Scholarly article on topic 'Evaluation of performance measures for rural two-lane roads in Egypt'

Evaluation of performance measures for rural two-lane roads in Egypt Academic research paper on "Agriculture, forestry, and fisheries"

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{"Two-lane highways" / "Performance measures" / "Platooning variables" / "Traffic flow" / "Follower density"}

Abstract of research paper on Agriculture, forestry, and fisheries, author of scientific article — Ibrahim Hassan Hashim, Talaat Ali Abdel-Wahed

Abstract This paper presents an empirical evaluation of the relationship between operational performance and platooning phenomenon in rural two-lane roads in Egypt. Seven performance measures and three platooning variables were defined and calculated for eight study sites using traffic data from roads in Minoufiya governorate, Egypt. Using graphical and statistical analyses, the associations between the performance measures and the platooning variables were examined. The results showed that the follower density performance measure was found to have the strongest correlations to platooning variables. Among the platooning variables investigated, traffic flow in the direction of travel has the highest correlations with performance measures. The study demonstrated that the relationship between follower density and traffic flow is better described by a quadratic form. Finally, threshold values for different levels-of-service were proposed. This might help traffic engineers, in Egypt, to evaluate operational performance using criteria that reflect the local conditions of the area under study.

Academic research paper on topic "Evaluation of performance measures for rural two-lane roads in Egypt"

Alexandria Engineering Journal (2011) 50, 245-255

FACULTY OF ENGINEERING ALEXANDRIA UNIVERSITY

Alexandria University Alexandria Engineering Journal

www.elsevier.com/locate/aej www.sciencedirect.com

ORIGINAL ARTICLE

Evaluation of performance measures for rural two-lane roads in Egypt

Ibrahim Hassan Hashim a *, Talaat Ali Abdel-Wahed b1

a Department of Civil Engineering, Faculty of Engineering, Minoufiya University, Shebin El-Kom, Egypt b Department of Civil Engineering, Faculty of Engineering, Sohag University, Sohag, Egypt

Received 8 June 2011; accepted 14 August 2011 Available online 28 September 2011

KEYWORDS

Two-lane highways; Performance measures; Platooning variables; Traffic flow; Follower density

Abstract This paper presents an empirical evaluation of the relationship between operational performance and platooning phenomenon in rural two-lane roads in Egypt. Seven performance measures and three platooning variables were defined and calculated for eight study sites using traffic data from roads in Minoufiya governorate, Egypt. Using graphical and statistical analyses, the associations between the performance measures and the platooning variables were examined. The results showed that the follower density performance measure was found to have the strongest correlations to platooning variables. Among the platooning variables investigated, traffic flow in the direction of travel has the highest correlations with performance measures. The study demonstrated that the relationship between follower density and traffic flow is better described by a quadratic form. Finally, threshold values for different levels-of-service were proposed. This might help traffic engineers, in Egypt, to evaluate operational performance using criteria that reflect the local conditions of the area under study.

© 2011 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V.

All rights reserved.

* Corresponding author. Tel.: +20 104872929.

E-mail addresses: hashim1612@hotmail.com (I.H. Hashim), tala at_444@yahoo.com (T.A. Abdel_Wahed). 1 Tel.: +20 124445576.

1110-0168 © 2011 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. All rights reserved.

1. Introduction

Rural two-lane highways are an important type of uninterrupted flow facilities in which there is no obstructions to the movement of vehicles along the road. Such facilities represent the majority of the highway system in Egypt, as they constitute about 75% of all paved rural highways. Measuring traffic performance at these facilities is a complex issue due to their unique characteristics, since a single lane is provided for travel in each direction resulting in higher level of interaction between vehicles traveling not only in the same but also in opposing directions. Traffic engineers usually search for methods to define the traffic capacity and quality of traffic flow for different highway facilities. Highway Capacity Manual (HCM) uses

Peer review under responsibility of Faculty of Engineering, Alexandria University.

doi:10.1016/j.aej.2011.08.001

Percent-Time-Spent-Following (PTSF) as the primary level of service (LOS) measure for two-lane highways [1]. The PTSF is defined as ''the average percentage of travel time that vehicles must travel in platoons behind slower vehicles because of an inability to pass'' [1].

The HCM procedures use either equations or field measurements to estimate PTSF. As it is impractical to measure the PTSF in the field, the HCM proposes using a surrogate measure, percent followers (i.e. the percentage of vehicles with headways less than three seconds (3-s rule)). Studies revealed that the PTSF equations produce results that are inconsistent with the 3-s rule [2-5]. Due such limitation in PTSF measure, alternative performance measures were introduced by many authors in many countries to fit their local conditions. Examples of such alternative measures include follower density, average travel speed of passenger cars, platoon percentage (the percentage of headways less than three seconds), density, percent of vehicle impeded (PI), and others [4-9].

The main aim of this paper is to evaluate several performance measures for estimating the traffic operational characteristics on two-lane highways using data from rural roads in Minoufiya governorate, Egypt. The performance measures include average travel speed, average travel speed ofpassenger cars, average travel speed as a percentage of free-flow speed, average travel speed of passenger cars as a percentage of free-flow speed of passenger cars, percent followers, follower density, and percentage of vehicle impeded. The evaluation was carried out by examining the level of association between the performance measures and pla-tooning phenomenon. Platooning is an important phenomenon that has crucial implications on traffic operation and quality of service on two-lane highways. The amount of platooning on two-lane highways is more likely to be a function of traffic flow in the direction of travel, opposing traffic flow, percentage of heavy vehicles, percent no-passing zones, standard deviation of free flow speeds and other variables. The paper uses three pla-tooning variables; flow rate in the direction of travel, opposing flow rate and percentage of heavy vehicle. The associations between these three platooning variables and performance measures were examined graphically, and statistically using correlation and regression analyses. Furthermore, threshold values for different levels-of-service were proposed, based on the best performance measure found.

2. Background studies

The primary level of service (LOS) measure for two-lane highways, Percent-Time-Spent-Following (PTSF), was first introduced in 1985 Highway Capacity Manual and was called then Percent-Time-Delayed (PTD) [10]. Although, PTSF considers a very appropriate performance measure as it well relates to the platooning phenomenon, a major determinant of performance on two-lane highways, it cannot be easily estimated in the field. Therefore, the HCM 2000 [1] suggests estimating the PTSF as the percentage of vehicles traveling with headways less than three seconds (the 3-s rule). Few recent studies investigated the relationship between the 3-s rule measure and the HCM PTSF estimates using field data. Luttinen [2] at the Helsinki University of Technology collected data from 20 two-lane highway sites in Finland. The data were used to create a model to estimate the percent headways less than

3 s (or PTSF) based on flow rates in the observed and opposing directions. Dixon et al. [3] at the University of Idaho gathered data at five points along Highway 12 in Idaho. Field values of the 3-s rule were compared to PTSF estimates computed using HCM procedures. Van As, with the South African National Roads Agency, collected data from 25 two-lane highways [4]. The comparison between HCM PTSF model and percent followers measured in the field was done. Al-Kaisy and Durbin [5] at Montana State University collected data from six two-lane highway sites in Montana and compared the field measured percent followers to the PTSF calculated using the HCM directional analysis. All such studies reveled that there are high discrepancies between the HCM PTSF and HCM surrogate measure estimates using field data.

Therefore other studies proposed the use of performance measures other than those used by the HCM. Density was used as the service measure for two-lane highways in German highway capacity manual. It was calculated as flow divided by the average travel speed of passenger cars, as reported by Brilon and Weiser [6]. Brilon and Weiser reported that the PTSF had never been considered as a substantial measure of effectiveness in Germany as it does not directly express the degree of efficiency of traffic operation. Van As [4] introduced follower density (number of vehicles with short headways per unit length) as a new service measure for two-lane highways in South Africa. Among other performance measures considered by the same project are: the follower flow (number of vehicles with short headways per hour), percent followers (percentage of vehicles with short headways), percent speed reduction due to traffic, total queuing delay, and traffic density. Catbagan and Nakamura [7] recommended also follower density as a performance measure for two-lane expressways in Japan. In this study, density was calculated as the flow rate divided by the average spot speed at the detector location. Catbagan and Nakamura [8] recommended to develop a more logical and realistic method of identifying followers. So, a more logical definition of a follower can be stated as ''a vehicle traveling below its desired speed due to the presence of a relatively slower lead vehicle''. Al-Kaisy and Freedman [9] suggested Percent Impeded (PI) as a new performance measure for two-lane highways. This measure is based on segregating the impeded vehicles in a platoon from the ''happy to follow'' vehicles. ''Happy to follow'' refers to vehicles that are in platoon yet are driving at their desired speed; they do not wish to be driving faster.

3. Performance measures examined

The following seven performance measures were investigated in the paper.

• Average Travel Speed (ATS): In every version of the HCM, speed has been used as a performance measure for two-lane highways. Average Travel Speed (ATS) is a good choice for a performance measure as it relates well to road user perceptions of the quality of traffic flow.

• Average Travel Speed of Passenger Cars (ATSPC): Passenger car speeds tend to be more sensitive to increase in congestion than heavy vehicle speeds [11]. However, this measure does not have a reference point for across-site comparisons [12]. Same limitation is also valid in the case of ATS.

• Average Travel Speed as a Percentage of Free-Flow Speed (ATS/FFS): It indicates the average speed reduction due to interaction with other vehicles. Therefore, an increase in vehicle interaction will result in a lower percentage of ATS/FFS and a lower level of service. This performance measure addresses the reference point issue related to ATS and ATSPC. The free-flow speed could differ greatly from site-to-site, thus using free-flow speed as a point of reference could allow fair across-site comparisons [12].

• ATSPC as a Percentage of Free-Flow Speed of Passenger Cars (ATSPC/FFSPC): This measure is similar to the previous measure except that only cars are considered in the speed measurements. This measure is likely to be more sensitive to increases in congestion than ATS/FFS as speeds of passenger car are more affected by high traffic volumes than speeds of heavy vehicle [6].

• Percent Followers (PF): Percent followers represent the percentage of vehicles with short headways in the traffic stream. This performance measure can easily be measured in the field by using a headway cut-off value of 3 s, as recommended by the HCM [1].

The main disadvantage of using percent followers as a sole performance measure is that it does not accurately reflect the effect of traffic level, which is an important performance criterion in the HCM quality of service concept. Theoretically, low traffic levels could still have high percent followers if speed variation is relatively high and passing opportunities are limited. Therefore, the use of percent followers alone could be misleading [13].

• Follower Density (FD): Follower density is the number of followers in a directional traffic stream over a unit length, typically one kilometer or one mile. The first use of this measure was reported by Van As [4] in South Africa. The major advantages of using follower density are accounting for both the freedom to maneuver and the degree of congestion, through the percent followers and the density, respectively. Furthermore, it is compatible with density that is the service measure for basic freeway sections and multi-lane highways [1]. Follower Density (FD) is calculated from the following equations:

Density (D) = flow rate (Q)/average travel speed (ATS) (1)

Follower Density (FD)= density (D)x Percent Followers (PF) (2)

Headway data could be used to estimate Pp using headway platoon definition. According to this platoon definition, vehicles in a platoon primarily involve those that are impeded by slower vehicles ahead as well as those that travel very close to their desired speeds (happy-to-follow). Platoon leaders are used here as a representative sample of slow-moving vehicles to estimate the average speed of slow-moving vehicles. Distribution of desired speeds can be established using speed data of vehicle traveling under free conditions including of course platoon leaders. The average speed of slow-moving vehicles along with the distribution of desired speeds can then be used to determine the percentage of vehicles with desired speeds higher than the average speed of slow-moving vehicles. This percentage is then used to derive the probability Pi. This approach is based on the assumption that the distribution of desired speeds for vehicles in platoons is the same as that for vehicles outside platoons [9]. Fig. 1 shows the probability Pt assuming a normal distribution for desired speeds.

4. Data collection and preparation

The scope of this research focuses on the intercity rural two-lane roads in Egypt. Therefore the analysis of this paper used eight sites from two-lane roads in Minoufiya governorate. The selection of the study sites encompasses all rural two-lane roads inside Minoufiya governorate. All roads have a posted speed limit of 60 km/h. The chosen sites are located on straight sections with level terrain to avoid the effect of the longitudinal gradient, and far from the influence of intersections, driveways and horizontal curves. Also, the chosen sites have relatively similar geometry characteristics (pavement and shoulders widths). The average pavement width is about 7 m and the average shoulder width is about 1.5 m.

Roadside automatic traffic counters were used to collect the traffic and speed data used in this paper. Speed and traffic data collection were carried out in working days, during daylight hours. During all data collection periods, the weather was clear and the pavement was dry and in a good condition. Data collection duration, vehicular counts, overall percentage of heavy vehicles, maximum flow rates per direction and maximum directional split ratio at the study sites during the data collection durations are provided in Table 1.

Data set at each direction of travel on each site was divided into 5-min intervals. In each interval, vehicle counts were multiplied by twelve to convert them into flow rates. The average

• Percent Impeded (PI): This measure was introduced in 2008 by Al-Kaisy and Durbin [14] with the name of Percent Following. In 2010 Al-Kaisy and Freedman [9] renamed this measure to percent of vehicle impeded in the traffic stream (PI). PI can be calculated from the following equation:

PI = Pp x Pi (3)

where Pp is the probability of a vehicle being part of a vehicular platoon using time headway definition of platoon (certain cut-off value (usually 3-s)) and Pi is the probability of a vehicle being impeded so traveling at a speed that is less than the desired speed.

Average speed of slower vehicles

I / 1/

Desired speed

Figure 1 Theoretical speed distributions with probability pi representation [9].

Table 1 Data collection durations and vehicular counts, percentage of heavy vehicles, directional split ratio and maximum directional

flow rate.

Site Duration of data Traffic counts in both Overall percentage of Max . directional 5- Maximum

No. collection (hours) directions (vehicles) heavy vehicles (%) min. flow rate (vph) directional split

ratio (%)

1 5.00 1670 5.2 348 57

2 8.00 2916 4.1 360 52

3 8.50 3051 4.3 372 52

4 8.75 3437 4.4 420 52

5 8.00 7430 3.3 972 51

6 8.00 3572 3.0 432 54

7 8.00 4005 2.0 564 53

8 8.25 4139 2.2 588 53

travel speed was equal to the output mean speed. The average travel speed of passenger car was obtained when all classes were excluded except passenger cars. The free flow speed was calculated by averaging the speed of all vehicles traveling with headways greater than eight seconds, according to Al-Kaisy and Karjala [12]. The measure of percent followers was calculated using the HCM procedure for estimating the PTSF surrogate measure, i.e. the percentage of vehicles traveling with headways less than three seconds [1]. The follower density was obtained based on Eqs. (1) and (2). Percent impeded was calculated according to Eq. (3).

Fig. 2 presents an example of the main relationships of traffic flow parameters at one of the study sites for one direction; other sites show relatively similar patterns. The figure shows the three relationships (Average travel speed (ATS)-Density), (Flow Rate-ATS) and (Flow Rate-Density). The relationships show that the traffic stream is in un-congested state, as these roads usually carry relatively low traffic volumes. From these relationships, it is clear that the variation of ATS with traffic volume is relatively low. However, the variation of density with traffic volume is much clearer and proportional.

5. Relationships between performance measures and platooning variables

The relationships between the examined seven performance measures and traffic flow in the same direction of travel were plotted. Example of these relationships is presented in Fig. 3, for one of the study sites, for one direction of travel. Other sites showed relatively similar patterns.

Several issues can be noticed by observing the plots presented in Fig. 3:

• For the relationship between flow rate and the two average travel speeds (ATS, ATSPC), the general hypothesis is as flow increases the average speed will decrease. These relationships are consistent with the general expectation.

• For the relationship between traffic flow and average travel speed as a percent of free-flow speed for all vehicles (ATS/ FFS) as well as for passenger cars (ATSPC/FFSPC), the hypothesis is as flow increases the speed ratios decrease. It is obvious that the relationship is consistent with the general expectation.

2 3 4 Density (veh/km)

100 200 300 5-min. Flow Rate (vph)

c 400 (v

te 300 200 100 0

2 3 4 Density (veh/km)

Figure 2 Traffic stream relationships for one study site, at one direction of travel.

100 200 300

5-min. Flow Rate (vph)

100 200 300

5-min. Flow Rate (vph)

♦ ATS/FFS ■ ATSpc/FFSpc

2.5 2 1.5 1

100 200 300

5-min. Flow Rate (vph)

♦ ♦ ♦♦Î ♦ ♦

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100 200 300

5-min. Flow Rate (vph)

100 200 300

5-min. Flow Rate (vph)

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♦ ♦

♦ ♦

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100 200 300

5-min. Flow Rate (vph)

Figure 3 Relationships between 5-min directional flow rate and different performance measures for one study site, at one direction of travel.

• For the relationship between the percent followers (PF) and traffic flow, the hypothesis is that as traffic flow increases the percent followers will also increase. The relationship exhibits a positive trend consistent with the hypothesis.

• For the relationship between the Follower Density (FD) and traffic flow, the hypothesis is as flow increases the follower density will also increase. It is obvious that the relationship is consistent with the general expectation. Moreover this trend is stronger and more consistent than the trends exhibited in the previous relationships.

• The last relationship is between traffic flow and Percent Impeded (PI). The hypothesis is as flow increases the value of PI will also increase. The general trend is slightly consistent with the hypothesis.

The relationships of the performance measures with opposing traffic flow were also examined using graphical plots. Fig. 4 shows those relationships at the same study site. ATS, ATSPC and speed ratios ATS/FFS and ATSPC/FFSPC exhibited relatively the same previous trend shown in Fig. 3. For the plots of percent followers, follower density and percent impeded,

no obvious trends were observed, as in Fig. 4, unlike the case of Fig. 3.

Finally the relationships of the performance measures with the third platooning variable, percentage of heavy vehicles, were also examined, at the same study site, as in Fig. 5. According to the plots in this figure, no clear relationships existed between all of the measures and the heavy vehicle percent especially for percent followers, follower density and percent impeded measures. However, ATS, ATSPC, ATS/FFS and ATSPC/FFSPC measures have a weak downward trend.

For all studied cases, it was evident that the relationships of performance measures with opposing flow rate and percentage of heavy vehicles showed lower correlations than that with flow rate, as shown in Figs. 3-5.

6. Statistical analysis

This section discusses the correlation and regression statistical analyses describing the relationships between the three pla-tooning variables: flow, opposing flow and percent of heavy vehicles, and the examined seven performance measures. Addi-

^ 80 /h

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0 100 200 300 400

5-min. Opposing Flow Rate (vph)

100 80 60 40 20 0

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0 100 200 300 400

5-min. Opposing Flow Rate (vph)

♦ ATS/FFS ■ ATSpc/FFSpc

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0 100 200 300 400

5-min. Opposing Flow Rate (vph)

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100 200 300 400 5-min. Opposing Flow Rate (vph)

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Figure 4 Relationships between 5-min opposing traffic flow rate and different performance measures for one study site, at one direction of travel.

tionally, threshold values for different levels-of-service were proposed, based on the best performance measure found.

6.1. Correlation analysis

This section is devoted to describe the correlations between the three platooning variables and the performance measures. This could help for better understanding of the association between performance measures and platooning variables. Table 2 shows the correlation coefficients between performance measures and traffic flow rate at individual study sites, at each direction of travel (e.g. NB, SB). Underlined values represent correlations that have inconsistent signs with the intuitive relationships between flow rate and performance measures. According to Table 2, the majority of the signs of the correlation coefficients are in the expected direction. For example, the Follower Density (FD), Percent Followers (PF) and Percent Impeded (PI) showed positive correlations with flow rate. This means that follower density, percent followers and percent impeded tend to increase as traffic flow rate increases. Alternatively, speed-related variables (ATC, ATSPC, ATS/FFS, and ATSPC/FFSPC) showed negative correlations with traffic flow rate, meaning the higher the traffic the lower the speed. Also, follower density followed by percent followers and percent impeded showed the highest and most significant correlations with traffic flow rate respectively. Although most of speed-re-

lated measures have correlation coefficients with signs that are in the expected directions, the majority of them have insignificant correlations with traffic flow rate. Another important observation is that the two measures ATS and ATS/FFS had approximately the same correlation to traffic flow platooning variable as well as in the case of ATSPC and ATSpC/FFSpC. Moreover, the correlations with ATS and ATS/FFS are usually higher than those with ATSPC and ATSPC/FFSPC. This suggests that restricting speed-related measures to passenger cars does not much improve the sensitivity to platooning variables.

Table 3 shows the correlation analysis between opposing traffic flow rate and different performance measures at individual study sites, for each travel direction. Underlined values represent correlations that have inconsistent signs with the hypothesized logical relationships between opposing flow rate and performance measures. As in Table 3, performance measures and opposing flow rate exhibited relatively lower correlations compared with flow rate. In general, the signs of the correlation coefficients are in the expected direction. The majority of the correlation coefficients are insignificant at the 5% level.

Table 4 shows the correlation analysis between percentage of heavy vehicles and different performance measures at individual study sites, for each travel direction. Underlined values have signs that are inconsistent with the hypothesized logical

10 15 20 % HV

10 15 20 % HV

♦ ATS/FFS ■ ATSpc/FFSpc

10 15 20 25 % HV

5 10 15 20 25 % HV

2.5 2 1.5

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; «•- ♦ ♦

♦ ♦ ♦ ♦ ♦

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0 5 10 15 20 25 30 % HV

0 5 10 15 20 25 30 % HV

Figure 5 Relationships between HV percentage and different performance measures for one study site, at one direction of travel.

Table 2 Correlation coefficients between performance measures and directional flow rate for each direction of study sites.

Site No. Performance measure 1 2 3 4

NB SB NB SB NB SB NB SB

ATS 0.20 -0.08 -0.10 -0.17 -0.11 -0.20 -0.15 -0.21*

ATS/FFS 0.19 -0.08 -0.10 -0.17 -0.11 -0.20 -0.16 -0.21*

ATSPC -0.03 0.05 -0.09 0.03 -0.09 -0.12 -0.17 -0.12

ATSPC/FFSPC -0.03 -0.06 -0.09 0.14 -0.08 -0.12 -0.17 -0.13

PF 0.30* 0.48* 0.26* 0.54* 0.50* 0.51* 0.28* 0.59*

FD 0.69* 0.69* 0.61* 0.75* 0.72* 0.78* 0.80* 0.70*

PI 0.45* 0.34* 0.27* 0.40* 0.44* 0.30* 0.17 0.43*

Site No. 5 6 7 8

Performance measure NB SB EB WB EB WB NB SB

ATS 0.22 -0.04 0.04 0.00 -0.20* 0.14 0.13 -0.11

ATS/FFS 0.23 -0.04 0.03 0.00 - 0.20* 0.14 0.14 -0.10

ATSPC 0.22 -0.05 0.08 -0.05 -0.17 0.00 0.10 -0.15

ATSpc/FFSPC 0.22 -0.05 0.08 -0.05 -0.16 0.00 0.10 -0.14

PF 0.67* 0.50* 0.41* 0.57* 0.44* 0.44* 0.28* 0.59*

FD 0.79* 0.87* 0.69* 0.84* 0.83* 0.78* 0.66* 0.73*

PI 0.58* 0.38* 0.33* 0.53* 0.15 0.26* 0.44* 0.34*

Underlined correlations represent counterintuitive relationships between flow rate and performance Correlation is significant at the 5% level (2-tailed). measures.

Table 3 Correlation coefficients between performance measures and opposing traffic flow rate for each direction of study sites.

Site No. Performance measure 1 2 3 4

NB SB NB SB NB SB NB SB

ATS -0.02 -0.07 -0.22* 0.09 -0.03 -0.08 -0.26* -0.18

ATS/FFS -0.01 -0.07 -0.22* 0.09 -0.03 -0.08 -0.26* -0.18

ATSPC -0.19 -0.06 -0.16 0.12 0.00 -0.06 -0.22* -0.15

ATSpc/FFSPC -0.19 -0.06 -0.16 0.19 0.00 -0.06 -0.23* -0.15

PF 0.04 0.22 0.13 0.09 0.04 -0.02 0.17 0.29*

FD 0.11 0.15 0.13 0.00 0.04 0.07 0.24* 0.22*

PI 0.15 0.24 0.07 0.17 0.02 -0.06 0.14 0.22*

Site No. 5 6 7 8

Performance measure NB SB EB WB EB WB NB SB

ATS -0.15 0.36 0.04 -0.28 -0.20 -0.06 0.13 0.25

ATS/FFS -0.15 0.37 0.03 -0.28 -0.20 -0.05 0.14 0.26

ATSPc -0.09 0.32 0.08 -0.18 -0.17 -0.03 0.10 0.28

ATSPc/FFSPc -0.08 0.32 0.08 -0.18 -0.16 -0.03 0.10 0.28

PF 0.05 0.16 0.41* 0.02 0.44* 0.02 0.28* -0.26

FD 0.00 -0.12 0.69* -0.02 0.83* -0.03 0.66* -0.34

PI 0.01 0.06 0.33* 0.00 0.15 0.00 0.44* -0.18

Underlined correlations represent counterintuitive relationships between opposing flow rate and performance measures. correlation is significant at the 5% level (2-tailed).

Table 4 Correlation coefficients between performance measures and percentage of heavy vehicles for each direction of study sites.

Site No. Performance measure 1 2 3 4

NB SB NB SB NB SB NB SB

ATS -0.09 0.04 -0.15 -0.04 -0.25* -0.28* -0.19 -0.06

ATS/FFS -0.09 0.04 -0.14 -0.04 -0.25* -0.28* -0.19 -0.06

ATSPc 0.01 -0.12 -0.10 0.13 -0.13 -0.09 -0.09 0.01

ATSPc/FFSPc 0.01 -0.12 -0.10 0.15 -0.13 -0.09 -0.08 0.01

PF 0.02 -0.06 -0.10 0.02 0.14 0.05 -0.10 0.00

FD -0.01 -0.11 -0.08 0.06 0.20 0.02 -0.01 0.00

PI -0.02 0.01 -0.08 0.06 0.17 0.07 -0.15 0.07

Site No. 5 6 7 8

Performance measure NB SB EB WB EB WB NB SB

ATS -0.04 0.12 -0.03 -0.05 -0.06 -0.08 0.07 0.05

ATS/FFS -0.03 0.12 -0.04 -0.05 -0.06 -0.08 0.07 0.05

ATSPc -0.02 0.03 0.12 0.05 0.14 -0.16 0.19 0.10

ATSPc/FFSPc -0.02 0.03 0.12 0.05 0.14 -0.17 0.19 0.10

PF -0.02 0.16 -0.10 0.04 -0.06 0.15 -0.05 -0.11

FD -0.06 0.12 -0.04 0.02 0.00 -0.02 -0.03 -0.11

PI -0.11 0.19 -0.12 0.04 -0.11 0.21* 0.00 -0.05

Underlined correlations represent counterintuitive relationships between percentage of HV and performance measures. correlation is significant at the 5% level (2-tailed).

relationships between percentage of heavy vehicles and performance measures. According to Table 4, performance measures and percentage of heavy vehicles exhibited very low correlations compared with flow rate. The vast majority of the correlation coefficients are insignificant at the 5% level.

Another correlation analysis was conducted between pla-tooning variables and the seven performance measures using data from all study sites in one data set. Table 5 shows the correlation results. The most important observations that can be discerned upon examining Table 5 are:

• In general, flow rate followed by opposing flow rate demonstrated higher correlations with almost all performance measures compared to percentage of heavy vehicles. The correlations of percentage of heavy vehicles and performance measures indicated either illogical relationships or very week associations.

• The highest and significant correlations with flow and opposing flow were found in the following order: follower density, percent followers, percent impeded, ATS, and ATSPC respectively. ATS/FFS and ATSPc/FFSPc showed

Table 5 Correlation coefficients between performance measures and the three platooning variables for all data sets.

Performance measures Platooning variables

Flow Opposing flow Percentage of HV

ATS -0.32* -0.31* 0.02

ATS/FFS 0.04 0.06 -0.07*

ATSPC -0.27* -0.28* 0.06

ATSpc/FFSPC 0.00 0.00 0.00

PF 0.54* 0.33* -0.04

FD 0.87* 0.51* -0.04

PI 0.47* 0.28* -0.03

Underlined correlations represent counterintuitive relationships between platooning variables and performance measures. Correlation is significant at the 5% level (2-tailed).

either illogical relationships or week correlations. ATS/FFS had a week but significant correlation with percentage of heavy vehicle.

6.2. Regression analysis

To gain more insights into the strengths and limitations of each of the proposed performance measure, a stepwise linear regression analysis was conducted using data from all study sites as one data set. The objective is to produce the best relationship between each performance measure and platooning variables. The criteria used to assess the accuracy of the produced models were:

• Each of the independent variables (Flow, Opposing flow and% HV) should have regression coefficients that are significantly different from zero (based on the significance level of the t-test), and whose sign should logically explain the effect of this variable on the dependant variable (i.e. performance measure).

• The coefficient of determination R2 must be as high as possible and significant at the 95% confidence level. R2 values only give a guide to the "goodness-of-fit" and do not indicate whether an association between the variables is statistically significant. This is determined by the significance level of the F statistic. For a confidence level of 95%, if the F statistic is associated with a probability of <0.05, there is a statistically significant association between dependent and independent variables.

Having applied these criteria the best models were selected. Details of the regression analysis of these models are shown in Table 6. The table shows one model for each performance measure; no model to fit the criteria was found for ATSPC/ FFSPC measure. However, as in Table 6, the model between Follower Density (FD) as a performance measure, and follow and opposing flow as platooning variables, was found to be the best one. This model has a much higher coefficient of determination R2. It is also found significant at the 95% confidence level as the significance of F statistic < 0.001. Also the coefficients of the platooning variables (flow and opposing flow) were significantly different from zero at the 95% confidence level as the t-test statistics equal 54.1 and 4.5 respectively. This model has a logical explanation for the effect of platooning variables (flow and opposing flow) on performance measure, follower density. The positive signs of the flow and opposing flow mean that follower density tends to increase as flow and opposing flow increase. In other words, operational performance tends to decrease as total traffic flow increases. This model can be written as follows:

FD = -1.81 + 0.009311 Flow + 0.0000779 OpposingFlow (4)

It can be seen that the best model, in Table 6, was selected on the basis of the coefficient of determination R2 as well as t-test results. However, the t-test results showed that the major contributing variable is flow and the contribution of opposing flow could be very limited. Therefore another model considering only platooning variable (flow) was developed. Details of the regression analysis of this model are shown in Table 7, also it can be written as follows:

Table 6 Results of the best regression models between different performance measures and platooning variables.

Variable Performance measure ATS ATS/FFS ATSPC ATSpc/FFSPC PF FD PI

Constant Coefficient 66.97 0.792 67.54 No model was found 0.091 -1.81 0.04296

Flow t (p-value) Coefficient 116 (0.00) -0.0172 265 (0.00) 94.75 (0.00) -0.0172 to fit the required criteria 12.2 (0.00) 0.000583 -27.1 (0.00) 0.009311 11.1 (0.00) 0.000294

Opposing flow t (p-value) Coefficient -7.5 (0.00) -0.0154 -6.1 (0.00) -0.0173 19.8 (0.00) 0.0000732 54.1 (0.00) 0.000779 20.3 (0.00)

% HV t (p-value) Coefficient -6.8 (0.00) -0.132 -6.2 (0.00) 2.5 (0.01) 4.5 (0.00)

Goodness-of-fit t (p-value) -2.726 (0.006)

R2 0.13 0.01 0.10 0.30 0.753 0.22

F (p-value) 108.6 (0.00) 7.43 (0.006) 79.6 (0.00) 312 (0.00) 2222 (0.00) 412 (0.00)

Table 7 Results of the linear regression analysis between follower density and directional flow rate.

Variable Coefficient T p-Value R2 F (p-value)

Constant 1.093 -27.8 0.00 0.75 4364 (0.00)

Flow 0.009723 66.1 0.00

FD = —1.093 + 0.009723 Flow (5)

Based on Tables 6 and 7, the variations in the coefficient of determination R2 between competing models in Eqs. (4) and (5) was very small, very little accuracy would be lost (a decrease of 0.003 in R2) if considering only the flow in the direction of travel as a platooning variable. This would reduce the data collection required to assess the relationship between operational performance and flow rate, and make the model simpler for practitioners to use. This model could be presented graphically, as in Fig. 6.

However, the scatter plots of the observed values, in Fig. 6, indicate that the best relationship could not be linear. Therefore, many other mathematical forms for the independent variable (traffic flow) were considered. The quadratic form was found to display the best relationship between follower density and flow rate, as in Eq. (6) and Table 8. The model has a very high coefficient of determination R2 as well as significant t-test statistics. This model was also presented graphically in Fig. 6. The figure shows that there is a good conformance between the observed and estimated values, in most cases, based on the quadratic form.

FD = 0.001692Flow + 1.193 x 10—5 Flow2 (6)

In general, the results of the statistical analysis showed that follower density has the strongest association with platooning variables in rural two-lane roads in Egypt. Also, among the three platooning variables investigated, traffic flow in the direction of travel showed the highest correlation with performance measures. Such findings agree with those reported by other researchers, such as Al-Kaisy and Karjala [12]. Moreover, the best relationship between follower density and directional traffic flow rate was found to follow the quadratic form.

6.3. Proposed level-of-service (LOS) thresholds in Egypt

The analysis of this research was employed to propose suitable threshold values for different levels-of-service for rural roads in Egypt based on the follower density, the best measure found. Considering that, the HCM proposes using percent followers (PF) as a surrogate measure, instead of Percent-Time-

5-min. Flow Rate (vph)

Figure 6 Relationships between follower density and flow in the direction of travel.

Table 8 Results of the quadratic regression analysis between follower density and directional flow rate.

Variable Coefficient T p-Value R2 F (p-value)

Flow 0.001692 11.62 0.00 0.89 5599 (0.00)

Flow2 1.193 x 10-5 32.71 0.00

Spent-Following (PTSF), to assess the operational performance and LOS on rural two-lane roads, as explained earlier. Consequently, the relationship between follower density and percent followers, using data from all study sites as one data set, was developed, as in the following equation

FD = 0.96PF + 12.90 PF2(R2 = 0.81) (7)

Based on this relationship, the follower densities that correspond to the HCM threshold levels-of service values were determined and presented as shown in Table 9. The table shows that the follower density can vary from level-of-service to another for a certain percent followers.

Although the proposed thresholds are still considered preliminary, they might help traffic engineers in Egypt to assess traffic operational performance using criteria that reflect the local conditions of the area under study. Also, it is hoped that, following further research, the core of knowledge in this area, using data from other Egyptian roads, will mature and a common approach to define levels-of-service for different road facilities can be developed.

7. Summary and conclusions

The primary objective of this paper is to investigate the relationship between operational performance measures on rural two-lane roads in Egypt and platooning phenomenon. A wide variety of performance measures were defined and calculated using traffic data from eight rural two-lane study sites in Mino-ufiya governorate, Egypt. The measures are average travel speed, average travel speed of passenger cars, average travel speed as a percentage of free-flow speed, average travel speed of passenger cars as a percentage of free-flow speed of passenger cars, percent followers, follower density, and percent impeded. The platooning phenomenon was represented by three variables; flow in the direction of travel, opposing flow

Table 9 Proposed level-of-services thresholds in rural two-

lane roads in Egypt.

LOS HCM*, Percent-Time-Spent- Egypt, Follower

Following (PTSF) Density (FD)

A 640.00 62.4

B >40-55 >2.4-4.3

C >55-70 > 4.3-6.8

D >70-85 > 6.8-9.9

E >85.00 > 9.9

* The HCM LOS criteria are for two-lane highways class II [1],

which is the same category of the roads under study.

♦ Observed ■ Linear a Quadratic

and percentage of heavy vehicles. The investigations that were carried out graphically and statistically reached the following conclusions and results:

• correlations were found between examined performance measures and platooning variables. However, follower density, percent follower and percent impeded were found to have strong correlations to platooning variables. On the contrary, speed-related measures; average travel speed, average travel speed of passenger cars, average travel speed as a percentage of free-flow speed, average travel speed of passenger cars as a percentage of free-flow speed of passenger cars were found to have weak correlations to platooning variables.

• Among the platooning variables investigated, traffic flow in the direction of travel has the highest correlation with the performance measures, followed by opposing follow. The results also provided no evidence that the percentage of heavy vehicles have any obvious correlations with performance measures.

• Regression analysis was used to produce the best relationship between each performance measure and platooning variables. Several models were developed, discussed and presented. Generally, the model between follower density as a performance measure, and flow and opposing flow as platooning variables, was found to be the best one. However, the study demonstrated that the relationship between follower density and flow is better described by a quadratic form. Therefore, a new model was recommended between follower density and flow. As the model includes only flow, as independent variable, this would reduce the data collection required to assess the operational performance, and make the model simpler for practitioners to use.

• As the overall findings confirmed that, for Egyptian rural two-lane conditions, the follower density is a promising measure for studying operational performance; threshold values for different levels-of-service were proposed, based on this measure. This might help traffic engineers, in Egypt, to assess traffic operational performance using criteria that reflect the local conditions of the area under study.

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