ANALYSIS OF SPEED-DENSITY TRAFFIC FLOW MODELS ON A MERGE INFLUENCE SECTION IN AN UNINTERRUPTED FACILITY

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1 ANALYSIS OF SPEED-DENSITY TRAFFIC FLOW MODELS ON A MERGE INFLUENCE SECTION IN AN UNINTERRUPTED FACILITY Tcheolwoong DOH Proessor Transportation Engineering University o Hanyang Sa-3dong, Sangrok-gu, Ansan OREA Fax : cheolung@hanyang.ac.kr yungwoo ANG Proessor Transportation Engineering University o Hanyang Sa-3dong, Sangrok-gu, Ansan OREA Fax : kyungwoo@hanyang.ac.kr Hyunsang IM Ph.D Transportation Engineering University o Hanyang Sa-3dong, Sangrok-gu, Ansan OREA Fax : ihyunsang@naver.com Wookag OO Ph.D Transportation Engineering University o Hanyang Sa-3dong, Sangrok-gu, Ansan OREA Fax : trkw@lycos.co.kr Abstract: An uninterrupted acility relects the interrelation o cause and eect on the traic volume speed density; thereore, i a ramp o traic low is merged into the main line at a merged section, single variables (such as speed or density) change, as well as interaction eects. Thus, this study used temporally- and spatially-continuous traic data or various traic conditions in order to ind changes to correlations and interaction eects in a speed-density traic low model with a merging section. These changes were also analyzed in comparison with other sections. As a result o this analysis, it was ound that the downstream section where traic lows (decelerated by merging) can be depicted with "" model and that the spatial transition occurs as traic low moves arther downstream. It was also ound that the upstream, merge and downstream sections showed heterogeneous traic low characteristics, i.e., the ree low speed and the speed change rate versus low density were dierent rom each other. ey Words: Inluence Section, Traic Flow Models, Heteroskedasticity, Spatial Autocorrelation, dummy variable 1. INTRODUCTION In a merged section in an uninterrupted acility, the main traic increases by the inlow o ramp traic (which has dierent eatures rom the main traic). Also, irregular traic turbulence occurs due to lane changes, acceleration or deceleration. Traic low orms an interaction between the volume, speed and density o traic; thereore, i a ramp s traic low merged onto a main line at a merged section, not only do single variables change (such as speed or density) but the interaction eects also change. However, existing studies on merge 1764

2 traic low are mostly conined to analyses o turbulence that is caused by single variables, such as the standard deviation o the speed and acceleration; thus, studies on changes in traic low (qualitative changes) that are caused by changes to speed-density interactions are not available. This study was designed to analyze interaction eects in a traic low model by using temporallyand spatially-continuous traic data or a merging section. We computed a space-traic low model that represents the merging section, in which the model shapes are homogeneous. In the space model, the speed and density at separate spots o a merging inluence section will change due to mutually dierent eatures; such changes will progressively spread to neighboring spots, which thereby results in spatial autocorrelation and heteroskedasticity. To address this problem, the White-estimator method has been applied, which recalculates statistics without modiying coeicients while considering heteroskedasticity; also, the space-traic low model, which is statistically signiicant and based on traic low theory, was established. In addition, the spatial statistical technique was applied to sections upstream while variables that indicate the speed-density correlations were analyzed downstream. Hence, this study presents changes in the speed-density correlations o the main traic that are caused by ramp traic low at a merging section. To analyze the speed-density traic low model with a merging inluence section, this study uses the Gunja Bridge merging section o the Dongbu Highway (OREA) as a case study. This merging section normally shows diverse traic situations, such as luctuating traic volume or the main and ramp traic and congestion during rush hour. The spatial scope o this analysis includes not only the junction (where merging with ramp traic occurs) but also the section that is inluenced by merging (upstream 400 m and downstream 500 m or a total o 1.08 km). As or the temporal scope o this analysis, the survey was implemented twice so as to better relect the traic situations o a day that involves recurrent congestion; as a result, continuous temporal and spatial data could be recorded. For this traic survey, 40 detectors were installed at regular intervals, as shown in <Fig. 1>, to measure the passing time, speed and length o vehicles at each spot. Upstream 400m 300m 200m 100m SP S1 S2 EP 100m 200m 300m 400m 500m Lane 1 Lane 2 Lane 3 <Figure 1> Spatial distribution o the installed detectors (NC-97) by lane location 1765

3 Literature Review Theoretical Background And Data Characteristic Inluence Section Speed-Density Traic Flow Model Results d Section Traic Characteristic Inluence Section Traic Flow Model Speed-Density Traic Flow Model Heteroskedasticity and Spatial Autocorrelation Occur and Overcome Volume, Speed, Density Data Basic Statistic Analysis Traic Flow Model by Lane-Spot Homogeneity Spatial Traic Flow Model(White Estimator) Using Dummy Variables Corelation Variation Analysis Results and Discussions <Figure 2> Study Process 2. LITERATURE REVIEW 2.1 d Section s Traic Characteristics Using the data obtained rom the detectors at a merged section o the Singal JC, Gyeongbu Expressway (OREA), im et al. (1997) developed a ormula or the merging traic volume that is able to analyze the eect o the ramp traic volume. They suggested that the ramp traic volume at a merging section shows a larger eect than the main traic does. In an analysis o the traic breakdown and the capacity decline at a merging section, im and Park (1998) suggested that the probability o a traic breakdown occurring increases as the ratio o the ramp traic volume to the merge traic volume increases, or as an entering-pattern variable (such as the platoon requency, standard deviation, duration, etc.) o the ramp traic volume, which lows into the main traic, grows longer. In a study that used actual traic data rom three dierent expressway-ramp merging sections (Santa Monica I-405, Roscoe I-405, Backlick I-95), im et al. (2004) analyzed the relation between ramp-traic low and main low in a congested situation in order to conirm that the traic volume that was entering the ramp and the traic volume o the main traic lane have a negative correlation. They also conirmed the spatial extent o the eect on the main traic low that was caused by the traic volume advancing onto the ramp by using the speed and density o the main traic as well as changes to the pattern o the correlation coeicient. Through an analysis o traic low eatures at merging sections and by utilizing a space-time diagram, im and im (2007) observed the characteristics o main line vehicles (such as lane changes, acceleration and deceleration) in order to see how they are aected by an inlux o vehicles rom a merging section. They also suggested a methodology that can ind the time and location o traic breakdowns that occur in each lane through the analysis o individual vehicle data. 2.2 Inluence Section s Traic Flow Model To study the correlation between the traic variables (such as the traic volume, speed and occupancy rate), which were collected by installing detectors (NC-97) at a merging section and ramp, im, Shin and two others (2006) developed the U (Density-Speed) linear model (). This model can estimate the traic density by using the space-averaged speed on a 1766

4 ramp in an urban highway. The authors claim that it is an eective model or the uture estimation o traic density at a junction and or the analysis o traic delay. As a model or estimating the traic speed at a downstream section with traic eatures o an upstream section (when assuming that the traic characteristics downstream are aected by those upstream), im et al. (2007) developed a model that can orecast speed (the dependent variable) at the terminal point o a merged section. They proved the eectiveness o the model with the speed at a merging section near a downtown area; this speed had a high degree o correlation with the speed at the upstream section and the ramp. The speed at the merging section between the downtown areas showed a high correlation with the speed o the upstream section as well as with the traic volume upstream. As explained above, the existing studies on traic-low analysis or a merging inluence section are either ocused on the traic low breakdown that is caused by interactions between the ramp traic volume and the traic variables o the main low, or ocused on estimating the traic variables within merging sections. However, there is no research on changes in the speed-density interactions o the main-traic low that are due to the ramp-traic low. In this study, we analyzed the correlation between the speed and density o the main traic low that are inluenced by merging traic. 3. THEORETICAL BACGROUND AND DATA ANALYSIS TECHNIQUES 3.1 Speed-Density Traic Flow Model There are several available models o traic low. The linear model () is mathematically simple, but it cannot express a realistic congestion density. As or exponential models (Greenberge and ), the jam density or ree low speed does not match well with observations. As mentioned above, there are limitations associated with expressing speed-density relationships in diverse traic situations when using just one model; thus, a complex model that includes speed-density interactions is required. This study ocused on an analysis o a basic linear model () and exponential models (Greenberge and ) in order to ind the speed-density correlation at each spot in a road section that is inluenced by merging traic. The main ormulas or the various models are shown in <Table 1>. <Table 1> Speed-density traic low models Models Model Formula Year Linear U U 1 j 1934 Exponential Greenberg U U ln j m 1959 m U U e

5 3.2 Heteroskedasticity and Spatial Autocorrelation For a given section o road where merging occurs, the ramp traic and the main traic have dierent eatures; thus, the traic low characteristics at each spot are inluenced by interactions that are caused by the merging process. Hence, during the computation o spatial traic low models, which calculate traic data or each spot, heteroskedasticity occurs where the size o the variance in the error per spot is not regular due to the particular characteristics o the data. Also, spatial autocorrelation, where the spatial error cannot be maintained, occurs as a result o mutually giving and receiving eects upstream and downstream or between lanes. When establishing a speed-density space-traic low model, which includes spatial autocorrelation and heteroskedasticity, the density calculations (the explanatory variable) can become inaccurate; this causes increased variation and conidence interval broadening. Thereore, the spatial autocorrelation and heteroskedasticity should be considered while recognizing that the result o an analysis can be distorted by the spatial dependency and spatial heterogeneity o cross-sectional data. To solve the problem o heteroskedasticity, the weighted least squares (WLS) method can be used, where the density coeicient (an explanatory variable) can be weighted. For this type o speed-density traic low model, the constant and density coeicients are indices that represent the ree-low speed, critical speed, jam density and critical density. Thus, in order or the traic low phenomenon to occur in a rational manner, the heteroskedasticity should be considered without changing the constant and density coeicients o the traic low model that are provided by the method o ordinary least squares (OLS). Hence, in this study, the White-estimator was applied to study the occurrence o spatial autocorrelation and heteroskedasticity. The White-estimator was proposed by White (1980), who suggested that an accurate estimation can be ensured by calculating variables with the least square estimation, even though the variable X is related to the heteroskedasticity. This ormulation is written as: Est. Asy. Var[ b] 1 n 1 X ' X 1 2 ' X ' ei xi xi n n n i1 n where e i is the residual or the sequential order and i is used to estimate the asymptotic variation o the least square estimation. The useulness o the White-estimator in the OLS analysis was demonstrated in various studies (Cra, 1980). The adjusted-white estimation is a method that enhances reliability when estimating parameters under heteroskedasticity; this technique was applied in this study to enhance the reliability o our statistical analysis without changing the speed intercept and the coeicient o density. X Basic Statistic Analysis o the Volume, Speed, and Density Data The traic data that was collected or this study are shown in <Table 2>. There were 12,504 samples (collected every 5 minutes); 12,108 samples were rom 39 locations on the main line (13 spots per lane over 3 lanes) while 396 samples were rom one location on the ramp. The surveyed traic volume was rom 84 to 2,040 vphpl while the average traic volume per lane was 1,007 vphpl on the main line and 1,084 vphpl on the ramp. Thus, both the main line and the ramp had similar levels. To survey by lane, lane 1 had 1,073 vphpl, lane 2 had 1,165 vphpl and lane 3 had 830 vphpl; thus, lane 2 has the largest traic volume while lane 3 has the smallest volume. 1768

6 The vehicle speeds ranged rom to kph, which represents diverse traic conditions. The average speed was kph on the main line and kph on the ramp; thus, the speed on the ramp was evidently lower than the average speed on the main line. The traic density ranged rom 1.00 to vpk, while the average density was vpk on the main line and vpk on the ramp. According to our analysis, the reason why the density on the ramp is comparatively higher is because the ramp has a similar traic volume to the main line, but with a lower speed. Volume (vphpl) Speed (kph) Density (vpk) <Table 2> Basic Statistics or the Volume, Speed and Density Section Lane 1 Lane 2 Lane 3 Main Lane (Lane1,2,3) Ramp Average 1, , , , , Standard Dev Range 1,872 1,728 1,872 1,956 1,440 1,956 Minimum Maximum 1,980 2,040 1,956 2,040 1,692 2,040 # o Data 3,768 3,672 4,668 12, ,504 Total (Main+Ramp) Average Standard Dev Range Minimum Maximum # o Data 3,768 3,672 4,668 12, ,504 Average Standard Dev Range Minimum Maximum # o Data 3,768 3,672 4,668 12, , DATA ANALYSIS 4.1 Traic Flow Model by Lane In a traic low model, the traic volume, speed and density change in a causal sequence; thus, it is not easy to statistically estimate traic populations. However, by assuming that one dependent variable, y (speed), and one independent variable, x (density), have a linear relation, such a relation can be expressed with a speed estimation unction by using a speed-density correlation and by calculating the density with a regression analysis. This basic ormulation is as ollows: y a bx where y is the dependent variable (speed) and x is the independent variable (density). In this study, the regression analysis ormula included a t-distribution, which thereby veriies the existence o a linear relation between the two variables. Also, the coeicient o determination (R 2 ) was calculated so the model with the largest coeicient o determination was selected as the proper model. 1769

7 The determination coeicient (R 2 ) indicates how well the regression model matches the given data; in other words, the degree o contribution rom the independent variable (density) to the dependent variable (speed) is large i the determination coeicient is large. Thereore, i the determination coeicient is large, the density has a large eect on the speed, and the regression ormula accurately represents changes to the speed. To perorm a regression analysis o the dependent variable (speed) and the independent variable (density), a linear relation was assumed. 1) Model : U U U 1 U U j j j 2) Greenberg Model : U U ln U U U m m ln( j) m ln 3) Model : m U U e 1 ln( U) ln( U ) m <Table 3~5> shows the proper traic low model per lane and per spot by using the calculations o the speed, coeicient o density, t-statistics and coeicient o determination per model as well as the coeicient characteristics 1. The t-statistics o the constants and coeicients that were computed or each model s ormula were signiicant. Thus, the model with the largest determination coeicient (R 2 ) was selected as the best model or each spot. As a result o this analysis, it was ound that upstream, and at merging sections, the determination coeicient o the model was high; however, at downstream sections, the model was the best ormula. These data suggest that the speed-density relationship at the section where there was decelerated traic low (due to merging) was recovering; thus, it is concluded that the traic approaching the merged section and the traic leaving had qualitatively dierent low characteristics. Another characteristic o the traic low model is that, when the traic was changing inside o the same lane, the variation section ormed where the determination coeicients or the dierent models become similar. That is, when the best model changes rom the to model or rom the to, the determination coeicients o the two models are nearly the same. These variation sections ormed in the various lanes as ollows: in lane 1 in between 200m and 500m downstream, in lane 2 in between 100m and 500m downstream and in lane 3 in between the terminal merge point and 400m downstream. Thus, this model relects the situation where the characteristics o the main traic low gradually change (due to the eect o the ramp traic low) and then recover again. 1 The Greenberg model was excluded rom the analysis results because its determination coeicient was considerably lower than those o the other models. 1770

8 Upstream Upstream Section Section 400m 300m 200m 100m Start Point Section1 Section2 <Table 3> Lane 1 traic low model comparison per spot End Point 100m 200m 300m 400m 500m 400m 300m 200m 100m Start Point Section1 Section2 End Point 100m 200m 300m 400m 500m Constant (234.25) (251.42) (147.05) (215.21) (87.10) (190.69) (104.12) (165.99) (107.44) (145.22) (183.45) (194.87) (197.57) Density Coeicient (-67.72) (-77.45) (-45.92) (-66.93) (-27.00) (-60.85) (-36.38) (-58.64) (-39.47) (-49.88) (-62.20) (-67.43) (-73.65) R Constant (767.21) (803.89) (510.96) (719.87) (258.23) (594.46) (89.67) (515.82) (326.30) (408.62) (402.25) (444.90) (449.67) <Table 4> Lane 2 traic low model comparison per spot Constant (245.16) (190.16) (272.27) (143.63) (203.64) (231.34) (263.33) (251.03) (144.79) (182.84) (167.03) (162.23) (187.57) Density Coeicient (-67.86) (-57.78) (-80.17) (-47.07) (-68.70) (-80.23) (-95.37) (-95.93) (-62.54) (-70.33) (-57.38) (-60.05) (-67.85) R Constant (744.50) (591.57) (884.27) (509.91) (710.75) (717.39) (832.98) (807.80) (350.05) (430.96) (372.62) (410.86) (442.38) Density Coeicient (-93.46) ( ) (-67.54) (-91.38) (-30.73) (-76.53) (-42.50) (-74.16) (-48.74) (-50.43) (-49.72) (-57.48) (-66.16) Density Coeicient (-85.62) (-70.63) ( ) (-71.69) (-98.32) ( ) ( ) ( ) (-62.95) (-62.39) (-48.43) (-59.85) (-62.18) R R

9 Upstream Section <Table 5> Lane 3 Traic Flow Model Comparison per Spot 400m 300m 200m 100m Start Point Section1 Section2 End Point 100m 200m 300m 400m 500m Constant (245.16) (190.16) (272.27) (143.63) (203.64) (231.34) (263.33) (251.03) (144.79) (182.84) (167.03) (162.23) (187.57) Density Coeicient (-67.86) (-57.78) (-80.17) (-47.07) (-68.70) (-80.23) (-95.37) (-95.93) (-62.54) (-70.33) (-57.38) (-60.05) (-67.85) R ) Model : Constant = U, Density Coeicient = ( U j ) 2) Model : Constant = ln( U ), Density Coeicient = ( 1 m) 3) ( ) is t-statistics Constant (744.50) (591.57) (884.27) (509.91) (710.75) (717.39) (832.98) (807.80) (350.05) (430.96) (372.62) (410.86) (442.38) Density Coeicient (-85.62) (-70.63) ( ) (-71.69) (-98.32) ( ) ( ) ( ) (-62.95) (-62.39) (-48.43) (-59.85) (-62.18) R To illustrate a section where the speed-density per lane changes rom the model to the model, we look at the section o road where the traic moves downstream rom the terminal point o lane 3 (which is most directly aected by the merging traic) to where it changes into the inner lanes. <Figure 3> indicates lane 1 rom 200m to 500m downstream, lane 2 rom 100m to 500m downstream and lane 3 rom the terminal merging point to 400m downstream. The shaded regions in the lanes o <Fig. 3> indicate the typical traic pattern downstream rom an onramp, where the traic low moves towards the inner lane. Upstream 400m 300m 200m 100m SP S1 S2 EP 100m 200m 300m 400m 500m Model Area Model Area <Figure 3> Traic low model or each lane 1772

10 4.2 Spatially-Homogeneous Traic Flow Model In this section, we examine regions with homogeneous speed-density relationships. When the speed-density is changed by the eects o traic inlow rom a ramp, the space-traic low model can be established with a single model. However, when traic data is integrated at each spot and the interaction eects are considered, heteroskedasticity and spatial autocorrelation occur where the size o the error process variance per spot is irregular. Also, due to the characteristics o the cross-sectional data, this type o model is not independent o spatial errors. Hence, in this study, the heteroskedasticity was examined with the Breusch-Pagan test that enables analysis irrespective o the unctional orm o the independent variable. Also, while considering the heteroskedasticity, we enhanced the reliability o our model by recalculating the statistics and by maintaining a constant density coeicient or the speed-density traic low model, which was induced with OLS by applying the White-estimator method in order to not distort the rational traic low phenomenon. <Table 6> and <Fig. 4> through <Fig. 6> analyze the traic characteristics in terms o lane changes that are due to the merging process. Each spot was calculated by using the best itting space-traic low model, which changed every 100 m rom the merge terminal point to 500m downstream. <Table 6> Homogeneity space traic low model Lane Model Constant Density Coe. Adj. R 2 B-P 2 1) Lane 1 300m ~ 500m Lane 2 100m ~ 500m Lane 3 100m ~ 400m Coeicient OLS 2) t A.White 3) Coeicient OLS t A.White Coeicient OLS t A.White Coeicient OLS t A.White Coeicient OLS t A.White Coeicient OLS 1, t A.White ) is Signiicant Level (0.000) (0.000) (0.000) (0.270) (0.001) (0.000) 1) B-P 2 2 : Breusch-Pagan test. ( 2) OLS : t-statistics o Constant and Density Coeicient by Ordinary Least Square Method 3) A.White(Adjusted-White Estimate) : t-statistics o Constant and Density Coeicient by White Estimator Method At the spot that was downstream by 500 m, it was concluded that at lane 1, the speed-density traic low is dierent rom the spot that is downstream by 300 m. That is, while passing through the 500m downstream spot, the traic low that started to change 300m downstream was recovering again due to the characteristics o the upstream section. The section o lane 1 where the speed-density traic low changes due to merging was calculated to be 300m to 500m downstream o lane

11 End Point~ 100m~ 200m~ 300m~ 400m~ End Point~ 100m~ 200m~ 300m~ End Point~ 100m~ 200m~ 300m~ 400m~ End Point~ 100m~ 200m~ 300m~ End Point~ 100m~ 200m~ 300m~ 400m~ End Point~ 100m~ 200m~ 300m~ Journal o the Eastern Asia Society or Transportation Studies, Vol. 8, 2010 By the same method, the section o lane 2 where the speed-density traic changes due to merging was ound to be 100m to 500m downstream; the corresponding section o lane 3 was ound to be 100m to 400m downstream m 400m <Figure 4> Variation in the determination coeicient calculated by the traic low model (lane 1) m 400m <Figure 5> Variation in the determination coeicient calculated by the traic low model (lane 2) m 400m <Figure 6> Variation in the determination coeicient calculated by the traic low model (lane 3) To illustrate the space-traic low model or each lane with a geometric structure, lane 1 is analyzed 300m to 500m downstream, lane 2 is analyzed 100m to 500m downstream and lane 3 is analyzed 100m to 400m downstream, as shown in <Fig.7>. In conclusion, the traic low changes due to 1774

12 merging persist around the 400m to 500m downstream extent, starting at the terminal point o the ramp section. The characteristics per lane start to change irst in lane 3, which is connected with the merging or ramp lane, while recovery to the typical traic low shape is made irst in lane 3. As or lane 1, traic low change occurs at the shortest section o the arthest downstream section. As or lane 2, it was concluded that the traic low change is shown at the longest section where the change sections o lane 3 and lane 1 are interlinked. Upstream 400m 300m 200m 100m SP S1 S2 EP 100m 200m 300m 400m 500m Lane 2 1 Lane 3 1 Lane 1 1 Lane 2 2 Lane 3 2 Lane 1 2 <Figure 7> Homogeneous space-traic low model <Table 7> Speed-density traic low model per lane Lane Space Section Models & Formula Adj. R 2 Lane 1 Upstream 400m m U e 300m 2 U m Lane 2 Upstream 400m Start Point U e m 2 U m Lane 3 Upstream 400m Start Point U e m 2 U m 4.3 Dummy Variables Analysis In this section, we analyze the heterogeneous characteristics o the traic low in the main line downstream rom an onramp. Dummy variables were applied to represent the speed-density traic low or each lane and a spatial-statistic technique was used to analyze the changes to the traic low Heterogeneous traic low can be represented by dierences in the constants (speed) and the inclination (speed/density) o the speed-density model. The size o the constants determines the speed dierence per section in the same density state while the size o the inclination indicates the sensitivity o changes to the speed due to density changes. It was concluded that the model was the best or this purpose. However, at the downstream change section, the model was determined to be the most accurate since its 1775

13 ormula is easiest to interpret and the model maintains a level higher than R 2 =0.868; thereore, the model was selected or these tests. <Figure 8> gives an illustration o the dummy variables or the subdivided sections: the upstream section ( D ), merged section ( a D ) and downstream inluence section ( b D ). <Table 8> gives the c model ormulas that contain the section s dummy variables, where we assumed that the magnitudes o the speed and acceleration can change according to the density. Upstream 400m 300m 200m 100m SP S1 S2 EP 100m 200m 300m 400m 500m 1-Up ( ) 1- ( ) 1-Down ( ) D a 2-Up ( ) D a 3-Up ( ) D a 2- ( ) D b 3- ( ) D b D b 2-Down ( ) 3-Down ( ) D c D c D c <Figure 8> The dummy variables that are deined or each subsection o each lane <Table 8> model applied to the sub-sectional dummy variables U U U bdb cdc ( D ) ( D ) d b e c j Dummy Variables Upstream D a D b D c Here, D a through D c are the dummy variables or the subdivided section and b through e are the coeicients o the dummy variables. Also, bdb and cdc are the speed dierences in the ree-low speed ( U ) o the upstream section as compared to the merging section and the downstream section. Furthermore, D and d b edc correspond to the inclination, which signiies the speed change rate dierence ( U / ) against the density o the upstream section as compared to j the merging section and the downstream section. Hence, the model ormula that is given above is a regression equation that expresses the speed dierence and speed change rate per density or the upstream, merging and downstream sections. <Table 9> shows the coeicient estimations or the section s dummy variables, which were readjusted into a graph like that in <Fig. 9> in order to enable easily comparison o the analysis results o the dummy variables. 1776

14 Lane Lane 1 Lane 2 Lane 3 Total Lane U ( ) ( ) ( ) ( ) <Table 9> Coeicient estimations or the dummy variables Dierence o Speed b c j bd (-6.633) (-6.301) ( ) ( ) cd (0.742) (7.122) (-9.693) (-1.510) Variation Ratio o Speed/Density U / d b edc ( ) (3.309) (2.285) (66.588) (8.710) (-0.785) ( ) (13.881) (12.216) ( ) (11.507) (6.384) 1) ( ) is t-statistics and shade is signiicant value(signiicant level 0.05, t=1.96) R Speed(kph) Speed(kph) Upstream Inluence Density(vpk) <Lane 1> Density(vpk) <Lane 3> Upstream Inlunece Speed(kph) Speed(kph) Upstream Inlunece Density(vpk) <Lane 2> Upstream Inlunece Density(vpk) <Total Lane> <Figure 9> Speed-density correlation by the section s dummy variables Through this analysis, it was concluded that the upstream section, merging section and downstream section (which were applied as section dummy variables) show heterogeneous traic low eatures where the size o the ree low speed and the speed change rate versus the density are dierent rom each other. For the traic in the upstream section, the ree low speed and the speed change rate versus the density change were high in comparison to the other sections. As or the traic low in the merging section, the magnitude o the speed and the speed change rate were the lowest in comparison to the other sections. In the downstream section that was inluenced by the merging traic, the traic low at the merging section was aected by the eatures o the upstream section while the section is concluded to have a higher ree low speed and speed change rate than the merging section. 1777

15 Due to these characteristics, it is concluded that the traic turbulence (which is exhibited via the standard deviation o the speed or spatial changes to the speed) is most prominent in the upstream section. Also, the downstream sections shows the process o recovering to the characteristic o the upstream section ater passing through the merging section that causes low-eiciency traic low (composed o a low density and a low speed). For the upstream section, however, the model changes rom an exponential orm () to a linear orm () due to a speed-density correlation that maintains higher speeds (compared to other sections) within the density extent o 10 to 30 vpk, according to the results o this study. 5. RESULTS There are interaction eects between the parameters that describe the traic; thus, i the ramp traic low is merged onto a main line via a merging section, not only can the single variables (such as the speed or density) change but the interaction eects can also be seen. Hence, this study used temporally- and spatially-continuous traic data to determine the section o road where the interaction relationships changed due to a merging section. The results obtained rom this study can be summarized as ollows. 1 The speed-density correlation at the merging section ollows the model at the upstream section, which changes to the model at the downstream section (which is directly aected by the ramp traic low). Change section represents the section where the traic low (decelerated due to merging) is recovering. 2 As the traic low moves arther downstream rom the merge at the terminal point in lane 3, the section where the speed-density traic model per lane changes into the model shows a spatial transition to the inner lane in the section that is 100m to 500m downstream. 3 In the upstream section, the merging section and the downstream section, which are inluenced by the merging, display heterogeneous traic eatures where the size o the ree-low speed and the speed change rate versus the density change are dierent rom each other. 4 In order to establish cross-sectional traic data at separate spots (which are continuous) as a representative model o the space, the spatial autocorrelation and heteroskedasticity should be examined. It is also concluded that the method o recalculating statistics with the White-estimator is eective. The signiicance o this study is that it clariies the qualitative aspects o traic low and deines the space where the speed-density interactions change as a result o traic inlow merging rom the ramp. 1778

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