1. Introduction

Vehicle miles traveled (VMT), the number of miles traveled by vehicles is one of the most important measures to gauge the utilization of highway systems by vehicles. Intuitively, the greater the value of VMT is, the more emissions would be produced and the severer roadways would be deteriorated. Thus, VMT has been used in various important decision-makings such as air quality compliance and roadway pavement maintenance. In practice, VMT is usually estimated using various methods based on the collected traffic volume. Due to the significant consequences that would be caused by decision-makings using VMT, it is critical to have an accurate estimation of VMT.

Federal Highway Administration’s Highway Performance Monitoring system (HPMS) is responsible for the traffic count program to estimate VMT based on a traffic count-based method. In this method, the highway network in an area is divided into non-overlapping segments and VMT is estimated based on traffic counts for each segment and its length. For the Interstate highway system, the segment is defined as the section of road between interchanges. Because the length of each segment is known, the essence of VMT calculation is to derive traffic volume passing over each segment. Considering the cost of traffic counting, only a small number of segments are sampled and continuously counted for traffic for an entire year, while the remaining segments are counted for a short period time. For the segments with continuous counts available, annual average daily traffic (AADT) can be derived directly from the collected traffic volume. For the segments with short duration counts (also known as coverage counts), AADT has to be estimated. To capture the seasonal and weekday characteristics of traffic that cannot be derived from the coverage counts, correction factors (seasonal and weekday factors) can be calculated from the continuous counts and then applied to the coverage counts. AADT can then be estimated by combining the coverage counts and the factors. Given AADT for each segment, VMT for a segment can be calculated by multiplying its AADT by the length of the segment. VMT for an area can be obtained by adding up the VMT of each segment.

One major source of errors for the estimated VMT is from the usage of seasonal and weekday factors derived from other segments. This approach assumes that the annual traffic patterns between the segments from which the factors are derived and those to which these factors are applied are the same. This assumption may not be true in reality. It has been noticed that there are traffic count data for the segments with coverage counts that are collected by other agencies such as traffic management centers. As one part of Intelligent Transportation Systems (ITS), these sets of data are archived anticipating to be used for other purposes such as transportation planning, pavement management, and air quality analysis. Because these operational data including traffic counts are also collected year round and thus can be viewed as continuous traffic counts. Intuitively, they can replace the coverage counts in the corresponding segments to derive AADT without the need to use the seasonal and weekday factors from other segments. By doing that, the estimated VMT can be expected more reliable. An example showing the coexistence of both the ITS data and HPMS data is presented in Figure 1-1 and Figure 1-2. Figure 1-1 shows the Hampton Roads Smart Travel Center (HRSTC) stations in the five segments along I-264 and Figure 1-2 shows the VDOT coverage count stations along I-264. Note that I-264 is a major interstate highway in the Hampton Roads area.

Figure 1-1 HRSTC Stations in the Segmnets along I-264

Figure 1-2 Coverage Count Stations in the Segmnets along I-264

One significant issue of using the operational or ITS data is the unreliable data quality associated with it because of insufficient maintenance work. In some traffic operational centers, detectors are originally installed for the purposes of detecting incidents. Due to the unsatisfactory performance of incident detection using point detectors, this function has been discarded by some traffic management centers. Currently most centers use these traffic detectors only for monitoring traffic by displaying traffic conditions on TV monitor screens. As a result, maintaining detectors has become less important and the data quality suffering from frequent detector malfunctions is a major concern when the data are to be used for other purposes.

There are two ways to reduce the amount of missing data: (1) provide a quick response to maintenance service call and restore the detector condition back to normal as soon as possible; (2) enhance preventive maintenance such that the conditions of detectors can be upgraded to conditions when the detectors are installed at the beginning. Currently, some agencies deploy a policy where preventive maintenance is provided to a detector station only when an emergency maintenance is served to a failure in a loop detector station. Some other agencies provide preventive maintenance to a detector station based on a schedule even when there is no failure happening. The policy used to adopt in an agency relies upon various factors. To help the decision-making on such a policy, it is important to provide quantitative information about the life cycle (including both life and failure durations) of detectors.

The objectives of this study are twofold. The first is to determine the conditions under which ITS data can be used to replace the coverage counts to derive AADT. The second is to identify the relationship between life duration and traffic volume. In this study, the comparability between the ITS data and coverage counts is investigated by employing the Monte Carlo method. By using this method, the number of missing data in the ITS data more than which the ITS data cannot be used to replace coverage counts is determined. After determining this critical value, a procedure is developed by which ITS data can be combined with the data from HPMS to derive VMT for an area. By comparing the VMT values derived with and without considering ITS data, the difference in the estimated VMT was determined. From the difference in VMT that was caused by including ITS data, the importance of having ITS data can be well underscored.

The relationship between the life duration and traffic volume is investigated by developing linear regression models, from which whether traffic volume significantly influences the life duration of detectors can be identified. In HPMS, vehicles are categorized into thirteen classes. In this study, these thirteen classes are aggregated into four groups, which constitute the pool of predictor variables for the regression models. From the linear regression models, the groups of the vehicles that significantly influence the life duration of detectors can be identified. With the regression models developed, life duration of detectors can be predicted given the travel demand forecast into future, and then optimal maintenance policy can be developed correspondingly.

Traffic volume data collected by Virginia Department of Transportation (VDOT) and the Hampton Roads Smart Travel Center (ITS data) are used in the investigation of the VMT estimation. A maintenance database from VDOT is involved in identifying the relationship between traffic volume and detectors’ life durations. The database includes the information about the maintenance work for VDOT continuous traffic counts. The current procedure of maintenance work can be known based on the service information in the maintenance database.

The organization of this thesis is as follows. Chapter 2 introduces the current method used to estimate the AADT and VMT in Virginia. In Chapter 3, the methodology of the Monte Carlo method to determine the critical value of missing data is described. The linear regression method is also discussed in this chapter for identifying the relationship between the life cycle and traffic volume. Chapter 4 presents the results of the Monte Carlo simulation program and VMT estimation for an area (the Hampton Roads Area). Chapter 5 first discusses the components of continuous traffic counts, the installation and the maintenance work. It also describes the derivation of the loop detectors’ lifecycle from maintenance database, which is followed by the presentation of the results from the linear regression. Chapter 6 is devoted to conclusions made for this study and study needs identified for future.

2. Literature Review

2.1. VDOT Traffic Monitoring System

VDOT Traffic Monitoring System (TMS) is the part of the national HPMS. VDOT Mobility Management Division is responsible for the system management including data collection and maintenance. The collected data are processed for errors and then submitted to HPMS. As shown in Figure 2-1, ten continuous count stations were installed on the five segments for the purpose of continuously counting traffic volume. The remaining segments in the area are counted by coverage counts.

Figure 2-1 Continuous Count Stations from VDOT TMS

2.2. Hampton Roads Smart Traffic Center

Hampton Roads Smart Traffic Center (HRSTC) manages traffic on I-64, I-264 and I-564, as shown in Figure 2-2. There are eleven segments monitored by HRSTC on I-64, five on I-264, and two on I-564. The number of STC stations in each segment is listed in Table B-1 (Appendix B) with the coverage stations from VDOT TMS. The length of the segments is provided in Table B-2. (Appendix B)

In the HRSTC traffic monitoring area, there are zero CCS and 36 coverage count stations from VDOT TMS. In this study, VMT is calculated for the HRSTC area instead of the whole Hampton Roads area covered by TMS.

Figure 2-2 Traffic Stations from the Hampton Roads Smart Traffic Center

2.3. Methods for Computing AADT

Various methods have been used to estimate AADT and VMT for the interstate highway, urban roads and rural roads. A method to estimate AADT in a Florida County combining the GIS technology and the linear regression model was developed. (Zhao, 2001) The responsive variable is AADT on local roads in a large urban area. The predictor variables include function classification, are type, number of lanes, land use, and accessibility. The high-resolution satellite images were also used to improve the estimation of AADT and VMT. (McCord and Goel, 2002). The satellite imagery was used as additional source of data for AADT and VMT estimation. In this study, the data source is the traffic count stations placed along the roadway segments.

There are two basic procedures to calculate AADT based on the consciously collected traffic volume on the road segments. The first one calculates the AADT by simple taking the average of all available daily traffic volumes in a year. The advantage of this method is that it is simple and easy to program. However, this method will cause bias in AADT estimation if there are considerable numbers of missing days in the collected traffic due to the equipment malfunctions. The second procedure, which is proposed by AASHTO and also adopted by VDOT TMS, can be expressed as the following formula:

where twelve months in a year (=1, 2… 12),

seven days in a week (=1,2, …, 7), and

monthly average days of the week traffic.

This method is also known as an average of averages method. This method accounts for the missing days by give the same weight to each day of the week in each month. Considering the current situation that continuous traffic counts have missing data, the AASHTO can provide more reliable results than the first procedure.

The first step in AASHTO method is to calculate an average daily traffic volume for a Monthly Average Day in a Week (MADW). For the one-month complete data, MADW is the average value of the four or five daily traffic volumes for each day of week in a month. There are seven values of MADW for a month; each refers to each day of the week. For example, the MADW value for the Monday in a month is calculated as the average of all daily traffic volume on Monday in this month. After computing the MADWs, the Monthly Average Daily Traffic (MADT) for a given month can be derived by averaging the seven MADW values for that month. The AADT of one segment for a specific year is the average of the 12 MADT values in this year. For one year with complete traffic data, there are 84 MADW values, which can be expressed as a form of matrix shown in Table 2-1. From the equation for AADT above, it can be seen that this method takes the average of all 84 average values in the 84-cell matrix, where each day-of –week in each month is considered equally.

Table 2-1 84-Cell Table of MADW Values

	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec

For the segments where a coverage traffic count is located, AADT is calculated by applying seasonal and day-of-week factors developed from continuous traffic counts to coverage traffic counts. The formula to calculate the factors is as follows:

where = the seasonal and day-of-week factor for the jth day in a week of the ith month,

twelve months in a year (=1, 2,…, 12),

seven days in a week ( = 1, 2,…, 7), and

= monthly average days of the week traffic

Table 2-2 84-Cell Table of Season and Day-of-Week Factors

	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec

It can be seen from the formula that these factors can be derived by dividing the AADT by each value in the corresponding MADW table in Table 2-1. As a result, an 84-cell factor table can be derived as shown in Table 2-2. Given the factors derived from CCSs, AADT for a segment with a coverage count can be estimated by multiplying the daily traffic volumes collected for a short period of time in this segment by a seasonal factor in the factor table corresponding to the month and day of week that the daily traffic volumes are collected. The formula below demonstrates the calculation of the AADT for a coverage count segment, where two consecutive daily traffic volumes are collected.

where the annual average daily traffic estimated based on coverage traffic counts

twelve months in a year (=1, 2, …, 12),

seven days in a week (=1,2,…, 7),

the seasonal and day-of week factor, and

the daily traffic collected by the coverage traffic count

It can be seen from the formula, each of the two-day traffic volumes is multiplied by a factor. The average of these two AADT values generates the AADT for the segment.

2.4. Traffic Patterns in the MADW Table

While the method of using factors to convert coverage traffic counts to AADT is effective, it assumes that the traffic pattern in the coverage traffic count segment is the same as that in the continuous count segment. This assumption causes errors in the coverage count based AADT estimation when the traffic locations with the coverage and continuous counts do not match in reality.

The assumption on the same traffic patterns from these two types of stations can be presented as follows.

Let

, then

where the month when the coverage count was collected,

the day in a week when the coverage count was collected, and

the corresponding MADW value in the factor-deriving table.

For a daily traffic collected by a coverage count, I and J are fixed and thus in this equation can be viewed as a constant. It can be seen from the above formulas that applying the seasonal factor developed based on CCS to coverage daily traffic is equal to developing a new 84-cell table of monthly average days of the week traffic. Since is a constant value for a given coverage daily traffic, the traffic pattern implied in the new MADW table is the same as that of the CCS used for deriving the factors. It becomes evident that the factor method to convert coverage counts to AADT is based on the assumption that the traffic pattern in the coverage traffic count segment is the same as that in the continuous count segment.

An example from the Hampton Roads area is provided below for illustrating the difference in traffic patterns and values between the coverage and continuous count stations. Coverage count station 50155 is located in the same segment with STC station 58. The two-day counts from station 50155 with specification in Table 2-3 are used to derive the new matrix with the same implied traffic pattern as that from the factor-deriving CCS. Continuous count stations 150010, 150012, 150022, and 150079 are used to calculate the seasonal and day-of week factors (see Table 2-4). Station 58 is a traffic count station maintained by HRSTC and has the most available days among all STC stations after data quality checking. Therefore it is used to calculate the true traffic pattern of the segment.

Table 2-3 Coverage Count Station 50155

Coverage Count

Station ID

Date

Month

Day-of-Week

Traffic Volume

50155

25-APR-2000

58017

26-APR-2000

59921

Table 2-4 Seasonal and Day-of -Week Factors based on four CCS

	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Jan	1.06	1.20	1.14	1.09	0.92	1.43	1.87
Feb	0.99	0.94	0.94	0.92	0.87	1.29	1.54
Mar	0.96	0.95	0.93	0.92	0.84	1.24	1.47
Apr	0.93	0.95	0.92	0.88	0.84	1.22	1.39
May	1.01	0.92	0.90	0.89	0.80	1.12	1.31
Jun	0.92	0.91	0.88	0.86	0.79	1.00	1.24
Jul	0.95	0.97	0.89	0.88	0.80	1.01	1.24
Aug	0.92	0.91	0.91	0.86	0.81	1.01	1.24
Sept	1.08	0.96	0.91	0.91	0.84	1.17	1.44
Oct	0.94	0.94	0.91	0.89	0.81	1.15	1.37
Nov	0.93	0.93	0.89	0.99	0.93	1.28	1.48
Dec	1.06	0.97	0.96	0.94	0.89	1.30	1.74

The new complete 84-cell MADW table based on the coverage counts applied with factors is presented in Table 2-5. The true traffic pattern in the segment, where STC station 58 is located, is shown in Table 2-6. Note that there are two cells missing in Table 2-6 due to the data quality problem.

Table 2-5 84-Cells Table for Coverage Count 50155 with the Same Traffic Patterns

	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Jan	52411	46076	48475	50653	60128	38633	29665
Feb	55883	59068	58834	60302	63756	42765	36016
Mar	57749	58210	59610	60288	65715	44709	37563
Apr	59395	58017	60309	63133	66203	45369	39812
May	54978	60098	61290	62462	69471	49277	42174
Jun	59881	61037	62802	63978	70121	55277	44531
Jul	57978	57121	62453	63091	69247	54887	44785
Aug	59968	60813	61128	64479	67993	54845	44716
Sept	51391	57815	60746	60832	65937	47278	38470
Oct	58845	59172	61109	62392	68295	48203	40401
Nov	59241	59702	62323	55719	59595	43293	37455
Dec	52033	56878	57917	58741	62236	42539	31740

Table 2-6 84-Cells Table for STC Station 58 with the True Pattern

	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Jan	60014	60338	60716	61408	65864	46463	44674
Feb	59818	62021	63205	64882	69590	49133	48080
Mar	60132	60386	61855	61766	69367	48995	48520
Apr	61002	61462	64310	63617	65812	50970	47659
May	49628	64898	56424	43733	73680	37468	44113
Jun	66702	64974	67122	67505	75412	56890	55253
Jul	65011	63264	67557	66989	72155	56130	56179
Aug	65262	65097	66931	68493	69559	56256	55275
Sept		63353	64140	66910	70380	50942	47178
Oct	61957	62778	62820	65343	71046	50699	50710
Nov	61042	57820	63914	56546		46141	47952
Dec	36463	57223	62279	63090	65618	45103	41980

For the purpose of illustration, the traffic pattern based on the coverage count and the true pattern from Station 58 are plotted for the column on Wednesday (as shown in Figures 2-4). The upper and lower boundaries determined from the standard deviations of each MADW value on Wednesday are also shown in Figure 2-4. It can be seen from the plot that the traffic patterns and corresponding values are different from each other. Therefore, it is reasonable to expect that the accuracy of VMT estimation of a segment based on the short duration traffic count from VDOT can be improved due to the usage of the ITS data collected in the same segments.

Figure 2-4 Seasonal Variation of the MADW traffic on Wednesday

3. Methodology

3.1. Methodology for Comparing ITS and HPMS Data Based AADT

Even though developing a method to combine ITS and HPMS data is one of the major goals of this study, this section focuses on the methodology for comparing the AADTs derived from coverage counts and ITS traffic counts. It is because the comparison of these two AADT is one of the critical steps in the method of combining ITS and HPMS data.

In the case of coverage count based AADT calculation, a fixed number of coverage counts can be any consecutive weekdays. Table 3-1 shows two temporal distributions of coverage counts where the number of coverage count is two (2). Because of the use of factors, there is a discrepancy between the estimated and the true AADT for a roadway segment. In the case of ITS based AADT calculation, the number of daily traffic data available can be any places in the 365 days. Table 3-2 shows two temporal distributions of ITS data where the number of available day data is five (5). Following the AASHTO method to derive AADT, there is a difference between the estimated and the true AADT. By comparing the differences of coverage based AADT with those of ITS data based AADT, with the consideration of all the possible number of missing days of traffic data in a year, the likelihood that ITS based AADT is more accurate than the other can be derived. As a result, the number of missing day corresponding to a given likelihood for ITS data based AADT better than coverage count based AADT can be derived.

A direct solution for such comparison is to develop a simulation model where the temporal distribution of either coverage counts or ITS data can be generated. If the number of coverage counts is less than two, the number of temporal distributions can be exhaustively enumerated. Otherwise, the number of temporal distributions cannot be enumerated within a reasonable computational time. In such a case, a fixed number of the temporal distributions can be generated randomly with the satisfaction of constraint on certain criterion such as the difference of estimated and true AADT in this study.

Table 3-1 Temporal Distributions of Two Coverage Counts

	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Jan	^·	^·
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Jan		^·	^·
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec

Table 3-2 Temporal Distributions of ITS Counts with Five Days’ Data Available

	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Jan		^·
Feb					^·
Mar
Apr
May
Jun				^·
Jul
Aug		^·
Sept
Oct						^·
Nov
Dec
	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Jan
Feb		^·
Mar				^·
Apr
May					^·
Jun
Jul		^·
Aug
Sept
Oct							^·
Nov
Dec

The missing day of ITS traffic data can be in any of 365 days in a year. For a fixed number of missing days of traffic data, these missing days can be distributed over 365 days with a substantial number of combinations with regard to the locations of these missing days in a year. For instance, the total number of combinations of three-day missing case, i.e. the population of this case, is equal to. As the number of missing day increases, the case population will increase dramatically as shown in Figure 3-1. As can be seen from the figure, the number of combinations is significantly large even when the number of missing day is small. In this study, the Monte Carlo Method is used in the simulation for comparisons, for which a flow chart is presented in Figure 3-2.

Figure 3-1 Case Population vs. Missing Day

Figure 3-2 the Monte Carlo Method for Comparisons between STC and Coverage Counts

The basic idea behind the Monte Carlo method is to generate multiple trials with the satisfaction of constraint on criterion, the expected value of a random variable, which is the error of the computed AADT given a certain number of missing days of data in this study. The number of trials represents the number of iterations that the Monte Carlo method should run to obtain the estimates given the required accuracy. The percent difference (%D) is used here to describe the error of AADT estimates. The AADT computed with a complete one-year traffic data is taken as a reference value, or actual value, with which the estimated AADT with incomplete one-year traffic data is compared. The error with the AADT estimated from incomplete data is defined as:

For the case with a certain number of missing days, the same number of days is selected randomly to be missing days by the program. Then an estimated AADT is calculated using the ASSHTO method. This estimated value is compared with the actual value to generate the estimate error, which is the output of the simulation program.

The method to determine the number of iterations is based on the Central Limit Theorem. Let be a random sample of size n from a distribution with mean and variance. For a large n, is approximately normal with mean and variance. The random variable is approximately standard normal. In the simulation program, each error of AADT estimates for the case with a certain number of missing days is viewed as mentioned above. The average of the error (sample mean), i.e.,, calculated based on a number of iterations (n) is viewed as a random variable normally distributed with mean and variance . According to the rule of normal probability, approximately 99.7% of repeated sampling from a normal distribution fall within 3 standard deviation of the mean, which can be written as:

Since the average of the error is approximately normally distributed with mean and variance, then

, or

Here, the required accuracy can be defined as, which indicates the difference between the sample mean of the error and population mean. With the given value of the, the above equation can be written as and the number of iteration can be computed as .

In this study, the number of iteration for the simulation of STC stations can be reasonably determined based on the case with 364 days missing. This case can be equally viewed as the case with only one day left for the calculation of AADT, for which the total number of possible combinations is small and the errors can be derived without any computational difficulty. From this reasonable number of errors, the standard deviation of the last case can be directly obtained and used to determine the number of iterations (n).

Given the number of iteration determined and the number of missing day data, the errors from the simulation can be arranged in Table 3-3.

Table 3-3 Errors of AADT estimates in Simulation (the CCS error)

Case Iteration	1	2	.	.	.	364
1	Error 1,1	Error 1,2	.	.	.	Error 1,364
2	Error 2,1	Error 2,2	.	.	.	Error 2,364
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
n	Error n,1	Error n,2	.	.	.	Error n,364

In the simulation, a CCS was selected as the base data from which both coverage count and ITS data can be simulated. Their AADTs and errors can be derived correspondingly. The probability that coverage count based AADT is better than the ITS data based AADT can be calculated as follows:

where:

n = number of iteration for each missing day case, and

m = the number of two-day coverage counts that can be selected from CCS

= the number of observations that errors of AADT estimate from coverage counts are less than that from CCS

The number of missing days and related probability can be plotted with x axis (number of missing day) and y axis (probability), respectively.

3.2. Methodology for Determining the Relationship between Detectors’ Life Duration and Traffic Volume

Linear regression model is used to investigate the relationship between the life duration and traffic volume. The response variable Y is the life duration of the loop detectors. The possible predictor variables are a group of vehicle volume. A multiple linear regression model including all predictor variables is fitted at the first step. The selection of predictor variables in the model is based on the consideration of correlation matrix showing the correlation among the X variables and their t statistics obtained from the linear regression results. Each value of t statistics indicates whether the term can be dropped from the multiple regression model. It is a two-sided hypothesis-testing problem:

The test statistic:

where: regression coefficient, and

estimated standard deviation of

The decision rule for the testing is:

If conclude

where p = number of parameters in the regression modal that need to be estimated

In order to select the “best” subsets of predictor variables based on the F^* statistic, the forward stepwise regression method can be employed. The stepwise method is conducted by the following steps:

Step 1: Fit a simple linear regression model for each of the X variables in this study. F^* statistic is used to test whether equals zero or whether the slope of the corresponding simple linear regression model is zero.

where m = each of the X variables,

= test statistic for the regression of Y on the X variable represented by m,

MSR = regression mean square, , and

MSE = error mean square

Here measures the reduction of the total variation of response variable Y due to the use of predictor variable. The with the largest F* value is considered to be added into the model. If this F* value exceeds a predetermined value, then the corresponding will be added. Otherwise, no X variable will be included in the regression model. Suppose that is added in the step 1.

Step 2: Fit the regression model with two X variables. These two X variables include the added into the model in step 1 and another one from the rest of X variables. For each regression model, the partial F test statistics is:

where m represents the rest of X variable.

It tests whether the equals zero when and are in the regression model. The with the largest F* value is considered to be the second variable included in the model. If this F* value exceeds a predetermined value, then the corresponding will be added. Otherwise the stepwise procedure will stop here with only one variable in the model.

Step 3: Suppose in step 2, a second X variables is added in the model. Now the stepwise method will examine whether another X variable already in the model should be dropped based on the partial F test:

If this F* value is less than the predetermined value, then the corresponding X variable will be dropped; otherwise, it is retained. The stepwise method follows the same procedure until no further X variables can be either added or dropped.

4. VMT Estimate for an Area

4.14.1. Comparing ITS and HPMS Data Derived AADT

4.1.1. Iterations of the Monte Carlo Simulation Program

The Station 150012, located on I-664 east bound, has the most available days (358 days) in the year 2000 and is used as base data in the simulation program. The case with 357 days missing has the largest sample standard deviation and can be selected to determine the required iteration (n). The required accuracy is set as, which means that the average of the error () stay within the range of with the probability of 99.7%. The case with 357 day missing can be equally considered as the case with only one day available for the AADT estimate. The total number of combination is 358 and the corresponding estimate errors can be computed as the absolute value of the percent difference between the daily traffic and the actual AADT, which is calculated based on the 358 daily traffic counts. The standard deviation of the error for the case of missing 357 days is computed as . Then the number of iterations is calculated as follows.

4.1.2. Comparison between ITS and HPMS Data Derived AADT

The total possible combinations of two continuous weekdays that can be selected as coverage counts in the year 2000 are 191, and therefore 191 errors are obtained from the simulation program for coverage counts. These errors are compared with the errors output by simulation program based on CCS 150012. For each missing day case 3000 interactions generate 3000 errors, which are compared with each one of 191 errors obtained from the coverage count simulation. The number of observations that coverage count errors are less than the CCS errors can be used to compute the probability that the coverage count based AADT is better than STC based AADT given a certain number of missing days with STC. The number of missing days and corresponding probability were plotted as illustrated in Figure 4-1.

Figure 4-1 Coverage Counts vs. Continuous Traffic Counts in AADT Estimates

It can be seen that, with the number of missing days increasing, coverage count based AADT is more likely to have smaller errors than ITS data based AADT. From this curve, it can be seen that the probability that the error with coverage count based AADT is less than that with ITS based AADT can be obtained for each missing day case. The probability for coverage count based AADT to be more superior to STC based AADT is 50% when the number of missing days is about 330 for the ITS. The missing day of 330 is considered as the threshold to make a decision on coverage count. Using the same result, Figure 4-2 can be plotted to illustrate the impact of missing days on AADT estimates.

Figure 4-2 Sample Standard Deviation of Errors vs. Missing Day

4.2.1. Traffic Volume Database

The traffic volume data involved in this study are prepared and checked about the data quality to clean out the bad data before being used to calculate AADT. The data of the year 2000 from HRSTC and VDOT Mobility Management Division were collected from the archived system in the Smart Traffic Lab. The ITS traffic data is recorded continuously in 1-minuite interval; while TMS data from continuous traffic counts is in 15-minute interval.

In evaluating the qualities of the two datasets in terms of missing days in a complete one year, the same quality checking rules developed by VDOT Mobility Management Division are used to both datasets. Basically, the rules first determine the quality of each 15-minute traffic volume, and then decide whether each daily traffic volume can be used to estimate AADT. Judgments about the data quality are made based on the thresholds for 15-minute interval data. If they are bad, the 15-minute data is called as a “Hole”. The thresholds used include the minimum threshold and the maximum threshold. The minimum threshold is zero, which indicates that each 15-minute traffic volume has to be greater than zero. The maximum threshold takes the value of 3100 vehicles/lane/hour. The program determine the 15-minut data to be “bad” or as a “hole” if the 15-minute traffic volume exceed these two thresholds, i.e. 15-minute traffic volume < 0, or 15-minute traffic volume >3100/4 ´ number of lanes at the station.

The quality of daily traffic volume is determined based on the number of "holes" on that day. For a complete single day, there are 96 15-minute traffic counts in the datasets, which are also named as 96 data points. Only the days with complete 96 data points passing the quality check are considered as acceptable for the AADT calculation. Note that ITS traffic data are 1-minute traffic count. They are aggregated into 15-minute interval by simply adding up every fifteen 1-minute traffic counts for the purpose of data quality checking. The procedure of data quality checking is summarized as shown in Figure 4-4.

The results of data quality checking in terms of the number of data available for AADT estimate are presented in Table 4-1 for CCS stations and Table A-1 in Appendix A for STC stations. Among the ten CCS locations in the VDOT TMS in the Hampton Roads area, four stations, as shown in Table 4-1, are available for the study. Two CCS on I-664 and another two on I-264 are available with more than 330 days in the year 2000 that can be used to estimate AADT and VMT.

Table 4-1 Continuous Count Stations in the Hampton Roads Area

LINKID	ROUTE	From	To	Available Days in 2000 after quality checking
150022	IS-664 W	SR 135	SR 164	348
150012	IS-664 E	SR 135	SR 164	358
150079	IS-264 W	SR 239 Victory Blvd	SR 337 Portsmouth Blvd	336
150010	IS-264 E	SR 239 Victory Blvd	SR 337 Portsmouth Blvd	322
150037	IS-564 S	SR 406 International Ter Blvd	SR 337 Hampton Blvd	NA
150036	IS-564 N	SR 406 International Ter Blvd	SR 337 Hampton Blvd	NA
150033	IS-464 S	Freeman Avenue	Collector Road	NA
150028	IS-464 N	Freeman Ave	SR 337 Poindexter St	NA
150051	IS-64 W	SR 171 Oyster Point Rd	US 17 J Clyde Morris Blvd	NA
50163	IS-64 E	SR 171 Oyster Point Rd	US 17 J Clyde Morris Blvd	NA

Figure 4-4 Traffic Volume Data Quality Check

4.2.2. Imputation of Missing Information

The 84-cell table, as shown in Table 2-3 is the basis for determining whether imputation is needed. Basically, ITS data can be arranged into an 84-cell table with each cell representing the corresponding MADW. For a complete ITS or HPMS dataset, each cell in the table would have four to five daily traffic data of the same day-of-week in the same month. Due to the data quality problem with missing days of traffic, some cells in the table may contain no daily traffic and be blank. As a result, the 84-cell table may not be complete. If a traffic count with missing days has a complete 84-cell MADW table, then it is still considered as acceptable for AADT estimate without imputation. Otherwise the missing cells need to be imputed.

The first step in imputation is to find an ITS count station in the contiguous segments that have the similar traffic pattern. This station should have the same non-blank cells as the station being imputed. It should also have more non-blank cells, whose corresponding locations in the table of the incomplete station are empty. After identifying the imputation station in the contiguous segment, the seasonal and day-of-week factors are developed from the imputation dataset. The factors are computed by dividing the AADT by the MADW in each cell. The MADW in each non-blank cell of the incomplete station will be multiplied by the corresponding factor from the imputation station to get the adjusted value. The with-imputation-AADT is computed as the average of all the adjusted values from the incomplete station. The imputation is performed using the following formulas:

where the available month in a year of the incomplete station,

the available day in a week of the incomplete station,

the corresponding monthly average days of the week traffic in the

available cell of the incomplete station,

the corresponding seasonal and day-of-week factor in the imputation table, and

the number of the available cells in the table of the incomplete station

The effectiveness of this imputation method is evaluated using simulation model. While running the simulation program, a STC station with the best data quality is selected as base data. Based on this STC station, the number of missing day data can be generated using Monte Carlo method. Also, the “true” AADT can be calculated which can be used to compare the AADT derived after the missing day data are imputed. Another STC station in the contiguous segments is used as imputation dataset to impute the base data with generated missing data. The number of missing days will be plotted against the with-imputation-error and without-imputation-error, respectively, to illustrate the improvement of AADT estimates due to the imputation.

STC station 180 in segment 264-02 is selected as base data for simulation program because it has the most days and cells available in the MADW table. (refer to Table 4-2). It can be seen that the MADW table of STC 180 has five blank cells. Since it is the STC station with the best quality that can be found, the five empty cells will not be considered in the simulation program. STC station 172 in the contiguous segment 264-03 is used as the imputation dataset. Results of the simulation are shown in Figure 4-5.

Table 4-2 84-Cell Table of MADWs for STC 180

	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
January	67205	71192	74902	74346			42575
February	72387	75517	75901	78099	83424	64592	47913
March	72428	74342	75503	78216	84491	65701	47580
April	76527	76134	77641	81225	82560	65102	50243
May	69943	77834	79304	79500	88568	73276	54754
June	80994	79283	82169	79400	90295	75554	57468
July	80128	76185	82067	82448	88427	71879	56613
August	78482	74811		81966	82101	71971	54574
September		75849	77030	79171	82897	65363	45010
October	74032	76389	76098	78597	84095	63684	47310
November	72329	74637	78452	64108		59147	44183
December	32443	68428	75039	74986	79347	57813	40696

Figure 4-5 Errors of AADT Estimates with and without Imputation

Figure 4-5 indicates that, as the number of missing days increases, the imputation technique is becoming more powerful to reduce the errors of AADT estimate due to the missing information in the 84-Cell MADW table.

4.2.3. Computing VMT for the Interstate Highway System in the Hampton Roads Area

The VMT is derived for the study area following the two procedures where ITS data are either considered or not, respectively, using the following formula.

where number of the segments on I-264,

number of the segments on I-64,

number of the segments on I-564,

vehicle miles traveled in the study area,

annual average daily traffic in each direction on each segment, and

segment length in each direction

The results of AADT and VMT estimates on each interstate were summarized in Table 4-3, 4-4, 4-5, 4-6,

Table 4-3 VMT Estimate on I-564

Segment	Station	Imputation	AADT	Segment Length	VMT-STC	Total	Improve %
564-01 S	135	N	22,259	1.84	40,957	139,281	7.69
564-02 S	132	STC 135	38,262	0.8	30,610
564-01 N	139	STC 131	25,611	1.81	46,355
564-02 N	131	N	22,249	0.96	21,359
Segment	Station	Imputation	AADT	Segment Length	VMT-COV	Total
564-01 S	135	No Coverage	22,259	1.84	40,957	128,565
564-02 S	150038		26,007	0.8	20,806
564-01 N	139	No Coverage	25,611	1.81	46,355
564-02 N	50149		21,300	0.96	20,448

Table 4-4 VMT Estimate on I-264

Segment	Station	Imputation	AADT	Segment Length	VMT-STC	Total	Improvement (%)
264-01E	195	N	61,358	1.98	121,488	1,210,277	4.66
264-02E	180	N	71,135	2.34	166,455
264-03E	167	N	91,126	1.14	103,883
264-04E	160	STC 167	95,410	1.15	109,721
264-05E	STC failed		93,796	0.99	92,858
4-01W	194	STC 181	74,833	1.59	118,984
264-02W	181	N	71,608	2.74	196,205
264-03W	166	STC 181	90,836	1.21	109,911
264-04W	STC failed		96,347	1.93	185,949
264-05W	STC failed		96,347	0.05	4817
Segment	Station	Imputation	AADT	Segment Length	VMT-COV	Total
264-01E	50205		56,096	1.98	111,069	1,156,397
264-02E	50201		68,901	2.34	161,228
264-03E	50203		88,927	1.14	101,377
264-04E	50199		93,796	1.15	107,865
264-05E	50217		93,796	0.99	92,858
264-01W	50216		59,851	1.59	95,163
264-02W	50202		69,598	2.74	190,699
264-03W	50204		87,081	1.21	105,368
264-04W	50200		96,347	1.93	185,949
264-05W	781263		96,347	0.05	4,817

Table 4-5 VMT-STC Estimates on I-64

Segment	Station	Imputation	AADT	Segment Length (mi)	VMT-STC	Total
64-01E	31	STC 8	60,059	1.57	94,292	1,617,280
64-02E	24	STC 8	64,633	1.35	87,254
64-03E	22	STC 8	69,462	1.34	93,079
64-04E	39	STC 58	73,227	1.74	127,414
64-05E	58	N	59,161	1.19	70,401
64-06E	71	STC 58	72,131	1.26	90,884
64-07E	76	N	62,452	1	62,452
64-08E	92	STC 76	59,392	1.04	61,768
64-09E	105	STC 120	54,701	1.38	75,487
64-10E	120	N	49,429	0.31	15,322
64-11E	123	N	45,745	1.09	49,861
64-01W	15	N	57,459	1.17	67,227
64-02W	44	STC 6	65,503	1.75	114,631
64-03W	4	STC 6	51,150	0.83	42,454
64-04W	40	STC 6	73,875	2.2	162,525
64-05W	56	Y/ No STC	65,383	1.07	69,960
64-06W	69	STC 85	74,041	1.24	91,811
64-07W	81	STC 85	53,399	0.96	51,262
64-08W	91	STC 85	63,121	0.98	61,858
64-09W	104	Y/ No STC	52,930	0.92	48,695
64-10W	STC failed	Coverage	34,562	1.26	43,548
64-11W	122	Y/ No STC	38,984	0.9	35,085

Table 4-6 VMT-COV Estimates on I-64

Segment	Station	Imputation	AADT	Segment Length (mi)	VMT-COV	Total	Improvement %
64-01E	150,321		55,526	1.57	87,177	1,494,909	7.57
64-02E	950,169		63,173	1.35	85,284
64-03E	50,196		63,173	1.34	84,652
64-04E	50,308		62,056	1.74	107,977
64-05E	50,155		55,122	1.19	65,594
64-06E	50,307		63,728	1.26	80,297
64-07E	50,306		57,173	1	57,173
64-08E	50,305		50,499	1.04	52,518
64-09E	50,165		52,264	1.38	72,123
64-10E	50,392		45,954	0.31	14,245
64-11E	50,304		43,315	1.09	47,213
64-01W	150,071		54,327	1.17	63,562
64-02W	150,070	No Data	65,503	1.75	114,631
64-03W	850,070	No Data	51,150	0.83	42,454
64-04W	150,069		67,550	2.2	148,610
64-05W	150,068		65,609	1.07	70,201
64-06W	150,067		59,321	1.24	73,558
64-07W	150,066		62,697	0.96	60,189
64-08W	150,065		37,960	0.98	37,200
64-09W	150,064		53,741	0.92	49,442
64-10W	150,063		34,562	1.26	43,548
64-11W	150,062		41,390	0.9	37,251

As can be seen from the results of VMT estimates, the improvements of the estimates due to the usage of STC data are 7.69% for I-564, 4.66% for I-264 and 7.57% for I-64. The improvement of VMT estimates for the entire study area is computed as shown in the Table 4-7. It can be seen that VMT estimated with the consideration of ITS data is about 6% more than without considering ITS data.

Table 4-7 VMT Estimate of the Study Area

	I-564	I-264	I-64	Total
VMT-COV	128,565	1,156,397	1,494,909	2,779,871
VMT-STC	139,281	1,210,277	1,617,280	2,966,837
Improve %	7.69	4.66	7.57	6.30

5. Maintenance

5.1. Continuous Traffic Counting Equipments

The traffic sensors of the count station consist of inductive loops and piezoelectric sensors. The collected data can be stored in the equipment on site and then transmitted to a central location in VDOT central office through phone line and modem. The Automatic Data Recorder (ADR), manufactured by Peek Traffic Corporation, is selected as the traffic counter at the CCS locations. It functions as an on-site control center connected with loop and piezoelectric sensors, counting, restoring and transmitting collected traffic data. In the following paragraphs, the equipments of CCS will be described in detailed. The maintenance work for those counting equipments is discussed based on the information in the database and the interview with the contractor.

5.1.1. Components of the Continuous Count Station

A continuous count station mainly consists of in-road loop and piezoelectric sensors, automatic data recorder, and communications (Figure 5-1). Each of these equipments is introduced as follows.

· Inductive Loop Detectors

Inductive loops work by detecting a change of inductance caused by the vehicles running over the loops. In a CCS in TMS, two 6 feet by 6 feet loops are installed in a square saw-cut in each lane and used to collect traffic volume. Saw cut slots for loop wires and lead-in wires are cut in pavement and cleaned with compressed water and dried with natural evaporation before the placement of the loop wires. After having the loop wires placed at the bottom, the saw cut will be filled with loop sealant, which provides weather and chemical resistant waterproof seal. Usually the broken loop sealant leads to the damage of the loop and the corresponding lane stops recording traffic.

· Piezoelectric Sensors

Between the two loops in each lane, there is a piezoelectric sensor used for the purpose of classifying vehicles. The physical touch between the vehicle axles and piezoelectric sensor is converted into electronic signal, which is recorded by the ADR in the control cabinet. The installation of piezoelectric sensors is similar to that of loop sensors except that a different type of sealant is used to fill the saw cut of Piezo.

· Traffic Counter

An ADR is held in a weatherproof cabinet, also known as the control cabinet. The ADR works together with the loop detectors and piezoelectric sensors to count and classify traffic. Traffic data collected can be stored internally in the equipment and transferred to the database in the VDOT central office.

· Modem and Telephone Line

The traffic data stored in the ADR are transferred to the VDOT TMS central office through the modem and phone line. The modem is placed in the cabinet and relies on the phone line voltage for power. Their malfunctions will terminate the communication and transmission of traffic data with the database in the central office. However, the collected data can be temporarily stored in the equipment on site and retrieved by the central office after the problem is fixed.

Figure 5-1 Typical Layout of the Loop and Piezoelectric Sensors

5.1.2. Maintenance Work

Everyday VDOT TMS checks each one of these count stations to see if they are working properly. When VDOT TMS technicians identify the problems with the traffic counting equipments, they notify the contractor through service calls. After receiving the reports about equipment malfunctions, the contractor sends their crews to check the equipment and fix the problems on site. The equipment problems could be those on loop detectors, piezoelectric sensors, communications (phone line and modem), and count equipment in the cabinet. There is no planned or scheduled maintenance by the contractor. “Fix what’s broken” is how the contractor does the maintenance work. The detailed information of the maintenance activities are recorded in forms and delivered to VDOT TMS, where the information is put into a maintenance database. Note that VDOT TMS does have inspections scheduled for each location on the anniversary dates of the installation. The equipment problems identified during the inspection are also notified to the contractor for maintenance.

Different system components are treated in different way due to the distinct nature of the problem each component may have. Problems with loop and piezoelectric sensors were always solved by adjustment or replacement of the sensors. Communication problems happened when the modem did not answer the request or the phone line was busy. They terminated the communication and data transmitting between the on site traffic counter and TMS central office. In this case, the collected traffic data were stored in ADR and transmitted to TMS after resetting the modem or repairing the modem and phone line. Numerous factors could cause the ADR problems, which was solved by changing the battery, rebooting the system, or replacing with new equipment.

The performance of detector sensors is influenced by various factors including truck volume, pavement type and conditions, installation and weather. The broken pavement surface and sealant material make the sensors exposed to traffic and thus damaged by the vehicles. Due to the chemical reaction between the sealant and the pavement material, the loop sealant causes the erosion of pavement at the edge of the saw cut, which leads to the damage of loop and piezoelectric sensors. The quality of the contractor’s work will also affect equipments’ performance. The slots for loop wires are marked at the center of travel lane and then cut using diamond power saw. The saw cut is cleaned by high-pressure water and dried with compressed air and natural evaporation. Heat is not permitted by VDOT TMS to be used to dry the saw cut before the placement of sensor wires. The moisture left in saw cut slots would cause the sensors’ damage.

Figure 5-2 Control Cabinet with wooden Post and Solar Panel

5.2. Modeling for Life Durations of Loops

TMS VDOT recorded maintenance activities in a database, where a schedule form was created for each CCS to include the description of equipment problems and maintenance activities. The life cycle of the loop detectors can be defined and derived based on the maintenance schedule forms.

Loop failures could be caused by numerous factors such as traffic volume, pavement type and conditions, sealant materials, construction and maintenance operations, type of loop wire, contractor work quality, and weather conditions. The maintenance database involved in this study was designed to be an operational database and not a research quality database where every variable affecting the performance of equipments could be captured. The variables such as pavement conditions, sealant materials, type of loop wire, contractor wok quality cannot be made available from the database. Therefore this study only focuses on four groups of classified traffic volume and the investigation of the relationship between the loops life cycle and these traffic volume using linear regression method.

The life cycle of loop detectors consists of life and failure durations. They both can be derived from the schedule form in the maintenance database, where the maintenance work for each station was recorded. Because failure duration is not influenced by the same set of factors as those for life duration, this study is only focused on life duration. The life duration is defined as the time period during which a loop detector properly functions after the last repair is finished. It is computed as the number of days between the date when a problem is fixed and the date when the next failure occurs.

VDOT collects classified traffic volume based on the FHWA vehicle classes (see Appendix C) and aggregates vehicle classes into four major configuration groups as shown in Table 5-1. Since CCS cannot count the motorcycle accurately, the class 1(motorcycle) and class 2 (passenger car) are not distinguished by VDOT.

Table 5-1 Vehicle Classifications and Major Configuration Groups

Class	Classification	Major Configuration Group
1	Motorcycles	automobiles and other four-tire vehicles
2	Passenger Cars
3	Other Two-Axle, Four-Tire Single Unit Vehicles
4	Buses	other single-unit vehicle
5	Two-Axle, Six Tire, Single Unit Trucks
6	Three-Axle, Single Unit Trucks
7	Four or More Axle Single Unit Trucks
8	Four or Less Axle Single Trailer Trucks	single-trailer combination
9	Five Axle Single Trailer Trucks
10	Six or More Axle Single Trailer Trucks
11	Five or Less Axle Multi-Trailer Trucks	double-trailer combination
12	Six or Less Axle Multi-Trailer Trucks
13	Seven or More Axle Multi-Trailer Trucks

Linear regression model is used to investigate the relationship between the life duration and re-classified traffic volume. Since the maintenance database has very little information about the detector sensors in lane 3 and lane 4, this study only considers deriving life duration for detectors in lane 1 and lane 2. The response variable Y is the life cycle of the loop detectors in lane one (Loop1, 2) and lane two (Loop3, 4) respectively. The possible predictor variables are automobiles and other four-tire vehicles (X1), other single-unit vehicle (X2), single-trailer combination (X3), and double-trailer combination (X4).

A correlation matrix (refer to Table 5-2) shows the coefficients of simple correlation between Y and each of the X variables, as well as the coefficients of simple correlation among the X variables. From the correlation matrix, it can be seen that predictor variable X3 shows the highest degree of linear association with X4. The predictor X1 is also highly correlated with X2 and the correlation coefficient equaled 0.547. Among the four predictor variables, X3 shows the highest degree of association with Y and X1 the lowest.

Table 5-2 Correlation Matrix for Loop 1

	Life Cycle Y	X1	X2	X3	X4
Life Cycle Y	1.000
X1	0.121	1.000
X2	-0.273	0.547	1.000
X3	-0.435	-0.083	0.430	1.000
X4	-0.322	-0.093	0.237	0.900	1.000

A linear regression model based on all predictor variables is fitted for loops in lane 1, which can be expressed as:

where are coefficients. The results are shown in Table 5-3.

Table 5-3 Regression of Y on X1, X2, X3, and X4 (Loop 1)

	Coefficients	Standard Error	t Stat	R Square	# of Observations
Intercept	739.2886	104.0656	7.1041	0.24	117
X1	0.0254	0.0130	1.9580
X2	-0.4732	0.2864	-1.6523
X3	-0.1668	0.0805	-2.0730
X4	0.6527	0.6753	0.9665

Each value of t statistics in Table 5-2 indicates whether the term can be dropped from the above multiple regression model.

The decision rule for the testing is:

If conclude

where p = number of parameters in the regression modal that need to be estimated (p=5)

For and n=117, t (0.975; 112) = 1.98

Table 5-3 indicates that t statistics of predictor variable X3 is greater than 1.98, which means that the linear relationship between Y and X3 is statistically significant.

It is expected that the life duration of a loop decrease as the traffic volume increases. The reason is that pavement is easily damaged by high volume of heavy vehicles (trailer combination) and thus causes the detector sensor to be destroyed by the vehicle running over it.

The stepwise method is conducted by the following steps to select the “best” subsets of predictor variables based on the F^* statistic.

Step 1: Fit a simple linear regression model for each of the four X variables in this study. The predetermined F* value was which is = 3.92 in Step 1. From the linear regression results of Y on each of the four X variables, the F* is obtained as shown in Table 5-4, which indicates that X3 is the variable entering the model in the first step.

Table 5-4 F* for the Step 1 of Stepwise Method (Loop 1)

	MSR	MSE	F*
X1	256586.9	149130.786	1.7205493
X2	1298009	140074.942	9.2665322
X3	3296232	122699.09	26.864355
X4	1807389	135645.548	13.324353

Step 2: Fit the regression models with two X variables, which include X3 and another one from the rest of three X variables. From the linear regression results, the F* is obtained as shown in Table 5-5, which indicated that X4 is the variable with the highest F* value. Since the F* value of X4 is less than the predetermined F*, the stepwise method stops here. X3 is identified as the “best” subset of X variables.

Table 5-5 F* for the Step 2 of Stepwise Method (Loop 1)

	MSE (X1, X3)	MSR (X1 I X3)	F*
X1	122653.9594	127844.021	1.042315
	MSE (X2, X3)	MSR (X2 I X3)	F*
X2	122392.8535	157610.094	1.287739
	MSE (X4, X3)	MSR (X4 I X3)	F*
X4	119871.4688	445047.946	3.71271

The regression model of Y on predictor variable X3 is obtained and shown in Table 5-6.

Table 5-6 Linear Regression of Y on X3 (Loop 1)

	Coefficients	Standard Error	t Stat	R Square
Intercept	785.1486	63.25845	12.41176	0.189366
X3	-0.14366	0.027716	-5.18308	0.189366

The life duration of loops in lane 2 (loop 3 and 4) is studied following the same manner. The correlation matrix (Table 5-7) indicates that all X variables are highly correlated. Therefore the multi-collinearity effect cannot be ignored. Among the four predictor variables, X3 shows the highest degree of linear association with Y and X1 the lowest. The stepwise method selects X3 as the “best “subset of X variables. The result of linear regression is shown in Table 5-8, Table 5-9 and Table 5-10.

Table 5-7 Correlation Matrixes for Loop 3

	Life Duration Y	X1	X2	X3	X4
Life Duration Y	1
X1	-0.11310	1
X2	-0.27533	0.82539	1
X3	-0.29592	0.50697	0.68121	1
X4	-0.22049	0.41393	0.47471	0.77217	1

Table 5-8 F* for the Step 1 of Stepwise Method (Loop 3)

	MSR	MSE	F*
X1	207017.2	171804.1	1.20496
X2	1226945	160837.2	7.628491
X3	1417247	158790.9	8.925239
X4	786840.3	165569.5	4.752327

Table 5-9 F* for the Step 2 of Stepwise Method (Loop 3)

	MSE (X1, X3)	MSR (X1 I X3)	F*
X1	160194.0667	29701.64507	0.18541
	MSE (X2, X3)	MSR (X2 I X3)	F*
X2	158731.4834	164259.3152	1.034825
	MSE (X4, X3)	MSR (X4 I X3)	F*
X4	160488.977	2569.898294	0.016013

Table 5-10 Linear Regression of Y on X3

	Coefficients	Standard Error	t Stat	R Square
Intercept	748.8402	63.43249	11.80531	0.087567
X3	-0.17221	0.057643	-2.98751	0.087567

The results obtained here illustrate a negative relationship between the loop life duration and single-trailer combination traffic volume, which represents a group of heavy vehicles with large amount of volume detected on interstate highway in the state of Virginia. The model can predict what the life duration of the loop detectors stalled on a road section will be after knowing the heavy vehicle traffic volume collected on that road. This information can be used in the budget planning process and help determine the optimal maintenance policy.

6. Conclusions and Future Research

6.1. Conclusions

This study investigates the method to combine HPMS and ITS data to calculate VMT and establishes a relationship between life duration of loops and traffic volume. In developing the method to estimate VMT combining HPMS and ITS data, the impact of missing data on VMT estimation is quantified using the Monte Carlo simulation method. A critical number of missing days for ITS data is determined through comparing the AADTs that can be derived based on coverage counts and ITS traffic counts. Based on this critical value, a decision can be made as to whether or not the corresponding ITS traffic count can provide VMT estimate with less error than the coverage count. VMT values are computed for an area in the Hampton Road region with and without consideration of ITS data respectively. The percentage difference between these two values is 6.3%, which can be considered as the improvement brought by the usage of ITS data. Based on the investigation, it can be concluded that the Monte Carlo method is effective in quantifying the impact of missing data on VMT estimation. In addition, it can be seen that incorporating ITS data is important because it improves the accuracy of VMT estimation. Such improvements in accuracy are important for the application of VMT for various purposes such as pavement management, air quality analysis and financial investments.

Linear regression model is applied to investigate the relationship between the life duration of loops and classifications of traffic volumes. The results indicate a negative relationship between single-trailer combination traffic volume and life durations of loops. The developed model is useful when maintenance schedule and contracting decisions are made for a future year where traffic volume changes correspondingly.

6.2. Future Study Needs

The following needs are identified for study in future.

First, there is a need to investigate the impact of traffic patterns on the relationship between the number of missing day data and the likelihood that ITS data-based AADT is better than coverage count based AADT. This study was only based on one station that the data quality impact on AADT was investigated. As perceived, traffic pattern in one station can be described by the seasonal and week-day variation, and different patterns can be observed for different stations. Thus, the impact of data quality on AADT calculation basing on one station only cannot be viewed sufficient and is suggested for expanded investigation.

Second, it is necessary to develop a model for life duration of other system components such as the piezo, the ADR and the communications. Because both loops and piezo are buried in the pavement, their life may be influenced by similar factors. The ADR and communications are located off the road and thus will not be influenced by the factors related the pavement and traffic. Thus, different approach might need to be taken for modeling their life duration.

Third, linear regression models are limited by their modeling assumptions, which might not be valid in the case of deterioration of loop detector system. One of the major assumptions for linear regression model is that the probability distribution of the random error term is normal. From the fitted linear models (Table 5-6), the residual can be obtained and its histogram is plotted as shown in Figure 6-1. The histogram of residual suggests a departure from the normal distribution. Therefore advanced duration model, such as Weibull distribution, is suggested to further investigate the modeling of detectors' life durations and traffic volume. The duration model can provide a probability curve associated with a given number of traffic volume. From the curve, the life duration with the highest probability to happen is determined, based on which the preventive maintenance work can be scheduled.

Figure 6-1 Histogram of Residual for the Fitted Model

As mentioned above, the maintenance database in this study is not a research quality database and cannot capture all factors that affect the performance of the equipments. The life duration data is derived through reading each maintenance record in the schedule form. To which category of equipment problems a record can be put
into is based on the personal understanding of the maintenance record. In addition, a certain number of records cannot be clearly understood as to which equipment was being repaired. Therefore the duration derived from the maintenance database is not reliable.
A maintenance database, which includes all factors affecting the performance of traffic counting equipments, is needed for the further study.

Fifth, efforts need to be taken to develop maintenance policies by using the modeling results in this study. One practice in maintaining the loop system is to inspect the loops’ conditions because the in-house data quality checking cannot detect all the data problems and thus identify the malfunction in loops. By knowing the probability of failures in the loop system, the inspection can be scheduled in a more predictable manner.

References

1. U.S Department of Transportation, Federal Highway Administration, and Office of

Highway Policy Information, “Traffic Monitoring Guide”, 2001

http://www.fhwa.dot.gov/ohim/tmguide/

2. Washington State Department of Transportation, “Short Count Factoring Guide”, 2003

3. U.S Department of Transportation, “HPMS Field Manual”, 2000

4. Federal Highway Administration, “About Highway Performance Monitoring System (HPMS)”, 2002

http://www.fhwa.dot.gov/policy/ohpi/hpms/abouthpms.htm

5. AASHTO, “AASHTO Guidelines for Traffic Data Programs”, 1992

6. Fang Zhao and Soon Chung, “Estimation of Annual Daily Traffic in a Florida County Using GIS and Regression”, TRB 2001 Annual Meeting Paper, Washington, 2001

7. McCord, Goel, et al. “Improving AADT and VDT Estimation with High-resolution Satellite Imagery”, the Ohio State University, 2002

8. Hampton Toads Smart Traffic Center, “STC Strategic Business Plan 2001”, 2000

9. Neter, Kutner, Nachtsheim, and Wasserman. “Applied Linear Regression Model”, Third Edition

10. Jesse C. Arnold and J.S. Milton, “Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences”, Fourth Edition

11. T.W. Anderson and Jeremy D. Finn, “The New Statistical Analysis of Data”,1996

12. “Monte Carlo simulation in MS Excel”, 2003

http://www.projectsmart.co.uk/docs/monte_carlo_simulation.pdf

13. “Introduction to Monte Carlo Methods”, Access time: December 2003

http://www.chem.unl.edu/zeng/joy/mclab/mcintro.html

14. “Random Sampling and Sample Statistics in Excel”, Access time: December 2003

http://www.ms.uky.edu/~schadler/Comp1%20Handout%20ADS.doc

15. Cambridge Systematics, Inc. “Traffic Monitoring Systems Development Study”, Virginia Department of Transportation, 1994

16. Digital Traffic Systems, Inc., “Field Installation and Procedure Manual for Automatic Vehicle Classifications Sites”, Version 8.1, 2003

17. Peek Traffic, Inc., “User Manual for the Automatic Data Recorder”

Appendix A Traffic Volume Data from STC Stations

Table A-1 STC Stations in the Hampton Roads Area along I-264

Station_id	Direction	Available Days in 2000
195	EBL	197
185	EBL	163
182	EBL	203
180	EBL	211
176	EBL	163
172	EBL	209
167	EBL	208
165	EBL	95
160	EBL	200
157	EBL	NA
154	EBL	80
142	EBL	NA
140	EBL	NA
34	EBL	211
194	WBL	137
186	WBL	206
184	WBL	163
183	WBL	194
181	WBL	206
179	WBL	206
170	WBL	203
166	WBL	163
164	WBL	NA
159	WBL	118
156	WBL	NA
153	WBL	NA
148	WBL	NA
201	WBL	NA
35	WBL	NA

Table A-2 STC Stations in the Hampton Roads Area along I-64

Sation_id	Direction	Available Days in 2000
19	EBL	72
8	EBL	215
3	EBL	NA
22	EBL	162
68	EBL	11
24	EBL	91
26	EBL	82
31	EBL	55
47	EBL	112
43	EBL	NA
39	EBL	117
51	EBL	152
58	EBL	207
60	EBL	62
67	EBL	158
71	EBL	152
76	EBL	213
83	EBL	61
87	EBL	167
92	EBL	127
98	EBL	151
105	EBL	119
120	EBL	214
123	EBL	216
126	EBL	30
17	WBL	160
6	WBL	215
4	WBL	130
21	WBL	16
44	WBL	NA
23	WBL	14
30	WBL	53
15	WBL	193
46	WBL	NA
40	WBL	57
36	WBL	NA
54	WBL	176
56	WBL	52
62	WBL	106
65	WBL	158
69	WBL	110
80	WBL	112
81	WBL	NA
85	WBL	213
91	WBL	118
96	WBL	213
104	WBL	43
117	WBL	118
122	WBL	174
125	WBL	NA

Table A-3 STC Stations in the Hampton Roads Area along I-564

Station_id	Direction	Available Days in 2000
132	SBL	NA
135	SBL	202
138	NBL	118
139	NBL	126
131	NBL	214

Appendix B STC stations in the Hampton Roads Area

Table B-1 Number of STC Stations and Coverage Count Stations in Each Segment

Roadway	Segment	# of STC Station	# of Coverage Count Stations
I-64	1	2	2
	2	6	2
	3	6	2
	4	10	2
	5	4	2
	6	4	2
	7	5	2
	8	4	2
	9	3	2
	10	2	2
	11	4	2
I-264	1	2	2
	2	9	2
	3	6	2
	4	6	2
	5	7	2
I-564	1	3	2
	2	4	2

Table B-2 Lengths of Segments along I-64, I-264, and I-564

Roadway	Segment	Direction	Segment Length (mi)
I-64	1	East	1.57
		West	1.17
	2	East	1.35
		West	1.75
	3	East	1.34
		West	0.83
	4	East	1.74
		West	2.2
	5	East	1.19
		West	1.07
	6	East	1.26
		West	1.24
	7	East	1
		West	0.96
	8	East	1.04
		West	0.98
	9	East	1.38
		West	0.92
	10	East	0.31
		West	1.26
	11	East	1.09
		West	0.9
I-264	1	East	1.98
		West	1.59
	2	East	2.34
		West	2.74
	3	East	1.14
		West	1.21
	4	East	1.15
		West	1.93
	5	East	0.99
		West	0.05
I-564	1	North	1.81
		South	1.84
	2	North	0.96
		South	0.8

Appendix C Maintenance Data Collection

Table C-1 summarized the maintenance data and information that can be obtained from each maintenance form in the maintenance database. The maintenance forms are shown From Figure C-1 to Figure C-9.

Table C-1 Maintenance Form and Maintenance Data

Figure	Maintenance Data
C-1	physical location
	the date of installation
	the date of acceptance for use
C-2	repair cost
C-3	repair log
C-4	piezo types
	loop and loop sealant type
C-5	information about the inspection
C-6	the date when the problem was found
	the date when the problem was fixed
	the description of the problem
C-7	the date for the replace or reinstallation of sensors
C-8	inspection results
C-9	information about the equipment calibration