Estimation of Freeway Density Based on the Combination of Point Traffic Detector Data and Automatic Vehicle Identification Data

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1 Estimation of Freeway Density Based on the Combination of Point Traffic Detector Data and Automatic Vehicle Identification Data By Somaye Fakharian Qom Ph.D candidate and Research Assistant Department of Civil and Environmental Engineering Florida International University 0 W. Flagler Street, EC 0 Miami, FL Phone: (0) - sfakh00@fiu.edu Yan Xiao, Ph.D., P.E. Research Associate Department of Civil and Environmental Engineering Florida International University 0 W. Flagler Street, EC 0 Miami, FL Phone: (0) - yxiao00@fiu.edu Mohammed Hadi, Ph.D., P.E. (Corresponding Author) Associate Professor Department of Civil and Environmental Engineering College of Engineering and Computing Florida International University 0 W. Flagler Street, EC 0 Miami, FL Phone: (0) hadim@fiu.edu Haitham Al-Deek, Ph.D., P.E. Professor of Engineering Department of Civil, Environmental and Construction Engineering University of Central Florida 00 Pegasus Drive, Suite, P.O. Box 0 Orlando, FL -0 Phone: (0) - Haitham.Al-Deek@ucf.edu Paper Submitted for Presentation at the th TRB Annual Meeting (January 0) and Publication in the Transportation Research Record: Journal of the Transportation Research Board Word Count =, words + figures + tables =, words November, 0

2 Fakharian Qom et al. 0 0 ABSTRACT This study compares the results from three different freeway density estimation methods based on point detector data with the results obtained from the density estimation procedure of the Highway Capacity Manual (HCM 00). The three methods are referred to as the cumulative volume-based method, occupancy-based method, and the fundamental relationship-based method. The study also develops and tests a new method that integrates data from point traffic detectors and automatic vehicle identification (AVI) readers to estimate the density of freeway segments for both off-line and real-time applications. The four density estimation methods are compared to each other and the HCM method utilizing two case studies based on simulation modeling and real-world data. The results show that the density estimates based on the proposed segmentation method, cumulative volume method, and HCM method are generally closer to each other compared to the estimates based on the other two tested methods. The simulation case study shows that the density estimates from these three methods are also closer to density measurements obtained based on vehicle trajectories from simulation. The two case study results also indicate that the selection of density estimation method mainly affects the value of LOS during the intermediate congested conditions. Keywords: Density, Point Detector, Automatic Vehicle Identification, Simulation, real word ITS data.

3 Fakharian Qom et al INTRODUCTION Density, speed, and flow are the three basic parameters for macroscopic traffic analysis. The Highway Capacity Manual (HCM 00) () selects density as the performance measure to quantify the Level of Service (LOS) on freeway segments. Traffic density of a segment is defined as the number of vehicles on this segment divided by segment length. The average density per lane is normally reported by dividing the total density by number of lanes. Speed and flow are relatively easy to measure utilizing field devices. Traffic density has been measured based on snapshot photo of the traffic by an aerial camera along a segment or a camera on a tall building that covers a freeway. However, direct measurement of traffic density is not normally done due to the difficulty and cost associated with measuring the density along a segment length and this parameter is estimated based on other parameters such as speed, flow, and occupancy. The HCM 00 selects density as the performance measure to quantify the Level of Service (LOS) on freeway segments and present procedures to estimate density based on traffic flow and geometry variables. Increasingly, advanced traffic management and other Intelligent Transportation System (ITS) technologies are providing detailed data to quantify traffic conditions in off-line and real-time applications. However, accurate estimation of density based on this data is an issue since the most widely used sensors to support traffic management applications are point detectors, while density is a segment measurement. Increasingly, the implementation of Automatic Vehicle Identification (AVI) and Automatic Vehicle Location (AVL) technologies are being implemented. However, these devices only measure travel time and space mean speed on a segment and they cannot measure the traffic flow or density. Although dense point sensor system or camera could approximate continuous spatial coverage to support density measurement, the cost is prohibitive. In practice, point sensors such as microwave detectors and inductive loop detectors are normally installed at mile intervals in urban areas to provide volumes and speeds at the sensor point locations. Different methods have been used to estimate density based on point detector data. The availability of data from AVI technologies such as Bluetooth and electronic toll readers, AVL technologies such as those based on Global Positioning System (GPS) systems, and eventually connected vehicle technologies will allow fusing data from these sources for better performance measurements including density estimation. Data from these additional sources have the potential to compensate for the deficiencies of point sensors in performance measurements. For example, reliable traffic flow rate estimation from loop detector systems and accurate vehicle trajectories based on AVL technologies have been used to count vehicle numbers within segments, allowing better estimation of density in real-time than density estimation based on point detector data (). Other studies have investigated the use of trajectory data from AVL technologies to estimate spatial measures of system performance such as the extent of the back of queue and shockwaves, in addition to utilizing this data for travel time estimation, as is commonly done (, ). However, the deployment and market penetration of AVL technologies are still limited. On the other hand, there is an increasing trend of installing AVI technologies, particularly with the introduction of the cost-effective Bluetooth and Wi-Fi reader technologies. However, AVI technologies have been mainly used to estimate travel time and in some cases origin-destination flows. No attempts have been used to utilize AVI data to support the estimation of other spatial measures such as density. This study reviewed methods that can be used to estimate density based on point traffic detector data including the cumulative volume-based method, occupancy-based method, and the

4 Fakharian Qom et al fundamental relationship-based method. The study also developed and tested a new method to integrate data from point traffic detectors and automatic vehicle identification (AVI) readers to estimate the average density for freeway segments for both off-line and real-time applications. The density estimation methods were compared to each other and the HCM method utilizing two case studies using simulation modeling and real-world data. METHODOLOGY This section includes a discussion of the procedures tested in this study to estimate the density based on point detector and AVI data. Data Acquisition and Preprocessing The real-world point detector data used in this study were retrieved from an Intelligent Transportation Systems (ITS) data warehouse system, referred to as the Regional Integrated Transportation Information System (RITIS) (). The archived RITIS data originates from the raw 0-second detector data collected from the Florida Department of Transportation (FDOT) traffic management center software, the SunGuide system, which includes the measurements of speed, volume count, and occupancy. These raw detector data goes through data filtering, cleaning and aggregation procedures in RITIS. Thus, they were ready for use in freeway density estimation in this study. The real-world AVI data used in this study was collected from an electronic toll tag readers system installed at the roadside of the Florida Turnpike for the purpose of travel time estimation. When a vehicle equipped with electronic transponder travels in the reader detection zone, the vehicle tag ID and detection timestamp are read. Matching the unique tags at two detection stations allows the measurement of freeway segment travel time between a pair of readers. A detailed procedure was use to filter and clean the data before using it in this study. As the first step, the possible matching records at the downstream detection station are found for each tag detected at the upstream station. Procedures were used to resolve multiple matches of the same vehicle and to filter out the travel times of vehicles that have unusually high travel times due to these vehicles possibly stopping at intermediate point during their journey. The remaining matched records may still include some abnormal records that cannot be detected by a fixed threshold and need to go through another filtering step. In this step, the records are further filtered based on the inter-quartile range (IQR) method as discussed by Young et al. for Bluetooth data (). Based on this procedure, each matched travel time is compared to its nearest 0 neighbors and the inter-quartile range (defined as the difference between the th percentile and th percentile) is calculated. If the matched travel time is less than (th percentile IQR) or greater than (th percentile + IQR), it will be considered as an outlier and be discarded. Compared to the traditional statistical filtering method that estimates the standard deviation based on the average values and then uses times standard deviation as the threshold to identify outliers, this filtering method is more robust and is not affected by the outliers.

5 Fakharian Qom et al Density Estimation Based on Point Detector Data The parameters commonly measured by point traffic detectors are volume, occupancy, and speed. Other parameters can be estimated based on these three parameter measurements. This section discusses methods that can be used to estimate density based on point traffic detector data. Cumulative Volume- based This method is based on the fact that for a given time interval, the difference between the number of vehicles entering and leaving a segment is equal to the change in the number of vehicles within the segment and thus the change in density that is measured in vehicles per mile. Based on this principle, the number of vehicles within one segment can be calculated as follows: () Where Arrival volume from both mainline and on-ramps during period i, veh Departure volume from both mainline and off-ramps during period i, veh : Number of vehicles within the segment at the end of time period i Number of vehicles within the segment at the end of time period i- Iteratively applying Equation to the time period from i- to yields the following equation: ( ) () Where Cumulative arrival volume from both mainline and on-ramps at the time period i, veh departure volume from both mainline and off-ramps at the time period i, veh Initial number of vehicles within the segment As shown in Equation, the number of vehicles within the segment can be calculated by the difference between the cumulative numbers of the vehicles arriving and departing the segment plus the initial number of vehicles within the segment. The segment density can be then determined by dividing the number of vehicles within the segment by segment length and number of lanes. This is a simple method; however, it requires the on-ramp and off-ramp volume information for each time period, which is not available at many locations, particularly for realtime applications, since most traffic management agencies install traffic detectors only on the freeway mainlines and not on the ramps. This is a main concern with this method. This method also requires an estimation of the initial density, possibly in light traffic conditions after midnight. Occupancy based Occupancy is the percentage of time that each detector is occupied by the vehicles. It has the following relationship with density: ( ) ( ) ()

6 Fakharian Qom et al. 0 0 Where: : Density at detector location i, veh/ mi/ln Occupancy in percentage : Average vehicle length, ft : detector length, ft Once the densities at the upstream and downstream detector stations are determined using Equation, the segment density is normally estimated as the average of these two values. Although this method is commonly used, it has two disadvantages. First the occupancies are measured at points, thus they may not represent the condition along part of the segment, as is assumed by the method. Second, the average vehicle length and detector length have to be assumed or estimated, which reduces the accuracy of the estimation. The biggest problem of using a fixed vehicle length is the large variance due to trucks, motorcycles, cars towing boats, and so on in different times of the day/days of the week. Thus, using variable values of the average vehicle length by time of day and day of the week has been proposed but not implemented in practice. In this study, the summation of the average vehicle and detector lengths is assumed to be ft based on sensitivity analysis. This sensitivity analysis used in this research was to vary the vehicle length in the density estimation and the optimal vehicle length is obtained by comparing the density estimates with other methods. Fundamental Relationship-based The third density estimation method tested in this research utilizes the relationship between the three fundamental macroscopic traffic parameters: volume, speed, and density. Point detectors measure spot mean speed, which is the time mean speed, usually in 0-second intervals. The space mean speed ( ) at the detector station i is always equal or smaller than the time mean speed ( ) with the difference being proportional to the speed variance ( ) (). () 0 0 In estimating density, the time mean speed is available and the space-mean speed needs to be estimated from the time-mean speed for use in the calculation of density. An empirical relationship from reference () was used in this study to convert the time mean speed to space mean speed as shown in Equation, without the need to measure speed variance, which is not normally available from point detector measurements since these detectors do not measure individual vehicle speeds. () Once the space mean speed is obtained for each detector location, the density at detector station i can be estimated for the detector location using the relationship between the fundamental variables as follows: ()

7 Fakharian Qom et al Where : Density at detector i, veh/mi/ln V i : Traffic flow rate measured by detector i, veh/hr/ln : Space mean speed at detector i, mi/h N: number of lanes in the study segment Similar to the last step for the occupancy-based method, the average of densities at the upstream and downstream detector stations is calculated as the segment density D f. Density Estimation based Combination of AVI and Point Detector Data (Segmentation ) Density cannot be estimated based on AVI measurements unless the technology is able to match all vehicles between AVI readers (that is, AVI provides close to 00% sample size of the vehicles detection), which is not possible in the foreseeable future. Therefore, this study developed a new method is called segmentation method that integrates AVI and point detector data to estimate the segment density. In this method, a segment is divided into two subsgements; the first subsegment is assumed to have traffic conditions that are close to the conditions at the upstream detector station while the second subsegment is assumed to have traffic conditions that are close to the conditions at the downstream detector station. Instead of assuming the length for these two subsegments to be half of the segment length between the detector stations, as assumed in the occupancy-based method and the fundamental relationship-based method described earlier when discussing density estimation based on point detector data, the point detector-avi combination method, developed in this study, sets the subsegment lengths dynamically utilizing travel time measurements based on AVI readers and speed measurements based on detector data. This is done by assuming that the link travel time based on AVI data is equal to the summation of the travel times of the two subsegment, which can be calculated based on the space mean speeds estimated using upstream and downstream point detector data. The corresponding equation is presented as follows: () Where : Total link length, mi : Length of the first subsegment that is assumed to have similar traffic conditions as the upstream detector, mi L- : Length of the second subsegment that is assumed to have similar traffic conditions as the downstream detector, mi : Space mean speed measured by AVI, mi/h : Space mean speed calculated based on the time mean speed at the upstream detector utilizing Equation, mi/h : Space mean speed calculated based on the time mean speed at the downstream detector utilizing Equation, mi/h The developed density estimation method as presented in Equation is referred to in this study as the Segmentation. Then, the density for each link was calculated based on

8 Fakharian Qom et al point detector volume and speed measurement utilizing Equation. Once the density for each subsegment was calculated, the density for the whole segment was estimated using Equation. Where : Average density for the segment (veh/mi/ln) : Density for link i corresponding detector i (veh/mi/ln) : Length of link i, normal taken the half of the distance between two detectors, mi : Number of lanes in link i Note that the quality of AVI data and detector data has a great impact on the results of this method. Thus, the AVI and point detectors have to be well calibrated and maintained. Also in the absence of real-time point detector data, a combination of historical counts from point detector and space mean speed from AVI technology measurements can be used as inputs to the segmentation method, in the same manner that is described above. HCM Utilizing Highway Capacity Software For comparison purposes, the Highway Capacity Manual 00 (HCM 00) freeway facility procedure was also applied in this study to estimate density. The HCM procedure only requires the input of traffic flow at the mainline entrance as well as at on- and off-ramps. When the freeway facility is undersaturated, the HCM speed-flow relationship for each type of segment is used to determine the segment speed. Segment density is then either calculated by dividing flow rate by speed or estimated from empirical relationship depending on segment type. For the oversaturated traffic conditions, an analysis that is similar to cell transmission model is used to estimate the number of vehicles on the segment and in turn the segment density. In this research, the HCM 00 procedure-based Highway Capacity Software was applied to estimate density for the HCM method. HCM Procedure to Estimate the Level of Service In the HCM 00, LOS for basic, weaving, merging and diverging freeway segments is determined by the value of segment density. Similarly, density of freeway facility, defined as the weighted average of segment density based on the segment length and number of lanes, is used to determine the LOS for a freeway facility. Table lists the LOS criteria for a freeway facility. TABLE LOS Criteria for a Freeway Facility in the HCM 00 Level of Service Density (pc/mi/ln) A B > - C > - D > - E > - F > or any component v d /C ratio >.00 ()

9 Fakharian Qom et al ASSESMENT OF DENSITY ESTIMATION METHODS The methods mentioned in the previous section were evaluated in this study based on real-world data as well as a micro-simulation model. The utilization of simulation modeling in the assessment provided an opportunity to accurately measure the density based on vehicle trajectory data, thus providing a baseline data to compare to. Note that the direct simulation output of link density is not used in this study as the study segment does not coincide with the links defined in the simulation model. Trajectory data is used for this purpose. Trajectory data consists of spatiotemporal locations of individual vehicles at each timestamp, usually one second or less, and can be depicted as a series of vehicle coordinates in time and space. Such information has been used successfully to identify the number of vehicles on each segment for each timestamp to estimate the value of spatial measures such as segment density. The measures of effectiveness used in the evaluations of the results of the density estimation methods in this study are the root-mean-square error (RMSE) and mean absolute percentage error (MAPE). The definitions of these two measures are presented in Equations and 0. Both the MAPE and RMSE have been used in the past to measure model performance. While the MAPE gives the same weight to all errors, the RMSE gives errors with larger values more weights. Utilizing both measures at the same time is useful in assessing the model error. Where RMSE N MAPE N N N t D ( D t D t, e t t, a, e t, a ) D D t, e represents the estimated density for time interval t, and D t, a D t, a () *00 (0) is the corresponding reference value for density. N denotes the total number of time intervals during the study time period. DENSITY ESTIMATION ANALYSIS AND RESULTS The methods described in the previous section were evaluated in this study utilizing two case studies. The first case study is based on a CORSIM simulation model for State Road located in Miami, FL and the second case study utilized real-world detector and AVI data from a segment along the Florida Turnpike in Miami, FL. The analysis results for these two case studies are presented in this section. Comparison of Density Estimation Based on Simulation Data The case study based on simulation modeling was done because it allows the comparison of the results from different density estimation methods with the exact values of density that are determined from the simulated vehicle trajectory data. The measurements based on trajectory data can thus be used as reference measurements in the comparison. The simulation model used in this study is for the eastbound section of State Road located in Miami, FL. Point detectors

10 Density (veh/mi/ln) Fakharian Qom et al. 0 0 are set up along the mainline in this simulation model based on the real-world detector locations. The simulation model was calibrated and validated based on the real-world point traffic detector data as outlined in a report by Hadi et al. (). In order to compare different density estimation methods, a 0.-mile segment with one upstream point detector and one downstream point detector along this simulated corridor is selected as the study segment. Two virtual AVI readers are also introduced at the upstream and downstream of this study segment with locations that are exactly the same as the point detectors. In addition, a ramp detector is also added at the single ramp within this segment to detect the additional volume entering the segment from the ramp. The simulated detector data and AVI data were input to the five density estimation methods discussed in the previous section and Figure presents the analysis results for these five methods, as well as those from the simulated trajectory data. As shown in Figure, the densities estimated from various methods are very close under the uncongested conditions while the differences among these methods become more obvious during the congested conditions. It is also seen that the densities estimated from the segmentation method, HCM method, and cumulative volume-based method are more close to the results obtained based on the trajectory method Cumulative Volume-Based Segmentation Fundamental Relationship-Based Occupancy-Based Trajectory Data-Dased HCM :00 :0 :00 :0 :00 :0 0:00 0:0 :00 Timestamp FIGURE Density estimation results based on SR simulation

11 Fakharian Qom et al. 0 0 The MAPE and RMSE values in Table further confirm that compared to the other methods, the cumulative method and the segmentation method that combines point detector data and AVI data produces the closest estimation of density to the estimation based on the trajectory data. Note that the HCM method also produces very good estimates of density. In this case study, the MAPE of segmentation method, cumulative volume-based method, and HCM method are.%,.%, and.% respectively. The advantage of the proposed segmentation method in this study that combines point detector and AVI data is that it does not require on-ramp or off-ramp volumes and initial estimation of density, as is required by the cumulative volume method. Also, this method does not require estimating vehicle length and detector length as required by the occupancy-based method. Of course, it has the disadvantage that it requires installing both point detector and AVI sensors, although some agencies have already decided to install both technologies: AVI detectors for travel time measurements and point detectors for flow and occupancy measurements. The density estimation using the fundamental relationship-based method and occupancy method based on point detector data are less accurate. The MAPE for these two methods are. % and.%, respectively. The reason for this may be because the segment density is calculated based on the average density at the upstream and downstream detectors in these two methods. In addition to the RMSE and MAPE, the maximum positive and negative differences in density estimates between the five methods and the trajectory-based data are also reported in Table. As shown in this table, these five methods overestimate the segment density by about % % and underestimate the density by about % - %. TABLE Density Estimated Comparison for Case Study based on Simulation Results Fundamental Cumulative Occupancy- Segmentation HCM Comparison relationship- volume-based Based Based RMSE (veh/mi/ln) MAPE (%) Maximum Positive Difference Compared to the Trajectory (veh/mi/ln) [%] Minimum Negative Difference Compared to the Trajectory (veh/mi/ln) [%]..... [%] [.%] [0.%] [.%] [.%] - [-.%] - [-.%] - [-.%] - [-.%] - [-.%]

12 Fakharian Qom et al. 0 0 The densities estimated from various estimation methods were further converted to levels of service (LOS) following the LOS criteria for a freeway facility in the HCM 00. The LOS results are presented in Table. As shown in this table, the values of LOS resulted from various methods except for the fundamental relationship-based method are consistent during the uncongested conditions. All the methods also produce the same LOS under the very congested conditions. Some differences occur among these methods during the transition conditions between congestion levels, at the shoulder of the peaks. TABLE Estimated LOS for Case Study Fundamental Occupancy- Segmentation Time relationship- Based Based Cumulative volume-based HCM Trajectory Data-Based :00 C C C C C C : C C C C C C :0 D D D D D D : F F F E E E :00 F F F F F F : F F F F F F :0 E E E E E E : D E D D E D :00 B B B C C B : B B C C C C :0 C C C C C C : B C C C C C 0:00 C C C C C C 0: B C C C C C 0:0 C C C C C C 0: B B B B C C Comparison of Density Estimation Based on Real-World Data The second case study is based on electronic toll tag data and point traffic detector data along a.-mile study section of the Florida Turnpike (State Road ) northbound in Miami, FL between May 0, 0 and May, 0. A total number of four point traffic detectors are deployed along this study segment with two detectors located at each end of the study segment and two intermediate detectors. There are also two tag readers deployed along this study segment at the same location of upstream and downstream detector stations. The encrypted tag data were processed following the procedures described in the previous section to estimate the space mean speed and for use in density estimation. Data from point detectors and tag readers were aggregated at five-minute aggregation time intervals in this study. There is one on-ramp in the study segment. However, this ramp is equipped with permanent traffic detectors. Historical three-day traffic count collected from portable traffic monitoring stations (PTMS) is available for the on-ramp and used to approximate the on-ramp volume for the cumulative volume method.

13 Fakharian Qom et al Real-world traffic data from point traffic detector and toll tag readers was used in this case study to estimate density based on the five methods discussed in the methodology section. Unlike the simulation case study, baseline data of density is not available in this case study. Thus, the density estimation results from the HCM method are used as a reference to compare the different density estimation methods. Since the traffic results are similar for the investigated days, only the detailed density estimation results for May 0, 0 are presented Figure and Table as an example. Figure shows that the estimated density from the proposed segmentation method and cumulative volume method, which combines tag and detector data, are close to each other and to the HCM method. This is consistent with the results from the simulation case study. The results show that, during the most congested period, the density estimation based the occupancy method and fundamental relationship-based method are close to the estimates from the segmentation and fundamental diagram methods. This is also consistent with the simulation case study. This can be explained by the fact that the occupancy method and fundamental relationship-based method are based on measurements at points and they may not represent the conditions along a segment, except at fully congested links. The above results are confirmed by the MAPE and RMSE values in Table, which show that the density estimated using the segmentation method and cumulative volume-based methods are closer to the results of HCM method. As indicated in Table, the MAPE for segmentation method and cumulative volume-based method are.% and.%, respectively. However, the MAPE for the fundamental relationship-based and occupancy method are 0.%,.%, respectively. Since RMSE indicates only the average differences between all methods, the average density differences are not big. In some time intervals, one method estimates more than other methods. In other time intervals, that method may estimate less than other methods. So, the average differences alone cannot show the differences between all methods. So, the positive maximum and negative minimum differences between all methods are also shown in Table. The maximum and minimum density differences between various density estimation methods and HCM-based method are also presented in Table. Note that positive values of density difference in the table indicate that the estimated density from HCM method is lower than the corresponding estimation from all the other four methods and negative values indicate a higher density estimate from HCM method compared to the corresponding density from all the four methods. It is seen from Table that the maximum positive difference between the segmentation method and the HCM method during the study time period is about. veh/mi/ln and the corresponding percentage for the maximum difference is.%, while the minimum negative difference is about veh/mi/ln, that is, corresponding to.%. Figure show that the highest differences between the estimates from the five tested methods occur during the time intervals of partial queues on the segments, in the transition between the uncongested and fully queued segments. During this period, the segmentation and the cumulative-based methods produced somewhat higher densities that the other methods.

14 Density (veh/mi/ln) Fakharian Qom et al Fundamental Relationship-Based Occupancy-Based Segmentation Cumulative Volume-Based HCM FIGURE Density estimation Results for Turnpike (Milepost. Milepost 0.) TABLE Density Estimation Results for Case Study as Compared to the HCM Fundamental Cumulative Occupancy- Segmentation Comparison relationship- Volume-Based Based Based RMSE (veh/mi/ln) MAPE (%) 0 0:00 :00 :00 :00 :00 0:00 :00 :00 :00 :00 0:00 :00 0:00 Timestamp Maximum Positive Difference Compared to the HCM (veh/mi/ln) [%] Minimum Negative Difference Compared to the HCM (veh/mi/ln) [%] [.%] 0. [0.%]. [.%]. [.%] - [-.%] - [-.%] - [-.%] - [-.%]

15 Fakharian Qom et al. 0 Table presents the LOS results for Case Study. As with the results listed in Table for the simulation case study, it can be concluded that the density estimates resulting from the various estimation methods yield similar LOS during the uncongested conditions and fully queued segment, while the LOS may be a little different during the partially queued segments with different density estimation methods. It is interesting to note, that as with the simulation case study, the segmentation method and the cumulative volume-based method produced very similar LOS estimates, which indicates that the proposed segmentation method was able to produce better segmentation of the link to congested and uncongested subsegments, compared to the halfdistance assumption used in the segmentation with the occupancy-based and fundamental relationship-based methods. TABLE LOS Estimation Results for Case Study Fundamental Occupancy- Segmentation TIME relationship- Based Based AM Peak PM Peak Cumulative Volume-Based HCM :00 C C C C C : D C D D D :0 D D E E E : E E F F E :00 E E F F E : F E F F F :0 F F F F F : F F F F F :00 E E F F F : E D E E E :0 D D E D D : B B C C C :0 C C C C C : C C C C C :00 C B B C C : C C C C C :0 C B C C C : C B C C C :00 C C C C C : C C C C C :0 C C C C C : C B B C C :00 C B B C C : C B B C C

16 Fakharian Qom et al CONCLUSIONS Four freeway density estimation methods that utilize point detector data, and in one case point traffic data combined with AVI data, were compared in this study with the density estimates based on the HCM freeway facility procedure. The three compared point detector data-based estimation methods are the cumulative volume-based method, occupancy-based method, and fundamental relationship-based method. A new segmentation method that is based on the combination of point detector data and AVI data was also proposed in this study to estimate density and compared with the other methods. The results show that the density estimates based on the proposed segmentation method, cumulative volume method, and HCM method are closer to each other compared to the estimates based on the other two tested methods. The simulation results show that the density estimates from these three methods are also closer to density measurements obtained based on vehicle trajectories from simulation. The results show that the highest differences between the estimates from the five tested methods occur during the time intervals of partial queues on the segments, in the transition between the uncongested and fully queued segments. The results show that, during the most congested period, the density estimation based the occupancy method and fundamental relationship-based method are close to the estimates from the segmentation and fundamental diagram methods. This is also consistent with the simulation case study. The study results also indicate that the selection of density estimation method mainly affect the value of LOS during the intermediate congested conditions, in which the segment is not fully queued. Based on the results of this study, it is recommended to use the cumulative volume based method to estimate freeway density when detailed on-ramp and off-ramp detector data is available, in addition to freeway mainline data. However, if ramp information is not available and AVI data is available, the proposed segmentation method can be applied to estimate density. ACKNOWLEDGMENT The authors would like to thank the National Center for Transportation Systems Productivity and Management (NCTSPM) for funding this research. NCTSPM is a University Transportation Center (UTC) funded by the United States Department of Transportation (USDOT). REFERENCES. Transportation Research Board. Highway Capacity Manual. (00). Washington, D.C., 00.. Qiu, T. Z., X. Lu, A. Chow, S. Shladover. Real-time Density Estimation on Freeway with Loop Detector and Probe Data. California PATH Working Paper. FHWA-EXARP and Caltrans TO, April 0, 00.. Comert, G. and M. Cetin. Queue Length Estimation from Probe Vehicle Location and the Impacts of Sample Size. European Journal of Operational Research. Volume, Issue, August 00, Pages 0.. Izadpanah, P., B. Hellinga, L. Fu. Automatic traffic shockwave identification using vehicles' trajectories. In Transportation Research Board th Annual Meeting. CD-ROM. National Academies Press, Washington D.C., 00.

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