and applied, in which second-by-second vehicle activities generated by simulation models were commonly used for calculating emissions. However, the objective of any traffic simulation models was originally designed to capture traffic operational conditions on the roads instead of vehicle emissions. Traffic simulation models were generally calibrated and validated by aggregated traffic flow parameters such as the average (or distribution) of speed, flow, or queue length, instead of disaggregated and emission-sensitive parameters such as the instantaneous speed, acceleration, or power. Some latest research has indicated that traffic simulation models may not accurately represent vehicle dynamics at the second-by-second level (-). Song et al. () showed that traditional calibration methods were not able to guarantee the accuracy of the traffic simulation model for the emission estimation, thus the internal mechanism of traffic simulation models that affects vehicles dynamics, such as car-following models, need to be investigated. In this context, the objective of this study is to analyze typical car following models by comparing them with real world car-following activities, and to examine their accuracies in capturing vehicle dynamics for emission estimations. OVERVIEW OF EXISTING STUDIES With the rapidly evolving development of microscopic emission models for calculating vehicle emissions based on the second-by-second activities (-), coupling traffic simulation models with emission models has been a widely used approach for evaluating emission effects associated with alternative traffic scenarios (-). In these studies, frequently used simulation programs include traffic models of VISSIM (-, ), PARAMICS (, ), AIMSUM (), and INTEGRATION (), and fuel or emission models of MODEM (), CMEM (-), VT-Micro (), PERE (), PHEM (), IVE (), and MOVES (). However, the capability of a traffic simulation model in representing second-by-second vehicle dynamics for the purpose of emission estimation has been long questioned because most of existing traffic simulation models were generally validated by using aggregated traffic parameters (-, -) rather than instantaneous vehicle activities. Hallmark and Guensler () analyzed the simulation output of NETSIM, and reported that even though NETSIM may be calibrated correctly to predict aggregated flows or speeds, it does not adequately simulate instantaneous vehicle activity. NETSIM shows higher fractions of aggressive accelerations than field data. By comparing with the field data, Rakha et al. () pointed a major problem of car-following models is that they do not ensure that vehicle accelerations are realistic. The maximum acceleration model was proposed but its impact on emission estimation has not been examined. Based on TRB Annual Meeting

4 Song, Yu, and Xu speed/acceleration distributions derived from field trajectories, Zuylen et al. () showed that even if a procedure of calibrating parameters is good for output of traffic flows, VISSIM may not be good enough for its performance on emissions. A new parameter, ln(tad), was identified and calibrated, which improved the consistency between simulation results and the field data, however there were still non-negligible differences. Jackson and Aultman-Hall () analyzed the impact of horizontal and vertical curvatures on the second-by-second operation of a lead vehicle, and indicated that current microscopic traffic simulation models were not designed to provide data of the required accuracy by MOVES. After coupling VISSIM with PHEM emission model, Hirschmann et al. () found that a fine-tuning for the traffic simulation model was needed according to field vehicle trajectories besides parameters of the average speed and travel time. However, significant overestimations of emissions were observed even after the proposed fine-tuning calibration. By integrating the data from portable emission measurement system (PEMS) with AIMSUN simulation model, Swidan () indicated that the model validation was accepted on the macro level but it was not acceptable on the micro level. AIMSUN tended to generate higher time fraction in maintaining the constant speed while accelerated and decelerated more sharply than field vehicle trajectories. Although it was evidenced that current traffic simulation models may not be valid for emission estimations, and a majority of the above studies reported that the simulation or car following models overestimated emissions, however, sources of estimation errors are still not fully understood, thus no practical methods are identified to improve the performance of any model on emission estimations. Much of this problem can be attributed to the lack of applicable measurement methods of traffic dynamic characteristics associated with emissions (). In modeling efforts of recent years, because of its direct physical interpretation of and strong statistical relationships with vehicle emissions, the Vehicle Specific Power (VSP) has become a widely accepted explanatory variable for emissions models (). In such models, both emission rates and vehicle activities were derived by using a VSP binning method (), and running emissions of road the traffic were basically estimated by multiplying emission rates by the time spent in each VSP bin (VSP distribution). As a result, the evolution of emission models required traffic activities to be characterized by the parameter of the VSP distribution. By examining speed profiles on different links, Frey et al. () showed that VSP distributions of different runs were not statistically different within the range of the mean speed. Based on massive second-by-second field vehicle trajectories, Song et al. () found several stable regularities of speed-specific VSP distributions: (i) the VSP distribution approaches to the normal distribution; (ii) the mean of the VSP distribution increases monotonously with the travel speed; and (iii) the mean of VSP distributions is equal to VSP values of cruising at the corresponding travel speed. These regularities were also physically explainable (). By utilizing these regularities, Song et al. () provided that the VSP distribution from the VISSIM cannot represent real-world driving behaviors. The simulated VSP distribution led to over % overestimation errors of emissions. Furthermore, a sensitivity analysis on eight commonly-used VISSIM parameters TRB Annual Meeting

5 Song, Yu, and Xu illustrated that emission errors could not be reduced by the process of parameter calibration. The study suggested that the error source needs to be further investigated from the internal mechanism of the micro-simulation such as car following models. Various car-following models have been proposed, some of which have been incorporated into the commercial traffic simulation models over the past decade. Overviews and comparisons of car-following models can be found in several studies (-). According to the modeling logics, car-following models can be categorized into four brand groups: stimulus-response models, safety distance based models, psycho- physical models, and fuzzy logic based models. The GM or GHR model is the well known stimulus-response model which was originated from the research of Chandler et al. (). In these models, the response of a driver (acceleration) is a function of the stimulus (relative speed) he or she perceives. Numerous efforts have been made in an attempt to determine the best combination of model parameters, however, many contradictory findings were reported (). Safety distance based models assumes that the following vehicle keeps a safe distance or speed to avoid the possible collision. After the first model proposed by Kometani and Sasaki (), Gipps () enhanced the model by introducing an additional safety reaction time and the constraint of deceleration rates. Bando et al. () proposed an optimal velocity model (OVM), which determines the optimal or safety velocity according to the distance ahead. In order to avoid the unrealistic acceleration in OVM, Helbing and Tilch () developed a generalized force model (GFM) by adding negative velocity difference. Jiang et al. () improved GFM by considering both negative and positive velocity difference and proposed a full velocity difference model (FVDM). The Psycho-physical model is also termed as the action point model, in which thresholds are defined for several regimes (like free driving, following, closing in, and emergency) where the following car changes its behavior. Models developed by Wiedemann (, ) and Fritzsche () are widely used psycho-physical models in VISSIM and PARAMICS. Fuzzy logic based models are constructed by applying fuzzy-logic principles to the traditional car-following model (). The model divides selected inputs into a number of fuzzy sets, and logical operators are then used to produce the car-following behavior. However, few studies on the calibration of fuzzy sets have been reported (). Based on the above discussion, five recent and widely used car-following models were selected in this paper, namely OVM, GFM, FVDM, Wiedemann, and Fritzsche models, for a comparative analysis of their effects on emission estimations. METHODOLOGY General methodology in this research includes four steps. First, massive field trajectories of car-following driving behaviors on Beijing expressways were collected by using GPS devices. Second, a method based on the numerical simulation to generate the following car s activities was designed by using the field trajectory as the input of leading car for each car-following model. Third, the VSP distribution of both field and modeled car-following data were calculated and compared based on VSP regularities (). Finally, emissions estimated from each VSP distribution were TRB Annual Meeting

6 Song, Yu, and Xu compared, and error sources were discussed. Data Collection of Field Car-Following Trajectories Field car-following trajectories were collected on Beijing expressways (with the speed limit of ) by using GPS devices, Garmin GPS and GeoLogger V., mounted on the same type of light duty vehicles, Volkswagen JETTA with a. L conventional IC engine and gross weight of kg. A total of trajectories and, records of second-by-second car-following data were collected from to at Beijing Jiaotong University (). In data collection the driver was told to following the leading car and only the following car s trajectories were collected. The maximum instantaneous speed in these trajectories is. while the average speed is.. In order to analyze speed-specific VSP distributions, these trajectories were divided into, pieces of -second speed segments, and the average speed of the segment ranges from to.. Because this study does not include the discussion of the factor of the road grade, which is a sensitive parameter in calculating the VSP, the data collected on the gradient ramps or bridges are labeled by mapping the data on a GIS tool, and they are not included in calculating VSP distributions. The VSP value was calculated by using a typical equation (): () where v is the vehicle speed in the unit of m/s, a is the vehicle acceleration in the unit of m/s, and grade (%) is the vehicle vertical rise divided by the slope length, which is assumed to be zero in this paper. Numerical Simulation of Car-Following Models By using the field trajectory as the input of the leading car, programs were coded in MATLAB for each of OVM, GFM, FVDM, Wiedemann and Fritzsche models to generate the trajectory of a following car. For the first second of a trajectory, the speed of the following car was set to be equal to the leading car. The spacing headway was set to be the threshold of a safe headway for safety distance based models, while the threshold at which driver notices that he is approaching a slower vehicle for psycho-physical models. Since the average duration of a trajectory is over seconds, the effect of the above initiation of a following car on its VSP distribution was considered insignificant. The model formulas of OVM (Equations () and ()), GFM (Equations (), () and ()), and FVDM (Equations () and ()) are shown as follows. () () () (), () () TRB Annual Meeting

7 Song, Yu, and Xu () where and are the acceleration and speed of the following car, is the optimal speed function based on the spacing headway, is the sensitivity of the driver, H is the Heaviside function based on the negative speed difference, is the coefficient for the following constant, and,,,,,,, p and q are constants. The Wiedemann model defines four car-following regimes as shown in Figure, in which AX is the threshold of the desired distance between stationary vehicles including the length of the leading car (L n- ) and the desired front-to-rear distance, as shown in Equation (), where AX add and AX mult are constants, and RND n is a normally distributed parameter. ABX is the threshold of the desired minimum following distance at low speed differences, which is calculated as Equations () and (), where BX add and BX mult are constants, and v is defined in Equation (). SDX is the threshold of the maximum following distance, which is defined by Equations () and (), where EX add and EX mult are constants, and NRND and RND n are normally distributed random parameters. SDV or CLDV is the threshold of approaching or closing the leading car which can be calculated by Equations () and (), where CX const, CX add and CX mult are constants. OPDV is the threshold for the speed difference in an opening process (lower than the leader) as shown in Equation () where OPDV add and OPDV mult are constants. () () () () () () () () () The thresholds of SDV, SDX, OPDV and ABX constitute the regime of the following. When a vehicle passes either SDV or ABX into this regime, it is assigned the acceleration rate b null, while when it passes either OPDV or SDX into this regime, it is assigned the acceleration b null. b null is defined in Equation (), where BNULL mult is a calibration parameter, and RND n and NRND are normally distributed parameters. When a vehicle is located above all the thresholds in Figure, it is in the regime of free driving, in which it uses the maximum acceleration to reach its desired speed. When the desired speed is reached, it is assigned an acceleration of b null or b null. The maximum acceleration, b max, is defined by Equations () and (), TRB Annual Meeting

8 Song, Yu, and Xu where v max and v des are the maximum and desired speeds, and FAKTORV mult is a constant. When a vehicle passes the SDV or CLDV from the following regime to the regime of closing in, a deceleration of b n is assigned, as shown in Equation (), where b n- is the deceleration of the leading car. In the emergency regime, the front to rear distance is smaller than the ABX threshold, and a deceleration of (Equations () and ()) is assigned to avoid a collision, where b min is the maximum deceleration, BMIN add and BMIN mult are constants, and RND n is a normally distributed parameter. () () () () + () () Similar to the structure of the Wiedemann model, the Fritzsche model constructs five regimes (danger, closing in, following I, following II, and free driving) by six thresholds. PTN and PTP are the thresholds for the perception of negative and positive speed differences, as shown in Equations () and (), where s n- is the effective length (L n- + minimum gap between stationary vehicles), and k PTN, k PTP, and f x are model parameters. AD is the threshold of the desired distance which expresses the gap the driver wishes to maintain as defined in Equation (), where T D is a parameter of the desired time gap. AR is the threshold of the risky distance as defined in Equation (), where T r is the risky time. For a distance smaller than AR, the driver decelerates heavily to avoid collisions. AS is the threshold of the safe distance as shown in Equation (), where T s is a constant. AB is the threshold of the braking distance, which is defined in Equations () and (), where is a constant. () () () () () () In the regime of danger where is smaller than the AR threshold, the driver adopts its maximum deceleration. In the regime of closing in, when is between AB or AD and AR, and is larger than PTN, the acceleration (a n ) is assigned as shown in Equations () and (), where is the simulation time step ( second in TRB Annual Meeting

9 Song, Yu, and Xu this paper). In the regime of following I, when is between PTN and PTP and is between AR and AD, or is larger than PTP and is between AS and AR, the follower takes no conscious action, and a model parameter a null is used. When it passes the PTN threshold into this regime, it is assigned the deceleration rate a null and when it passes the thresholds PTP or AD, it is assigned the acceleration a null. In the regime of following II, when is larger than PTN, and is larger than AB or AD, it is closing in the leading car but is too large for any action to be necessary. In the free driving regime, when is smaller than PTN and is larger than AD, or is larger than PTP and is larger than AS, the follower accelerates with a normal acceleration ( ) to achieve the desired speed. When the desired speed is reached, a parameter a null is used to model its inability to maintain a constant speed. () () According to the testing vehicle and references (, -), parameters used in the numerical simulation are listed in Table. It should be mentioned that parameters of Wiedemann and Fritzsche models are referred from (-), while the exact differences between them and those used in VISSIM and PARAMICS are not publicly known (). Calculation of VSP Distributions and Vehicle Emission Factors After the numerical simulation, each of car-following models produced trajectories and, records of second-by-second car-following speeds and accelerations, which were then divided into, pieces of -second speed segments (, records of continuous data) for the calculation of speed-specific VSP distributions. After calculating the average speed of each segment, the, speed segments were further binned up by their average speed at an interval of. Consequently, there were speed-specific pools with speed bins from [, ) to [, ), and each pool contained hundreds of speed segments and over ten thousands records of continuous activity data. For each record, the VSP value was calculated according to Equation (). For each of speed-specific segment pools, the VSP distribution (time fraction in each VSP bin) was then calculated by using Equation (): (n is integer from - to ) () in which a binning method of equal VSP interval of kw/ton was applied in order to illustrate the mathematical relationship between the VSP distribution and the speed. After examining all the data, it was found that over percent of records fell into the VSP interval between - and kw/ton. Therefore, the VSP bin number n was set to one from - to. Speed-specific CO emission factors were then estimated by multiplying CO emission rates in each VSP bin with VSP distributions for each segment pool, as TRB Annual Meeting

10 Song, Yu, and Xu shown in Equation (). () where EF is the CO emission factor (g/km), ER i and VSPDistribution i are the CO emission rate and VSP fraction (in the unit of %) in VSP bin i, where i is the VSP bin number, and S avg is the average speed of the segment pool (m/s). CO emission rates were derived from the emission database collected by the portable emission measurement system (PEMS) at Beijing Jiaotong University (). The vehicle is a Volkswagen JETTA, manual transmission, gross weight of kg, and. L conventional IC engine. DISCUSSIONS Speed-specific VSP distributions of field trajectories and those generated from car-following models are compared, and then differences of the VSP distribution and estimated CO emission factors are analyzed. Further, the key factor that influences the VSP distribution in car-following models is discussed. Comparisons of Field and Simulated VSP Distributions Histograms of VSP distribution are illustrated in Figure, including field data, OVM, GFM, FVDM, Wiedemann, and Fritzsche models from top to down respectively. Field VSP distribution curves were also plotted over each histogram for the purpose of comparison. Only three speed bins of [, ), [, ), and [, ) were presented due to the limitation of the paper length while the field VSP distribution on a full range of speed bin can be referred in the literature (). The field VSP distribution demonstrated a normal distribution pattern with the mean value in VSP bins of, and kw/ton for each speed bin. OVM and GFM generated very close VSP distributions, which, however, were largely different from field distributions. For the speed bin of -, fractions in the central area (bins of - to kw/ton) were lower than those of the field data, while fractions of two sides (lower than - kw/ton and higher than kw/ton) were higher than those of field distributions. For the speed bin of -, the peak fraction (VSP bin of kw/ton) is far higher than that of the field data, while fractions on two sides were lower than those of the field data. FVDM simulated realistically the VSP distribution in speed bins lower than, but in higher speed bins, it produced slightly higher fractions in the central VSP area and lower fractions on both side areas. The Wiedemann model generated significantly higher values of peak VSP fractions and much lower fractions on the right side. It was also observed that there were isolated fractions in VSP bins of - kw/ton, which was consistent with the finding in the reference (). Considering that emission rates in VSP bins of - kw/ton were higher than those in lower VSP bins, these fractions may lead overestimations of vehicle emissions. The VSP distribution from the Fritzsche model had a good consistency with that of the real world data. In order to compare quantitative differences of the modeled VSP distribution TRB Annual Meeting

11 Song, Yu, and Xu with the field distribution, an indicator of Root Mean Square Error (RMSE) was applied as shown in Equation (). () in which, RMSEVSP j is the root mean square error of the VSP distribution for the speed bin of j, Model i and Field i are fractions of the car-following model and real-world VSP distributions for the VSP bin of i, and n is the total number of VSP bins ( in this study). The RMSE of five car-following models along with the average speed were illustrated in Figure. The higher RMSE value means a more unrealistic VSP distribution. OVM and GFM models had very consistent and also the highest RMSE curves which increased sharply when the speed is higher than. The RMSE of FVDM is the lowest one in the speed range of lower than. It increased after that but was still much lower than those of OVM, GFM, and Wiedemann models, which indicated that by adding the factor of the positive velocity difference based on GFM (), FVDM improves effectively the accuracy of its VSP distribution. The RMSE of the Wiedemann model tended to increase with the speed and was always higher than those of FVDM and Fritzsche. Overall, Fritzsche provided the lowest RMSE and kept a relatively constant RMSE curve along with the speed. The average RMSEs are.,.,.,., and. for OVM, GFM, FVDM, Wiedemann, and Fritzsche models respectively. Comparison of Field and Simulated Vehicle Emissions Speed-specific CO emission factors were calculated by using Equation () based on VSP distributions of the field data and car-following models, as shown in Figure. Overall, all emission factor curves had a similar trend of decreasing with the speed, however, OVM, GFM and Wiedemann models tended to overestimate emissions, which was consistent with previous studies on the traffic simulation model (,, ). The emissions estimated by FVDM and Fritzsche models presented good consistencies with real world emission factors. Relative errors of the emission estimation were illustrated in Figure. Average absolute relative errors were.%,.%,.%,.%, and.% for OVM, GFM, FVDM, Wiedemann, and Fritzsche models respectively, in which, errors of FVDM and Fritzsche were apparently lower than others. There are three points that need to be noted, (i) emission estimation errors of OVM, GFM or Wiedemann model varied significantly (from -% to %) with the speed, which would further lead to errors on the evaluation of the effect of emission reductions by traffic control alternatives, and (ii) low errors at the speed range of - did not mean that simulated vehicle activities were accurate. From Figure, it could be observed that the appearance of the low error was an offset of overestimation of the VSP distribution in the central area and underestimation in other areas. In addition, by comparing with higher estimation errors by VISSIM in study (), it may indicate that the Wiedemann car-following model explained partly the emission error of VISSIM, while other TRB Annual Meeting

12 Song, Yu, and Xu vehicle activity models in VISSIM such as the acceleration model of leading car needs further investigation. Comparison of Field and Simulated Acceleration Distributions In order to investigate the error source of the VSP distribution and the emission estimation in car-following models, their acceleration distributions were analyzed. The reasoning of the analysis was based on three logics, (i) in this study, the speed and acceleration are the only two factors in the VSP calculation, and the acceleration is more sensitive than speed to the vehicle power, especially when the speed is lower than when the aerodynamic resistance is not a major factor to the power demand, (ii) for speed-specific VSP distributions, by defining a small interval of the speed bin, the acceleration will be the dominant factor for the VSP, and (iii) the speed or speed distribution has long been a parameter for calibrating and validating a car-following model in traditional applications. Because FVDM was developed on the basis of OVM and GFM, and FVDM provided better VSP distributions and emission estimations than the other two, OVM and GFM models were not included in this discussion. Similar to the analysis approach of VSP distributions, the acceleration data were binned into bins with an equal interval of. m/s, and then speed-specific acceleration distributions of the field data, FVDM, Wiedemann, and Fritzsche models were calculated, as shown in Figure. The field acceleration distribution also demonstrated a normal distribution pattern with the mean value of m/s. FVDM generated very close distributions as did the field data. However, Wiedemann and Fritzsche models produced different distribution patterns though they both had peak fractions in the acceleration bin of m/s. The Wiedemann model produced much higher peak fractions and significantly lower fractions in slight acceleration bins (.-. m/s ) than did the field distribution. In addition, The Wiedemann model presented isolated acceleration fractions in the sharp acceleration area (around.-. m/s ) which moved left (decreased) with the increase of speed. The Fritzsche model produced a similar peak fraction as the field and FVDM acceleration distributions, and a slightly lower fraction in slight acceleration bins (.-. m/s ). The Fritzsche model also had isolated fractions in the sharp acceleration bin, but its position kept fixed in. m/s when the speed changed. The indicator of the RMSE of the acceleration distribution was calculated by Equation (), in order to quantify the difference of modeled and field distributions. () in which, RMSEACC j is the root mean square error of the acceleration distribution for the speed bin of j, Model k and Field k are fractions of modeled and the field acceleration distributions for the acceleration bin of k, and m is the total number of acceleration bins ( in this study, from -. to. m/s ). The calculation results were illustrated in Figure. TRB Annual Meeting

13 Song, Yu, and Xu It is observed that the RMSE of the acceleration distribution of FVDM was the lowest one with the average of. though it increased when the speed is higher than. The average of RMSE of the Fritzsche model was., which was slightly higher than that of FVDM. It decreased to be very low in the higher speed range of - because isolated fractions in the sharp acceleration bin of. m/s dropped. The RMSE curve of the Wiedemann model was. which was much higher than those of the other two models. By comparing Figure with Figure, each car-following model showed similar curves between the RMSE of acceleration and VSP distributions, which may indicate that the RMSE of the acceleration distribution is correlated with that of the VSP distribution. By examining RMSE values of the acceleration and VSP distributions from speed bins of to, the Pearson Correlation Coefficient between them are found as high as.,., and. for FVDM, Wiedemann, and Fritzsche models respectively. Based upon this finding, it can be derived that the acceleration is critical for the VSP distribution, thus improving the speed-specific acceleration distribution of a car-following model can improve effectively its VSP distribution, thus the accuracy in emission estimations. SUMMARY AND RECOMMENDATION Based on a large sample of field car-following trajectories and the method of the numerical simulation, VSP distributions from the real-world data and car-following models were compared and their implications to emission estimations were discussed. Main findings of this study could be summarized as follows: () VSP distributions generated by OVM and GFM differed largely from the field distribution, which led to two highest errors of emission estimations among five car-following models. Positive velocity difference is a critical factor, which improved significantly the accuracy of the VSP distribution of FVDM. () In psycho-physical models, the Wiedemann model overestimated peak VSP fractions while underestimated right side fractions. Also, it predicted isolated and unrealistic fractions in VSP bins of - kw/ton. The VSP distribution from the Fritzsche model had a good consistency with that of the real world data. () In term of the emission estimation, the VSP distribution is the explanatory parameter, however, it seems to be the sufficient condition but not the necessary condition for the accurate emission estimations, because an apparently accurate emission factor may be an offset of overestimation of the VSP distribution in one area while underestimation in another. This happened to OVM, GFM, and Wiedemann models in the speed range of - in this study. () The speed-specific VSP distribution is highly correlated with the acceleration distribution. The unrealistic depiction of acceleration distributions especially in sharp acceleration areas leads to errors of VSP distributions of car-following models. Therefore, improving the accuracy of the speed-specific acceleration distribution is an effective measure to improve the accuracy of the VSP distribution, thus the emission estimation. The paper provided a method based on the VSP/acceleration distribution for TRB Annual Meeting

14 Song, Yu, and Xu analyzing car-following models in the light of the emission estimation. Although the result shows different performances of car-following models, it is observed that existing models, such as FVDM and Fritzsche, have the potential to generate realistic VSP distributions. Wiedemann and Fritzsche models have various thresholds and parameters for the regime judgment and acceleration assignment which affect VSP distributions, whichneed further investigations. In addition, the Wiedemann car-following model may only explain partly errors of the VSP distribution in VISSIM (), which indicated that other inner models which control vehicle activities like lane-change/ overtake and acceleration of the leading car need further studies. ACKNOWLEDGEMENTS This research is supported by the National Basic Research Program of China #CB, and the Fundamental Research Funds for the Central Universities #JBM. This paper is also supported in part by the Natural Science Foundation of China (NSFC) # and and the National Science Foundation (NSF) grant #. The authors would be thankful to all the personnel who either provided the technical supports or helped on data collection and processing. REFERENCES. Swidan, H. Integrating AIMSUN Micro Simulation Model with Portable Emissions Measurement System (PEMS): Calibration and Validation Case Study. Master thesis of North Carolina State University,.. Zuylen, H., J. Li, Y. Chen, F. Viti, and I. Wilmink. Optimizing Traffic Control for Emissions with a Valid Simulation Program - The calibration of a simulation model for emission estimation. th Transportation Research Board Annual Meeting, #-. Washington D.C., January.. Song, G. and L. Yu. Applicability of Traffic Micro-Simulation Models in Vehicle Emission Estimations: A Case Study of VISSIM. st Transportation Research Board Annual Meeting #-. Accepted for publication in Transportation Research Record: Journal of the Transportation Research Board, Transportation Research Board of the National Academies, Washington, D.C., January.. Barth, M., F. An, T. Younglove, G.. Scora, C. Levine, M. Ross, and T. Wenzel. Comprehensive Modal Emissions Model (CMEM), Version., User's Guide. Univ. of California, Riverside, Riverside, California,.. Ahn, K., H. Rakha, A. Trani, and M. Van Aerde. Estimating Vehicle Fuel Consumption and Emissions based on Instantaneous Speed and Acceleration Levels. Journal of Transportation Engineering., Vol., No., pp. -.. Park J. Y., R. B. Noland, and J. W. Polak. Microscopic Model of Air Pollutant Concentrations: Comparison of Simulated Results with Real-world and Macroscopic Estimates. In Transportation Research Record: Journal of the TRB Annual Meeting

15 Song, Yu, and Xu Transportation Research Board, No., Transportation Research Board of the National Academies, Washington, D.C.,, pp. -.. Stathopoulos, Fotis G. and R. B. Noland. Induced Travel and Emissions from Traffic Flow Improvement Projects. In Transportation Research Record: Journal of the Transportation Research Board, No., Transportation Research Board of the National Academies, Washington, D.C.. pp. -,. Nam, E., Christine A. Gierczak, and James W. Butler. A Comparison of Real-World and Modeled Emissions under Conditions of Variable Driver Aggressiveness. nd Transportation Research Board Annual Meeting CD-ROM, Washington, D.C., Jan.. Servin O., K. Boriboonsomsin, and M. Barth. An Energy and Emissions Impact Evaluation of Intelligent Speed Adaptation. Proceedings of the IEEE Intelligent Transportation Systems Conference, Toronto, Canada, September -,, pp. -.. Zhang, B., L. Shang, and D. Chen. Evaluation of Urban Traffic Intersection Vehicle Emission Based on Microscopic Traffic Simulation. Computer and Communications,, (), pp. -. (In Chinese).. Chamberlin, R, B. Swanson, E. Talbot, J. Dumont, and S. Pesci. Analysis of MOVES and CMEM for Evaluating the Emissions Impact of an Intersection Control Change. th Transportation Research Board Annual Meeting, #-, Washington, D.C., Jan.. Liu, H., Y. Xiong, R. Gao, J. Teng, and M. Zhu. Investigating Vehicular Energy Consumption and Emissions at Intersections with Micro-Simulation Models. Urban Transport of China,, (), pp. -.. Hallmark, S. L. and R. Guensler. Comparison of speed-acceleration profiles from field data with NETSIM output for modal air quality analysis of signalized intersections. In Transportation Research Record: Journal of the Transportation Research Board, No., Transportation Research Board of the National Academies, Washington, D.C.,, pp. -.. Rakha, H., M. Snare, and F. Dion. Vehicle Dynamics Model for Estimating Maximum Light Duty Vehicle Acceleration Levels. In Transportation Research Record: Journal of the Transportation Research Board. No., Transportation Research Board of the National Academies, Washington, DC.. pp. -.. Jackson, E. and A. Lisa. Analysis of Real-World Lead Vehicle Operation for Modal Emissions and Traffic Simulation Models. In Transportation Research Record: Journal of the Transportation Research Board. No.. Transportation Research Board of the National Academies, Washington, DC,. pp -.. Hirschmann, K., M. Zallinger, M. Fellendorf, and S. Hausberger. A New Method to Calculate Emissions with Simulated Traffic Conditions. th International IEEE Annual Conference on Intelligent Transportation Systems. Madeira Island, Portugal, September -,. pp. -. TRB Annual Meeting

16 Song, Yu, and Xu. U.S. Environmental Protection Agency. Motor Vehicle Emission Simulator (MOVES) User Guide for MOVESb. EPA--B--b. Washington, D.C., USA,.. Frey, H.C., Unal, A., Chen, J., Li, S., and Xuan, C. Methodology for Developing Modal Emission Rates for EPA s Multi-Scale Motor Vehicle & Equipment Emission System; EPA-R--, U.S. Environmental Protection Agency,.. Frey H.C., N. M. Rouphail, and H. Zhai. Speed- and Facility-Specific Emission Estimates for On-Road Light-Duty Vehicles on the Basis of Real-World Speed Profiles. In Transportation Research Record: Journal of the Transportation Research Board, No., Transportation Research Board of the National Academies, Washington, D.C.,, pp... Song, G., L. Yu, and Z. Tu. Distribution Characteristics of Vehicle Specific Power on Urban Restricted Access Roadways. Journal of Transportation Engineering, ASCE,, vol., pp. -.. Song, G and L. Yu. Characteristics of Low-Speed VSP Distributions on Urban Restricted Access Roadways in Beijing. In Transportation Research Record: Journal of the Transportation Research Board, No., Transportation Research Board of the National Academies, Washington, D.C.,, pp. -.. Brackstone, M. and M. McDonald. Car following: A Historical Review. Transportation Research Part F.,, (), pp. -.. Ranjitkar, P., T. Nakatsuji, and A. Kawamura. Car-Following Models: An Experiment Based Benchmarking. Journal of the Eastern Asia Society for Transportation Studies,, Vol., pp. -.. Panwai, S. and H. Dia. Comparative Evaluation of Microscopic Car-Following Behavior. IEEE Transactions on Intelligent Transportation Systems., Vol., (), pp. -. Olstam, J. and A. Tapani. Comparison of Car-following Models. VTI meddelande A. Swedish National road and Transport Research Institute. Linköping, Sweden,.. Chandler, R., R. Herman, and E. Montroll. Traffic Dynamics: Studies in Car Following. Operations Research,,, pp. -.. Kometani, E., and T. Sasaki. Dynamic Behaviour of Traffic with a Nonlinear Spacing-Speed Relationship. In Proceedings of the Symposium on Theory of Traffic Flow, Research Laboratories, General Motors. New York: Elsevier,, pp. -.. Gipps, P. G. A Behavioural Car Following Model for Computer Simulation. Transportation Research Part B,, (), pp. -.. Bando M., K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, Dynamical Model of Traffic Congestion and Numerical Simulation, Physical Review E,, (), pp. -.. Helbing D, and B. Tilch. Generalized Force Model of Traffic Dynamics. Physical Review E,, (), pp.-.. Jiang R., Q. W, and Z. Zhu. Full Velocity Difference Model for A Car-Following TRB Annual Meeting

17 Song, Yu, and Xu Theory. Physical Review E,, (), pp. -.. Wiedemann, R. and U. Reiter. Microscopic Traffic Simulation: the Simulation System MISSION, Background and Actual State. Project ICARUS (V) Final Report. Brussels: CEC,.. Fritzsche, H. A Model for Traffic Simulation. Traffic Engineering and Control,, (), pp. -.. Zhao, X., and Z. Gao. The Stability Analysis of the Full Velocity and Acceleration Velocity Model. Physica A.,, pp. -. TRB Annual Meeting

18 Song, Yu, and Xu LIST OF TABLES TABLE Parameters Used in Numerical Simulation TRB Annual Meeting

19 Song, Yu, and Xu LIST OF FIGURES FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE Thresholds and regimes in the Wiedemann and Fritzsche car-following models Comparison of field and simulated VSP distributions RMSE of VSP distributions of car-following models CO emission factors estimated by field data and car-following models Relative errors of emission estimation by car-following models Comparison of field and simulated acceleration distributions RMSE of acceleration distributions of car-following models TRB Annual Meeting

20 Song, Yu, and Xu Table Parameters Used in Numerical Simulation Parameter Value Parameter Value Parameter Value. m AX mult. RND N (.,.) BX add. RND N (.,.). s - BX mult. T D. s m EX add. T r. s EX mult. T s. s. m BNULL mult.. m/s -. m b max f x.. b min k PTP.. OPDV add. k PTN. p. s - OPDV mult. a null. m/s - q s - CX a n. m/s -. m - NRND N (.,.) s n-. m. RND N (.,.). s AX add. RND N (.,.) TRB Annual Meeting

21 Song, Yu, and Xu Upper limit of reaction Y 轴 Free Driving SDX SDV Closing in Y 轴 Free Driving PTN Following II AB Following CLDV AD OPDV ABX Following I Closing in PTP Emergency AS AX AR Damger (a) Wiedemann Model (b) Fritzsche Model FIGURE Thresholds and regimes in the Wiedemann and Fritzsche car-following models TRB Annual Meeting

22 Song, Yu, and Xu OVM Data OVM Data OVM Data GFM Data GFM Data GFM Data FVDM Data FVDM Data FVDM Data.. - Wiedemann.. - Wiedemann.. - Wiedemann Fritzsche... - Fritzsche... - Fritzsche VSP (kw/ton) VSP (kw/ton) VSP (kw/ton) FIGURE Comparison of field and simulated VSP distributions TRB Annual Meeting

23 Root Mean Square Error (RMSE) Song, Yu, and Xu.. OVM GFM FVDM Wiedemann Fritzsche.. Average Speed () FIGURE RMSE of VSP distributions of car-following models TRB Annual Meeting

24 CO Emission Factor (g/km) Song, Yu, and Xu.... OVM GFM FVDM Wiedemann Fritzsche.. Average Speed () FIGURE CO emission factors estimated by field data and car-following models TRB Annual Meeting

25 Error of Emission Estimataion (%) Song, Yu, and Xu % % % % % % % -% -% Average Speed () OVM GFM FVDM Wiedemann Fritzsche FIGURE Relative errors of emission estimation by car-following models TRB Annual Meeting

26 Song, Yu, and Xu % % % % % - % % % % % FVDM - % % % % % % Wiedemann - % % % % % Fritzsche - % % % - % % % FVDM - % % % Wiedemann - % % % Fritzsche - % % % % % % % % % % % - % % % FVDM - % % % Wiedemann - % % % Fritzsche - % % % % % % % % % % % % Acceleration (m/s ) Acceleration (m/s ) Acceleration (m/s ) Acceleration (m/s ) FIGURE Comparison of field and simulated acceleration distributions TRB Annual Meeting

27 Root Mean Square Error (RMSE) Song, Yu, and Xu.... FVDM Wiedemann Fritzsche. Average Speed () FIGURE RMSE of acceleration distributions of car-following models TRB Annual Meeting