Average speed is an essential input to the air quality analysis MOBILE6 model for the calculation of emissions factors. Traditionally, speed is obtained from travel demand models; however, such models are not usually calibrated to speeds. Furthermore, for rural areas where such models are not available, no reliable method is available for estimating speed. In this study, we developed a procedure based on the model in the Highway Economic Requirement System to estimate average speed using as input various data such as roadway characteristics and traffic conditions. The model was confirmed to be powerful based on the statistical comparisons between the estimated and measured speeds. Various implementation issues including the impact of data quality and potential applications are also discussed.
KEYWORDS: Speed estimation, air quality.
The increasing use of motor vehicles has resulted in a much degraded air quality in recent decades. The Clean Air Act requires transportation planners to monitor and assess the performance of transportation systems regularly; while the enactment of the Clean Air Act Amendments of 1990 signified the importance of combining travel demand and air pollutant emissions forecasting.
The commonly used air quality analysis model, MOBILE6, provides estimates of current and future emissions from highway motor vehicles. It has been employed by most states in compliance with the U.S. Environmental Protection Agency (EPA) requirement. MOBILE6 is an emissions factor model that employs information such as vehicle classification and age distribution, average operating speed, and vehicle-miles of travel (VMT). The outputs of the model include emissions factors for hydrocarbons (HC), carbon monoxide (CO), nitrogen oxides (NO x ), carbon dioxide (CO 2 ), particulate matter (PM), and toxic pollutants from cars, trucks, and motorcycles under various conditions (Cook and Glover 2002). Even though MOBILE6 has national default values for each category, area-specific inputs on a variety of parameters are preferred (e.g., annual mileage accumulation by vehicle class, average speed distribution by hour and roadway type, distribution of VMT by roadway type, and distribution of VMT by vehicle class).
Among the parameters required by the model, average speed is the most important because emissions rates are highly sensitive to changes in speed. Furthermore, the emissions rates of the three major pollutants, HC, CO, and NO x , are also very sensitive to VMT by time of day and average speed (Tang et al. 2003). This calls for an accurate estimate of average operating speed.
Various methodologies can be applied to speed estimation. Dowling et al. (1997) provide a comprehensive review of these methods. Here, we briefly discuss several commonly used methods.
The standard Bureau of Public Roads (BPR) equation was developed in the 1960s. Even though it does not accurately reflect the relationship between volume and speed, it has been widely used as a simple tool to predict mean speed, as shown in the following equation.
S = predicted mean speed
FFS = free-flow speed
v = volume
c = practical capacity
a = 0.15
b = 4
The free-flow speed, capacity, and volume can be determined by creating various lookup tables based on area and facility types. The uniform parameter values for a and b do not distinguish facilities in different types. This method could result in an estimation error of approximately 40% (Dowling et al. 1997).
Several improvements have been made to enhance the accuracy of the standard BPR equation. Separate curves were fitted for urban interrupted facilities. Data on critical segments of the facility replaced the facility averages. Based on an updated speed-flow relationship, the value of a was set at 0.05 for signalized facilities and 0.20 for all other facilities, while the value of b was set at 10. Furthermore, free-flow speed was estimated using an equation instead of the lookup table.
Despite the improved performance of the enhanced BPR technique, BPR-type equations are not capable of addressing the spill-back of physical queues formed at urban interrupted facilities. Therefore, this method should be limited to long-range planning applications that do not usually require high precision (Dowling et al. 1997).
The ARTPLAN technique is a planning procedure developed by the Florida Department of Transportation and is powerful in dealing with urban facilities controlled by signals (Dowling et al. 1997). Subsequently, the model was expanded to cover urban streets with stop sign control and conditions in which demand exceeds capacity. A similar procedure for rural facilities with interrupted flows was also created. Although the ARTPLAN technique outperforms the enhanced BPR technique for mean speed estimation on urban uninterrupted facilities, it still produces large errors. For example, it was observed that for urban arterials the estimation error could be up to 25% or 33% (Dowling et al. 1997).
In Kentucky, travel demand models (TDMs) are the primary tool for obtaining average speed estimates. These models were developed for large urbanized areas such as Louisville, Lexington, and the Northern Kentucky area. Some smaller urbanized areas also have their own TDMs. The enhanced BPR function is used in the model (Bostrom and Mayes 2003). However, these models do not presently include procedures for calibrating speeds. Furthermore, Kentucky currently has no reliable procedure for estimating speeds in areas without a TDM. Bostrom and Mayes (2003) provide a summary of the air quality attainment issues and highway speed estimation for MOBILE6 in Kentucky.
The objective of this research was to develop a procedure to estimate average speed on different roadway types. This paper evaluates the performance of such a procedure by comparing the estimated speeds with speed data collected in the field. Several issues that arose during the implementation of the model will also be discussed.
Based on the requirements of the air quality analysis and available data, we developed a procedure based on the internal speed model of the national version (v3.26) of the Highway Economic Requirement System (HERS) (USDOT 2000b), from which the state version (HERS-ST) is derived. HERS is a cost and benefit analysis tool that uses engineering standards and economic criteria to provide decision support on future infrastructure investment levels. HERS consists of a number of internal models that generate intermediate parameters for the cost and benefit analysis. One of the parameters is a speed model that calculates average effective speed (AES) for each segment of a roadway. This information can subsequently be used to calculate the costs of travel time, the external costs, and the total vehicle operating costs.
The HERS speed model requires many data items on facilities and traffic. Such information includes roadway geometric parameters, pavement condition, speed limit, traffic control devices, and traffic composition. Since HERS was designed to run based on the format of the Highway Performance Measurement System (HPMS) sample data, most required data items are available, at least for the sample segments.
The HERS speed model uses an aggregate probabilistic limiting velocity model to determine the free-flow speed (FFS) on a roadway. The delay due to traffic control devices or the presence of other vehicles on a uninterrupted facility is estimated based on facility type. The average AES is then obtained from the FFS and the delay. Figure 1 shows the general procedure for estimating average effective speed. The complete procedure for the HERS speed model can be found in the HERS Technical Report v3.26 (USDOT 2000b).
Based on the HERS speed model, an Excel macro was programmed to calculate the AES for each roadway segment. The average speeds were then grouped by county and by functional class for the purpose of air quality analysis.
We tested the HERS speed model using the data from the 2002 HPMS extract for Kentucky. This set includes state and locally owned roadways with a total of over 9,000 segments and over 13,500 miles. The mileage breakdown by functional class is shown in table 1. In addition to the data items in the HPMS format, the HERS speed model also needs information on heavy vehicle percentages by vehicle type on the segments (as specified in USDOT 2000b). However, these data are unavailable for most segments. Therefore, a lookup table was created to estimate this information based on the statewide heavy vehicle distribution by functional class and the total heavy vehicle percentages on each segment.
In order to evaluate the performance of the speed model, we compared the estimates to the field data collected through various efforts. Limited speed data are available in Kentucky, especially after 1995 when the speed limit compliance program was discontinued by the Federal Highway Administration (Bostrom and Mayes 2003).
Two primary sources of speed data exist in Kentucky. One is a study of the impact of speed limit changes on highway safety, in which extensive speed data were collected on various roads in Kentucky (Agent et al. 1997). Another is a recent effort to collect speed data in Christian County, Kentucky. Although these data were not collected in the same year as the HPMS data extract used for the HERS model, they were chosen to be compared with the model output because they are the most complete sets (in terms of covering various roadway types) of speed data. This time mismatch may introduce some errors to the validation process, especially at the segment level. However, the error at the route (a sequence of segments) level could be less due to the smoothing effect of the aggregation. Additionally, in an attempt to offset the impact of the mismatched time periods, several items (e.g., signal density) in the input data file, to which the speed output may be very sensitive, were updated during the validation process based on field data from Christian County. This case is also discussed in a later section to illustrate the importance of having accurate input data.
In the 1997 study, speed data were collected on 86 sample routes, covering all highway functional classes except for local roads and rural minor collectors. Based on the beginning and ending mile points for each of these routes, the matching sequence of segments was extracted from the 2002 HPMS data. The average effective speeds for these segments can be obtained via implementing the HERS speed model. The overall average speed for each route containing multiple segments was estimated as total mileage traveled divided by total time spent on the route. Table 2 lists a few sample roadways for which the comparison between measured and estimated speeds was made.
For rural Interstates with a 65 mile-per-hour (mph) speed limit, the differences between the estimated and measured speeds ranged from 0.2 mph to 5.9 mph. For urban Interstates and other arterials with a speed limit of 55 mph, such differences ranged from 11.4 mph to 2.2 mph. A paired t -test was chosen to test the equality of the underlying population means between the model output and measured samples. Prior to the test, preliminary analyses were conducted to ensure that the data did not violate the assumptions of the test. The first assumption was that the paired differences should be independent of each other, which was satisfied because the speed data came from different roads. Secondly, the paired differences should be normally distributed. The normal probability plot for the paired differences was constructed in which the close agreement with the straight line was observed. Then, the Lilliefors test for goodness of fit to a normal distribution was conducted. Under the significance level α , the hypothesis that the paired difference has a normal distribution was accepted.
After the assumptions were confirmed, the paired t -test was conducted. With a p value of 5.6 × 10 -5 , the result recommended that we reject the null hypothesis that the two sets of speeds are from populations with equal means. In other words, the estimated and measure speeds were statistically different. However, the test also showed that the average measured speeds were no more than 1.1 mph higher than that of the estimated speeds when α = 0.05. The p value at this time was 0.08 and the t statistic was 1.77 and was lower than the critical t statistic (1.99 in this case). The 95% confidence interval for the average difference between the measured and estimated speeds was (0.18, 3.59). This implies that the extent of the differences between estimates and measurements was not very large, although the difference was statistically significant.
To eliminate the potential impact of the speed limit on the sample means, paired t -tests were conducted for sample groups with different speed limits. Under the significance level of 0.05, test results showed that for roadways with a 65 mph speed limit (i.e., rural Interstates), the average estimated speed was approximately 1 mph higher than the average measured speed. The 95% confidence interval for the difference between the estimated and measured speeds was (0.69 mph, 2.97 mph) for these roads. For roadways with a speed limit of 55 mph, the HERS speed model underestimated the speed by approximately 2 mph. The 95% confidence interval for the difference between the two was (3.84 mph, 1.74 mph) for these roads. Although the differences between the estimated and measured speeds were statistically significant, the absolute estimation errors were not substantial as indicated by the mean difference and the confidence intervals.
A larger difference was observed between the estimated and measured speeds on roads with lower functional classes. This was primarily attributable to the model's sensitivity to various factors such as traffic signal density. A detailed discussion on this topic will be presented in the next section.
In 2005, Christian County in Kentucky was designated by EPA as a nonattainment area. It became crucial to obtain accurate speed estimates for different types of roadways in this county in order to establish the future emissions budget. Speed data were collected during a three-month period in summer 2004 on a number of roadways throughout the county. The effort covered approximately 50% of the total mileages (both state and locally maintained) and over 70% of state-maintained facilities in the county. The sample segments were selected based on the recommendation in FHWA's Travel Time Collection Handbook (Turner et al. 1998). Each road was traveled at least twice, once during the peak and once during the offpeak periods.
The HERS model was tested on the same highway segments in Christian County on which the speed survey was conducted. Table 3 shows the comparison between the estimated and measured speeds for several sample roadways in the county. The differences between the two sets of speeds were mostly within 5 mph with few exceptions. However, the paired t -test could not be applied in this case because the data violated the assumption that the paired differences between the two sets of speeds should be normally distributed.
Therefore, nonparametric tests need to be used, because they do not usually make distributional assumptions. The most commonly used alternative for the paired t -test is the Wilcoxon paired signed rank test. The Wilcoxon signed rank test first sorts the absolute values of the differences (between estimated and measured speeds) from smallest to largest, and then assigns ranks to these absolute values starting with the smallest as rank 1. The sum of the ranks of the positive differences is then calculated. When the null hypothesis (i.e., the median difference in paired data is zero) is true, the sum of the ranks of all positive differences is approximately the same as that of the negative differences. The Wilcoxon signed rank test was conducted to compare the estimated and measured speed data. With a p -value of 0.40 under α = 0.05, the test did not find enough evidence to reject the null hypothesis that the underlying population speeds had the same median. When the population distribution is symmetric (as was the case for Christian County data), the median is approximately equal to the mean. The test was also conducted for sample differences in each functional class. It subsequently recommended the acceptance of the null hypotheses as well.
Considering the speed variation on highways by various functional classes, the speed samples were grouped according to roadway functional class. The speed sample size and mileage are summarized in table 4 together with the aggregated average speeds from the HERS model and field measurement in Christian County.
An Excel-based software tool was developed to implement the HERS speed model on highway data stored in the HPMS format. Additional data items, such as truck percentage breakdowns by truck type, were prepared separately. The tool calculates the average effective speed for each segment and then aggregates them to the county level for each functional class. Specifically, the average travel time on each segment was estimated from the segment length and the average effective speed. The countywide average speed was then calculated as total distance traveled (i.e., total length of all segments) in a functional class divided by total travel time on the road segments in that functional class.
Although the HERS speed model performed very well in estimating the average speed for each roadway segment, its accuracy at the county, regional, or state level is largely dependent on the availability and accuracy of the input data.
The HERS model uses highway inventory data in the HPMS sample format to calculate the average speed. However, such data are not available for all highways. Usually, most state-maintained highways are inventoried, but not much information is available for those that are locally maintained unless they are HPMS sample sections. Moreover, many state-maintained roads that are in lower functional classes may not have been inventoried. An accurate estimate of speed would call for adequate samples in each functional class. Intensive effort might be necessary to ensure that enough data are available, particularly for roadways in lower functional classes.
The accuracy of the input data also affects the performance of the speed model. Like any model, the validity of the speed model output depends on the validity of the input. Some inconsistencies were found in the HPMS extract. For example, the sum of the curve (or grade) lengths must equal the segment length (USDOT 2000a); however, a number of segments did not satisfy this requirement. Furthermore, the unavailability of curve (or grade) data on some segments is treated by the speed model as if the segment was all tangent (or leveled), because both scenarios would have a "0" code in the curve (or grade) class fields. However, these segments may not indeed be curve-free (or leveled) as indicated by the horizontal (or vertical) alignment adequacy rating. In other words, the HERS speed model does not distinguish the "no data" scenario from the "no curve (or grade)" scenario. In order to improve the accuracy of the model output, efforts should be made to assure the accuracy of each data item.
Special attention should be paid to the accuracy of data items, such as the density of traffic control devices, because they tend to have a significant impact on the delay estimates. During the model validation process, significant differences between the estimated and measured speeds were observed on several roads. Table 5 lists several roads in Christian County with "Initial AES" estimates significantly different from the observed speeds at the same sites. Further investigation revealed that there are some differences in the density of traffic control devices, speed limit, and lane width between the 2002 data extract and the information collected in 2004. After the input file was updated based on the latest information, the HERS model produced an updated output (also shown in table 5). Significant improvement of estimation accuracy can be seen on many of these roadways.
The HERS model is also quite sensitive to the speed limit, which is one of the parameters used to calculate the free-flow speed. The maximum speed resulting from the speed limit (VSPLIM) is assumed to be at least 6 mph above the speed limit in the HERS speed model.
In Kentucky, the default speed limit for rural highways other than the Interstates and four-lane highways with a median is 55 mph. However, the prevailing speed may be severely restricted by the presence of sharp curves which, as discussed earlier, may not be accurately reported in the HPMS sample data. Nevertheless, the adjustment of the posted speed limit to reflect the prevailing operating speed may not be made on all segments. This is also recognized in the HPMS Field Manual (USDOT 2000a) in that it uses the horizontal alignment adequacy rating to describe the curves with design speed less than the prevailing speed limit. Under this circumstance, using the posted speed limits in the data table would yield an unreasonably higher VSPLIM. Combined with the incomplete curve data, which will over-estimate the maximum allowable speed on a curve (VCURVE), higher (and less accurate) estimates of FFS and AES will result.
On the other hand, the item "weighted design speed" in the HPMS data file contains the design speeds weighted by the length of horizontal curves and tangents on a segment. For a number of roadway segments in Kentucky, the weighted design speed could be as low as 40 mph while the posted speed limit is 50 mph. Therefore, in order to reduce the estimation error, in such cases, the effective speed limit (the lower one between the weighted design speed and posted speed limit) should be used.
Because other factors such as annual average daily travel (AADT) and truck traffic percentage and composition would also affect the average speed, a full-range sensitivity analysis for this model will require an extensive amount of speed data collected in the field. Nevertheless, this study demonstrates the sensitivity of the HERS model as well as the significance of data quality assurance efforts.
The HERS speed model was applied to the Kentucky statewide highway inventory data in the HPMS format. Then we grouped average speeds by county and functional class for air quality analysis application. However, a county-level sample size may be too limited to provide reliable speed estimates for each county.
Alternatively, all 120 counties in Kentucky were divided into 3 major groups according to demographic, economic, and topographical characteristics. Although Kentucky is largely a rural state, it contains three major metropolitan areas (Louisville, Northern Kentucky, and Lexington) with typical urban traffic patterns. The eastern Kentucky area is mostly mountainous with many slow-moving coal trucks on the highways; therefore, the statewide speed distribution was obtained for three types of areasurban, mountainous, and other rural areas (table 6). The areawide speeds by functional class could then be used to represent the countywide speed distribution. This method preserves the characteristics of each type of area while ensuring a relatively larger sample size to smooth out the impact of stochastic variation, which may result from the limited sample size for one specific county.
The average speed estimates obtained from the HERS model can be used in various applications. In the short term, it can be used as an input to the MOBILE6 model to compute the emissions factor for various automobile-related pollutants. In the long run, if the input data items, such as pavement condition and AADT are updated using their projected values for future years, the HERS speed model will produce the projected average speeds on these roads. Such speeds can be used to estimate the emissions budget for future years.
In addition to air quality-related analysis, speed data can also be used as part of the highway performance measures. The data provide quantitative supplements to the traditional level-of-service indices and serve as the basis for the estimation of travel time, all highly desirable information on highway performance.
The speed estimation procedure developed in this study is based on the HERS speed model. It uses the HPMS data format to compute speed on each roadway segment. The free-flow speed was first estimated and then adjusted based on delay experienced by each vehicle (on various types of facilities) to obtain the average speed estimate. Although a large number of data items are required as input, these data are available from the annual HPMS submission that is mandatory for all states. However, for those roadways that do not belong to the HPMS sample set (primarily local roads and rural minor collectors), additional data-collection efforts may be necessary.
The model performance was evaluated by two independent speed datasets collected in the field. Various statistical analyses attested to the power of the model for producing accurate speed estimates. Tests also showed that the model was quite sensitive to factors such as the density of traffic control devices. A periodic review and update of such information in the inventory data file may be required to ensure the accuracy of input data to the speed model.
Although default speed distribution by hour is available in MOBILE6, the area-specific hourly speed estimates are needed to increase the prediction accuracy of emissions factors. The next-generation of air quality model, MOVES (Motor Vehicle Emission Simulator), also calls for speed data at a much finer level than the daily average (USEPA 2004). Furthermore, the analysis of hot spots would require delay and queue length by time of day. Currently, an effort is being made to adapt the concept of the HERS speed model to the estimation of hourly speeds. This hourly speed model would provide further detail on the variation of speed, delay, and queue length over time, in addition to accounting for queue spillover during the peak period.
This study is funded by the Kentucky Transportation Cabinet and the U.S. Department of Transportation, Federal Highway Administration. The views presented in the paper are those of the authors alone.
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1H. Gong, Department of Civil Engineering, University of Kentucky, Lexington, KY 40506. E-mail: firstname.lastname@example.org
2 Corresponding author: M. Chen, Department of Civil Engineering, University of Kentucky, Lexington, KY 40506. E-mail: email@example.com
3J. Mayes, Division of Multimodal Programs, Kentucky Transportation Cabinet, Frankfort, KY 40622. E-mail: firstname.lastname@example.org
4R. Bostrom, Division of Multimodal Programs, Kentucky Transportation Cabinet, Frankfort, KY 40622. E-mail: email@example.com