2. LITERATURE REVIEW. Keywords: Design hourly factor ( K-factor), annual average daily traffic(aadt), design hour volume(dhv), road design

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1 Study on Estimating Design Hourly Factor Using Design Inflection Point Won Bum Cho Senior Researcher, Korea Institute of Civil Engineering and Building Technology, Korea Ph.D. Student, Department of Transportation Engineering, University of Seoul, Korea ABSTRACT Design hourly factor is defined as the Design hourly factor determines the certain amount of traffic as design hour volume of target year among hourly traffic distribution on a specific. Design hourly factor is very important design factor in aspect of construction and operational efficiency. This study is intended to evaluate the specific estimate process which is in conformity with the definition of design hourly factor and analyze the priority of estimated design hourly factors so as to review the feasibility of annual average daily traffic ratio for 30 th hourly volume or K 30 which has been applied as design hourly factor domestically and internationally. Moreover, based on hourly traffic data of national highway and expressway in operation, the cases of design hourly factor analysis were proposed after classifying them by major factor that have effect on traffic demand variation characteristics, thereby providing appropriate design hourly factors to help determine the factor in designing the. Keywords: Design hourly factor ( K-factor), annual average daily traffic(aadt), design hour volume(dhv), design 1. INTRODUCTION Design hourly factor (K-factor) is defined as the Design hourly factor determines the certain amount of traffic as design hour volume (DHV) of target year among hourly traffic distribution on a specific Design hourly factor is very important design factor in aspect of construction and operational efficiency and when design hourly factor is set too high, construction would be uneconomical because of overestimate of design hour volume and on the contrary, when design hourly factor is set too low, time zone when actual volume exceeds design hour volume occurs frequently, resulting in frequent traffic congestion [1,2,3,4]. Hence, design hourly factor shall be estimated by applying the hourly volume at the point where incline is changed rapidly on annual hourly traffic curve in order of scale (descending order) and average annual daily traffic (AADT) ratio so as to incorporate economic investment concept (construction cost versus maximum operational efficiency). Design hourly factor varies depending on traffic demand variation characteristics. The greater the design hourly factor the larger the traffic demand variation and the more the number of lane and annual average daily traffic the less the design hourly factor on a specific. Design hourly factor is also affected by geological features of the region where the passes or links as well as functional characteristics of the. For instance, design hourly factor at tourist region is the largest which is decreased gradually in order of rural and urban, indicating the different pattern between expressway and national highway that have different traffic demand characteristics. This study is intended to evaluate the specific estimate process which is in conformity with the definition of design hourly factor and analyze the priority of estimated design hourly factors so as to review the feasibility of annual average daily traffic ratio for 30 th hourly volume (K 30). Moreover, based on hourly traffic data of national highway and expressway in operation, the cases of design hourly factor analysis were proposed after classifying them by major factor that have effect on traffic demand variation characteristics, thereby providing appropriate design hourly factors to help determine the factor in designing the. 2. LITERATURE REVIEW 2.1 Design Hour Volume and Design Hourly Factor As annual average daily traffic ratio/rate, which is given as design traffic contains no hourly and directional traffic variation in monthly, weekly and daily traffic, such variation factors shall be considered using design hourly factor (K) and directional factor (D) when design the. Design hour volume among hourly traffic for design is calculated by multiplying annual average daily traffic (AADT) by design hourly factor (K) Thus the greater the design hourly factor the higher the traffic demand variation. Generally, as AADT is increased, design hourly factor of the is decreased and the value reaches the highest on in tourist region while the value is decreased gradually in order of rural, metropolitan and urban. Table 1 shows the pattern of hourly design factor [4] depending on annual average daily traffic (AADT) and Fig 1 shows the variation of design hourly factor depending on function [1]. 553

2 AADT Table 1: Design hourly factor depending on AADT (Washington State) Average K-Factor Number of Sites Included in Average K-Factor Urban Recreational Other Rural 0-2, ,500-5, ,000-10, ,000-20, ,000-50, , , , , >200, Figure 1: Variation of design hourly factor depending on function According to the Ministry of Land, Infrastructure & Transport (MOLIT) of Korea [5], design hourly factor in foreign countries is determined 30 th hour and Korea lacks the study on design hourly factor considering regional characteristics and thus it s necessary to adopt the 30 th hour volume as design hour volume but particular consideration is needed in case of expressway indicating significant variation in traffic over the year. In Germany, annual average daily traffic rate (K 30) for the 30 th hour traffic which is applied to design is as follows. Rural K 30= 0.09~0.11(6-lane expressway) 0.10~0.12( expressway) 0.10~0.13(2-lane rural ) Urban K 30= 0.080~0.085(downtown, beltway) 0.090~0.095(Outskirt, downtown) 0.095~0.105(suburb) When design hourly factor is set too high, construction would be uneconomical because of Over estimate of design hour volume and when design hourly factor is set too low, time zone when actual volume exceeds design hour volume occurs frequently, resulting in frequent traffic congestion. Hence, forecast of rational annual average daily traffic and estimate of design hourly factor considering regional characteristics and traffic demand variation pattern is most important. 2.2 Review of Design Hourly Factor Estimate Process Design hourly factor estimate process proposed by MOIT [1] is as follows. Arrange the hourly traffic data on a specific for a year in order of traffic volume, from high to low. Set the horizontal axis of the graph as traffic volume and vertical axis as hourly volume and draw hourly volume over the year in curve. Check the point where the curve is rapidly changed and calculate the ratio of hourly volume to annual average daily traffic (DHV/AADT=K). 554

3 Average design hourly factor in Korea proposed by MOLIT [1] is as Table 2. Table 2: Average design hourly factor in Korea Category of Design hourly factor 2-lane National highway Rural Urban 0.09 (0.07~0.10) 0.15 (0.12~0.18) 0.15 (0.12~0.18) 0.09 (0.07~0.11) According to MOLIT [2], as design hourly factor (K) varies depending on regional traffic demand pattern, it shall be determined using annual traffic data [6] and if not available, it may be determined using the value in Table 3. Table 3: Design hourly factor (K) by region, expressway Category Design hourly factor (K) Rural area Urban area 0.15 (0.12~0.18) 0.09 (0.07~0.11) 3. METHODOLOGY Design hourly factor estimate process is as Fig 2 containing in order of traffic data collection, establishment of design hourly factor estimate methodology, regional classification of through cluster analysis, identification of design hourly factor (proposal) from various standpoints and proposal of final design hourly factor. data with the least missing time was used in this study within the range that could secure the statistical significance. In case of national highway, the point where all hourly traffic data for 8,760 hours (1year) is secured among permanent traffic data was selected and in case of expressway, the point with 10% or less missing time during weekend and holiday season with total 8,760 hours (1 year) was selected Finally, in case of national highway, data from 94 2-lane s and 160 s was collected and in case of expressway, data from 121 s and 33 6~10-lane s was used. National highway with a 6- lane or wider was excluded because of no satisfying the requirements. 3.2 Establishment of Design Hourly Factor Estimate Methodology According to existing capacity handbook [2] in Korea, hourly traffic at the point where curve is significantly changed on annual hourly traffic curve arranged in order of traffic volume (descending order) and annual average daily traffic are used as the process to estimate the design hourly factor. But the method to estimate the point where curve is rapidly changed is not clarified and thus in this study, the procedure to identify the point where the relationship between hourly traffic arranged in descending order and the order curve was rapidly changed (hereinafter called Point of Inflection) was established and used for analysis. Arrange the hourly traffic data on a specific for a year in order of traffic volume, from high to low. Set the horizontal axis of the graph as hourly traffic to AADT and vertical axis as descending order of the value of horizontal axis (1~8,760, for a year) and draw in graph and link in (L 1). Where, L 1 is illustrated in various ways and in this study, regression analysis of the ratio of hourly traffic to annual average daily traffic (AADT) arranged in descending order was conducted to produce the curve and the values in the 1st to 1,000 th among total 8,760 hours were used. Figure 2: Design hourly factor estimate process 3.1 Traffic Volume Data Collection Hourly traffic data collected in 2010 on national highway and expressway was used in estimating design hourly factor. Design hourly factor based on annual investigation hours, 8,760hours (=365days 24hrs /day) would be preferred but missing time is inevitable due to maintenance of detection equipment. For such reason, the 3 From the curve (L1) obtained from above process, a node between the tangent passing (1 st priority) and the tangent passing (n-th where tangential gradient variation is near 0) is estimated. In this process, b was estimated using the characteristics in the form similar to the straight line (log curve) that is getting nearer to 0 as the rate of hourly traffic to AADT becomes lower and considering the tendency of the order, gradient variation was determined at six decimal place (round off to the nearest seven decimal place. 555

4 4 Value of vertical axis ( ) of e where the line(l3) linking d (bisection point of line (L2) linking a and b) and curve (L1) are crossing as design hourly factor (DHV/AADT=K). 4. CLASSIFICATION OF THE REGION CONSIDERING TRAFFIC DEMAND VARIATION CHARACTERISTICS Design hourly factor in tourist region is the largest which is gradually decreased in order of rural and urban. Tourist in the vicinity of tourist and recreational region has the concentrated traffic demand in holiday or tourist season and rural shows more traffic demand on weekends, tourist and holiday season than usual weekdays while rural shows less concentrated traffic demand than tourist and urban shows steady traffic demand on weekdays by commuters and less demand on weekends, Fig 4 shows traffic demand variation by region. Thus, design hourly factors shall be determined considering traffic demand variation by region where the passes through or connects. Figure 3: Determination of design hourly factor (KPOI) using inflection point Figure 4: Traffic demand variation pattern by region (hourly traffic to annual average daily traffic) According to Kim, Bumjin et al [7] as parts of the studies on classification of the region based on traffic demand variation characteristics, was categorized by cluster analysis using AADT, ratio of daytime and nighttime traffic, peak hour rate, average coefficient of weekdays and weekends and holiday season coefficient and Lim, Sunghan et al [8] used similar traffic characteristic coefficient with Kim, Bumjin [7] but additionally considered 30 th design hourly factor (K 30), directional coefficient when 30 th design hourly coefficient occurred and heavy vehicle rate and used Sunday coefficient instead of weekends average coefficient. Particularly, K 30, among the factors using in previous studies, was replaced with K POI which was estimated by incorporating the concept of inflection point. K POI is differentiated from K 30, because of incorporation of traffic demand variation. Holiday season coefficient was analyzed by incorporating seasonal traffic demand pattern during summer beginning Jul 19 toll Aug 15 and autumn from Sep 20 till Nov 15. Traffic characteristic variables used for previous studies and others used for this study are presented in Table 4. In this study, cluster analysis coefficient that can effectively explain traffic demand variation characteristics considering a 5-day workweek, increase in nighttime traffic and uniform daytime traffic pattern was adopted. 556

5 Variables (AADT, unit/day) Table 4: Traffic operational characteristic variables and application of cluster analysis Application to previous Characteristics studies Definition Meaning Touris Rural Urban A* B** t Applica tion of cluster analysis Annual total traffic /365 days Traffic demand None K30 30th time priority traffic /AADT KPOI D30 Heavy vehicle ratio Daytime traffic ratio Nighttime traffic ratio Time priority traffic on inflection point /AADT Rate of vertical traffic to bidirectional traffic for 30th time priority traffic Heavy vehicle traffic/total traffic hrs daytime (07~19) traffic /24-hour traffic 12 hrs nighttime traffic (19~07) /24-hiour traffic Peak ratio 1 peak hr traffic/ 240hr traffic Sunday factor Weekday mean factor Weekend mean factor Holiday mean factor Holiday season mean factor Sunday mean traffic / AADT Weekday mean traffic / AADT Weekend mean traffic /AADT Holiday mean traffic /AADT New Holiday season mean daily traffic /AADT Annual hourly volume variation Annual hourly volume variation Traffic distribution by direction High High Me d Me d None Low Low Vehicle types None Daily traffic variation (day/night) Daily traffic variation (day/night) Daily traffic variation (peak hour) Weekly variation (Sunday demand) Weekly variation (Weekday demand) Weekly variation (Weekend demand) Tourist (Summer) Tourist (Summer. Fall) * A: Lim, Sung-han et al [8], ** B : Kim, Bum-ki et al[7] None None None A 5-day workweek applicable to weekend Same as weekend factor High Me d Low Holiday season applicable to holiday demand High Me d Low O O O K-mean cluster analysis among non-hierarchical cluster analysis was used and was divided into 3 groups including urban, rural and tourist region. After cluster analysis, outlier was analyzed and removed and upper and lower limit to remove the outlier is as Equation (1), (2) Lower Outlier Q (Q 3 Q 1) (1) Upper Outlier Q (Q 3 Q 1) (2) Where, Q 1: 25-percentile, Q 3: 75-percentile. Table 5 7 show the distribution and median analysis result of characteristic values (design hourly factor, weekend mean coefficient, holiday season mean coefficient) As a result, the more the number of lane the less the characteristic value and the highest in tourist and is decreased gradually in order of rural and urban which is in conformity with general tendency 557

6 National highway Road Table 5: Distribution of design hourly factor (K) by 2-lane 6-lane or wider Urban Design hourly factor by region (KPOI) Rural Tourist Total Median ~ ~ ~ ~0.277 Median ~ ~ ~0.172 ~0.172 Median ~ ~ ~ ~0.189 Median ~ ~ ~0.135 ~0.135 National highway Category of Road 2-lane 6-lane or wider Table 6: Weekend mean coefficient by Urban Weekend mean coefficient by region (Note Rural Tourist Total Median ~ ~ ~ ~1.576 Median ~ ~ ~ ~1.267 Median ~ ~ ~ ~1.519 Median ~ ~ ~1.224 Note) Weekend mean coefficient = Weekend daily mean traffic /AADT ~1.224 Table 7: Holiday season mean coefficient by Category of Road Holiday season mean coefficient by region) Urban Rural Tourist Total National highway 2-lane Median ~ ~ ~ ~

7 Median ~ ~ ~ ~ lane or wider Median ~ ~ ~ ~1.480 Median ~ ~ ~ ~1.131 Note: Holiday season mean coefficient = Summer & fall holiday season daily mean traffic /AADT pattern and the higher K POI the lower K POI than K ANALYSIS OF DESIGN HOURLY (Fig 5~8) FACTOR Relation between K POI and K 30 on national highway and expressway was similar (Fig 6, 8) 5.1 Comparison between K30 and Difference between K KPOI POI and K 30 on a 2-lane Comparison between K 30, the 30 th design hourly national highway was most significant (Fig 5) factor and K POI calculated by incorporating the Point of which was reduced in order of a national inflection was made as follows. highway (Fig 6), expressway (Fig 7) and 6- K POI and K 30 have very high correlations (linear) and when K POI was low, K 30 was higher or similar lane or wider expressway (Fig 8) Distribution range of K 30 was larger than K POI indicating larger variation of K 30 (Table 8) Figure 5: K POI and K 30 on a 2-lane national highway 559

8 Figure 6: K POI and K 30 on a national highway Figure 7: K POI and K 30 on a expressway 560

9 Figure 8: K POI and K 30 on a 6-lane or wider expressway Table 8: Distribution of design hourly factor (K) Category of Region Classification Urban Rural Tourist Total KPOI K30 KPOI K30 KPOI K30 KPOI K30 National highway 2- lane 4- lane Total 4- lane 6- lane or wider Median ~ ~ ~ ~ ~ ~ ~ ~0.38 Median ~ ~ ~ ~ ~ ~ ~ ~0.22 Median 0.12 KPOI: 0.07~0.28, K30: 0.07~0.38 Median ~ ~ ~ ~ ~ ~ ~ ~0.21 Median ~ ~ ~ ~ ~0.14 Total Median 0.12 KPOI: 0.07~0.19,: 0.07~ Analysis of Design Hourly Factor Table 9 shows the result of estimating design hourly factor range and representative value considering the category, number of lane and region and was analyzed based on K POI using the concept of inflection point. Representative value was estimated using mathematical average upper and lower limit within the range of design hourly factor. According to analysis result, the more the number of lane the less the design hourly factor and was the highest in tourist and decreased gradually in order of rural and urban which was in 561

10 conformity with general tendency. When it comes to a 4- lane, characteristic value on a expressway was higher than national highway which was attributable to preference of expressway to national highway during holiday seasons. On the contrary, design hourly factor of a 6-lane or wider expressway was low in general because of the direct or indirect effect by traffic demand in the vicinity of metropolitan area and mixing of routine commuter traffic and recreational traffic. Table 9: Design hourly factor (K POI) considering category, number of lane and region Category of Category of Region Urban Rural Tourist Total National highway 2-lane 6-lane or wider Median Arithmetic mean No of point ~ ~ ~ ~ Median Arithmetic mean No of point ~ ~ ~0.172 ~ Median Arithmetic mean No of point ~ ~ ~ ~ Median Arithmetic mean No of point ~ ~ ~0.135 ~ Application of Design Hourly Factor Median value among the design hourly factors proposed as representative value has advantage of considering data distribution characteristics, but may cause the confusion because design hourly factor proposed in capacity handbook is based on arithmetic mean. Thus arithmetic mean of upper and lower limit would be desirable as representative value. When it comes to expressway, rural region and tourist region are mostly mixed and thus they need to be integrated and in case of a 6-lane or wider expressway, data is insufficient causing the lack of representativeness and a and 6-lane were integrated and represented by a single value. Final design hourly factor (K POI) is as Table

11 Table 10: Application of design hourly factor Category of region Category of Urban Rural Tourist National highway 2-lane or wider (0.102~0.144) (~0.121) (0.128~0.198) (0.091~0.153) (0.178~0.277) (0.116~0.172) ( or wider) (~0.130) (0.086~0.189) 6. CONCLUSIONS AND RECOMMENDATIONS In foreign countries, annual average daily traffic rate (K 30) is usually adopted as design hourly factor and this rate (K 30) is also used in Korea with insufficient research data without considering regional characteristics. This study thus is intended to propose the specific process of estimating the design hourly factor which incorporates the concept of inflection point and analyze the priority of design hourly factors so as to evaluate the feasibility of K 30 that has been commonly used domestically and internationally. As a result of evaluation, median of design hourly factor over entire national highway was 35 th and expressway was 34 th indicating no significant difference with K 30 that has been commonly used for design. Inflection point-based design hourly factor proposed in this study is based on inflection point which is conceptually feasible but somewhat complex in applying to the field and no significant difference with K 30 and accordingly, using annual average daily traffic rate to 30 th hour traffic would be acceptable. Traffic demand variation pattern by region and increase in number of lane was not fully incorporated into the capacity handbook of Korea, causing the limit in applicability. This study, in a bid to solve the problem, proposes the cases of analyzing the design hourly factor that incorporates the influential factors on traffic demand variation characteristics using the traffic data on national highway and expressway in operation for reference in determining the design hourly factor for design. Design hourly factor proposed in this study has the following features when comparing to existing capacity handbook. 6.1 National Highway Design hourly factor of a 2-lane was classified into urban region, rural region and tourist region (urban region: 012(0.10~0.14), rural region: 0.16(0.13~0.20), tourist region : 0.23(0.18~0.28)) Design hourly factor of existing 2-lane was proposed in a single value irrespective of category of the region 0.15(0.12~0.18) Design hourly factor of or wide was newly proposed by categorizing them into urban region, rural region and tourist region (urban region: 0.10(0.07~0.12), rural region: 0.12(0.09~0.15), tourist region: 0.14(0.12~0.17)) 6.2 Design hourly factor of rural region was proposed as 0.14(0.09~0.19): Comparing to existing rural region, 0.15(0.12~0.18), and representative value was decreased by 0.01 but the applicable region was expanded and the feasibility would be expanded. Design hourly factor of urban region was proposed as 0.10(0.07~0.13): Comparing to existing urban region, 0.09(0.07~0.11), and representative value was increased by 0.01 and the applicable region was also expanded. REFERENCES [1] Ministry of Land, Transport and Maritime Affairs, Korea Highway Capacity Manual, [2] Ministry of Land, Transport and Maritime Affairs, Korea Highway Capacity Manual, [3] Transportation Research Board, U.S Highway Capacity Manual, [4] Transportation Research Board, 2010 U.S Highway Capacity Manual, [5] Ministry of Land, Transport and Maritime Affairs, Guideline and manual for structure and facility [6] Ministry of Land, Transport and Maritime Affairs, Statistical Yearbook of Traffic Volume. 563

12 [7] Kim, Bumjin, Son, Yeongtea, A Study on The Value of Roads Grade K-factor in Roadway Design, Road Traffic, Korea Road Association, Journal of Korea Road & Transportation Association. no.105, pp.62~73, [8] Lim, Sunghan, Ha junga, Oh, Jusam (2005), Classification of National Highway by Factor Analysis, International Journal of Highway Engineering, vol.7 No.3, pp.43~52, AUTHOR PROFILE Won Bum Cho received his master s degree in transportation engineering at the Hanyang University in Korea. Currently, he is working as a senior researcher at the Korea Institute of Civil Engineering and Building Technology as well as a PhD student in transportation engineering at the University of Seoul in Korea. 564