ESTIMATION OF FREE-FLOW SPEEDS FOR MULTILANE RURAL AND SUBURBAN HIGHWAYS

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1 ESTIMATION OF FREE-FLOW SPEEDS FOR MULTILANE RURAL AND SUBURBAN HIGHWAYS Pin-Yi TSENG Professor Department of Traffic Science Central Police University 56, Shu Jen Road, Kwei Shan, Taoyuan, 33334, Taiwan Tel: Ext Fax: Feng-Bor LIN Professor Department of Civil and Environmental Engineering Clarkson University Potsdam, NY U.S.A. Tel: Fax: Sheng-Long SHIEH Research Assistant Department of Traffic Science Central Police University 56, Shu Jen Road, Kwei Shan, Taoyuan, 33334, Taiwan Tel: Fax: Abstract: Free-flow speed is a parameter that is being used extensively for capacity and level-of- service analysis of various types of highway facilities. As part of an ongoing effort to revise Taiwan Area Highway Capacity Manual, this study collects and analyzes free-flow speed data at the midpoints of seventy-six multilane rural and suburban highway segments in Taiwan. The objectives of this study are to develop models for estimating average free-low speed and for identifying the distribution of individual free-flow speeds. The most important variables that govern free-flow speed are vehicle type, speed limit, and the spacing between signalized intersections. The resulting models facilitate both manual analysis and computer simulation of rural and suburban highways. Key Words: Capacity analysis, Level-of-service, Free-flow speed, model, Rural and suburban highways 1. INTRODUCTION Free-flow speed is the speed of a vehicle when the vehicle movement is not interfered by other vehicles or interrupted by control devices. The mean value of the free-flow speeds of individual vehicles can be determined either as a space mean or as a time mean. Time-mean speed is the arithmetic mean of individual speeds; space-mean speed is the harmonic mean. Mean free-flow speed has a wide range of applications. For example, space-mean free-flow speed is the basis of many planning models that are used to estimate average travel speeds and capacities (Dowling, R., et al. 1997). And the estimated travel speeds, in turn, are being used for estimating fuel consumptions and vehicles emissions (Dowling, R., et al. 1997; Teply, S., et al., 1995). The U.S. Highway Capacity Manual (Transportation Research Board 2000) also uses space-mean speed extensively to analyze the capacities and levels of service of open 1484

2 highways and urban and suburban arterials highways. On the other hand, all microscopic traffic simulation models have to use time-mean free-flow speed and its related distribution of individual free-flow speeds as inputs for estimating travel time, delays, and fuel consumptions. Many researchers have investigated the problem of estimating free-flow speed (Dowling, R., et al., 1997; Agent, K. R., et al. 1998; Dixson, K. K., et al. 1999; Kyte, M., et al. 2000). In Taiwan, estimated average free-flow speeds are needed for simulation analysis of various types of highways. They are also needed in manual methodologies for capacity analysis of highway segments with uninterrupted traffic flows. Figure 1 shows an example of the need to predict average free-flow speed. It reveals that the relationship between flow and speed on a multilane rural or suburban highway is governed by its average space-mean free-flow speed. For a given flow rate, a highway segment with a higher average free-flow speed can be expected to have a higher average travel speed. Therefore, it becomes necessary to know the mean free-flow speed of a highway segment before an appropriate speed-flow relationship can be established and used as a basis for estimating capacity and level of service. Very little research, however, has been conducted in Taiwan to understand the characteristics of free-flow speed on multilane rural and suburban highways. As a result, the Taiwan Area Highway Capacity Manual (Institute of Transportation 2001) lacks a proper methodology for capacity and level-of-service analysis of this type of highways. As part of an ongoing effort by Taiwan s Institute of Transportation to revise the manual for capacity analysis, this study investigates the free-flow speed characteristics on Taiwan s rural and suburban highways. The objective of the study is to develop models for estimating the space-mean free-flow speed, time-mean free-flow speed, and the distribution of individual free-flow speeds. This paper presents the finding of the study Harmonic-Mean Speed (km/h) Tai 14B 5K+400 N. Tai 2 1K+940 S. Tai 2 1K+900 N. Tai 2 1K+940 N. Sibin Inside Lane Sibin Outside Lane Flow Rate (small veh/h/lane) Figure 1. Observed Relationships Between Flow Rate and Harmonic-Mean Speed on Taiwan's Multilane Rural and Suburban Highways 1485

3 2. DATA COLLECTION The multilane rural and suburban highways in Taiwan usualy have two or three fast lanes for passenger cars and other larger vehicles and one slow lane for motorcycles. Because of high land use intensity, these highways have a large number of signalized intersections. In between signalized intersections, there are intersections controlled only by STOP signs, YIELD signs, or flashing beacons. Many factors can affect the free-flow speed of a highway segment. They include but are not limited to the spacing between signalized intersections, lane width, shoulder width, lateral clearance, median type, grade, curvature, vehicle types, speed limit, land use and drivers behaviors. This study concerns only the free-flow speeds on straight and level segments that have median barriers. Seventy-six such segments were chosen for the study with the aid of Taiwan Highways Network Information System. Each segment lies between two signalized intersections. Thirteen of the study segments were on Sibin Expressway that connects small villages and towns in predominantly rural areas. Sibin Expressway has higher design standards than the other highways investigated in this study. The speed limit on Sibin Expressway is a uniform km/h. The speed limits on other investigated rural highways are km/h. As for suburban highways, the speed limits are typically km/h. The lane width of each study segments is in the range of 3.5 m to 4 m for fast lanes and 1.4 m to 4.6 m for slow lanes. The spacing between signalized intersections is between 0.4 km and 5 km. The number of median openings on each study segment is up to 9.1/km. And the number of non-signalized intersections that are at least 6 m in width is mostly less than 2 per km. Free-flow speeds of vehicles were measured with a laser gun at the midpoint of each segment under fair weather conditions. Vehicles were classified into small vehicles, large vehicles, and motorcycles. Small vehicles refer to passenger cars, vans, and pickup trucks. Large vehicles are trucks with more than two axles, heavy utility vehicles, and large buses. Only vehicles that were separated by headways of more than 5 s were sampled. Because the speed measurements were made under very light flow conditions, most sampled vehicles had headways far longer than 5 s. For each study segment, speed samples were collected from the inside fast lane, the outside fast lane, and the slow lane. No data were collected from the slow lanes on Sibin Expressway because of the absence of motorcycles. For each segment, the sample size is usually in the range of to 140 small vehicles, 30 to large vehicles, and 30 to 135 motorcycles. The standard deviations of measured free-flow speeds are about 9 km/h for small and large vehicles, and about 12 km/h for motorcycles. 3. HARMONIC MEAN FREE-FLOW SPEED By definition, harmonic-mean free-flow speed can be determined as: Vsf N N 1 i 1 ui (1) where 1486

4 V sf N u i = harmonic-mean free-flow speed (km/h), = number of sample vehicles, and = free-flow speed of vehicle i (km/h). To develop models for predicting V sf, this study examines the following factors that may affect harmonic-mean free-flow speed: Lane location Lane width Number of median openings and non-signalized intersections per km Vehicle type Spacing between signalized intersections (i.e., segment length) Speed limit Lane location has an obvious but small impact on free-flow speed. As shown in Figure 2, the harmonic-mean free-flow speed of small vehicles in an inside lane is higher than that in an outside lane. The average difference is about 4.3 km/h. The harmonic-mean free-flow speed of large vehicles has a similar characteristic, and the average difference between the inside lane speed and the outside lane speed is about 3.8 km/h. Because the speed differentials are small, speed data collected from the inside and the outside fast lanes of each study segment were aggregated for modeling purposes. Harmonic-Mean Speed in Outside Lane, km/h Speed Limit km/h km/h km/h Harmonic-Mean Speed in Inside Lane, Km/h Figure 2. Comparison of Speeds in Different Lanes The lane widths of the fast lanes examined in this study correlate to some extent with the speed limits of the study segments. Among the fast lanes that have a speed limit of km/h, 68% of them have a width of 3.5 m and most of the remaining lanes are 3.6 m wide. The widths of the fast lanes with a speed limit of km/h tend to be wider. Among them, 34% are over 3.7 m, 36.8% are between 3.5 m and 3.7 m, and the rest are 3.5 m. The fast lanes on Sibin Expressway have a width of 3.6 m. As for the slow lanes on segments with a speed limit of km/h, 88.5% of them are less than 2.5 meters in width. In contrast, 37.8% of the slow lanes on 1487

5 segments with a speed limit km/h are wider than 3.0 meters. As illustrated in Figure 3, for a given speed limit, the lane width has no discernible impact on mean free-flow speed. Harmonic-Mean Free-Flow Speed, km/h 75 Average Width of Fast Lanes 3.5 m m Intersection Spacing, km Figure 3. Variation of Harmonic-Mean Free-Flow Speed with Lane Width (Speed limit = km/h) Figures 4 and 5 show respectively how the harmonic-mean free-flow speeds of small vehicles and large vehicles vary with speed limit and the spacing between signalized intersections. On average, harmonic-mean free-flow speed increases rapidly when the spacing between signalized intersections increases from 0.4 km to about 2.5 km. The mean speed then reaches a more or less steady value. Figures 4 and 5 also show that the mean free-flow speeds of four segments on Tai-26 highway (lane width = 3.5m and speed limit = km/h) are all higher than the averages for other segments with the same speed limit of km/h. Tai-26 is a highway that serves primarily tourists. At present, it is not clear whether highways that serve primarily recreational traffic will consistently have higher mean free-flow speeds. For the slow lanes, Figure 6 shows that speed limit has little effect on the harmonic-mean free-flow speed. Like the mean speeds of small vehicles and large vehicles, the mean speed of motorcycles also increases with the spacing between signalized intersections and reaches a more or less steady value when the spacing is more than 2.5 km. But the impact of the spacing between signalized intersections is very limited. The relatively low top speeds of motorcycles are likely the reason behind this phenomenon. On average, the mean free-flow speed of the small vehicles is about 5 km/h higher than that of large vehicles on segments with a speed limit of either km/h or km/h. The speed differential between small vehicles and large vehicles tends to increase with speed limit. On Sibin Expressway, where the speed limit is km/h, the difference is about 11 km/h. The mean free-flow speed of motorcycles is about 18 km/h below that of small vehicles. Based on the characteristics of the free-flow speeds shown in Figures 4, 5, and 6, the models listed in Table 1 are developed to facilitate the analysis of multilane rural and suburban highways. In 1488

6 these models, V sf represents the harmonic-mean free-flow speed (km/h) and S is the spacing between signalized intersections (km). It should be noted that the number of median openings and non-signalized intersections per km has no significant impact on free-flow speed. Therefore, this factor is not used for the model development. 95 Harmonic-Mean Free-Flow Speed, km/h Speed Limit km/h km/h km/h Speed Limit km/h km/h km/h Tai-26 ( km/h) Estimates Intersection Spacing, km Figure 4. Variation of Harmonic-Mean Free-Flow Speed of Small Vehicles with Speed Limit and Spacing Between Signalized Intersections 85 Speed Limit km/h Harmonic-Mean Speed, km/h km/h Speed Limit km/h km/h km/h Tai-26 Estimates Intersection Spacing, km Figure 5. Variation of Harmonic-Mean Free-Flow Speed of Large Vehicle with Speed Limit and Spacing Between Signalized Intersections 1489

7 Harmonic-Mean Speed, km/h Speed Limit km/h km/h Estimates Intersection Spacing, km Figure 6. Variation of Harmonic-Mean Free-Flow Speed of Motorcycles with Speed Limit and Spacing Between Signalized Intersections Table 1. Models for Estimating Harmonic-Mean Free-Flow Speed Vehicle Type Small Vehicles Speed Limit (km/h) Models Standard Error of Estimate (km/h) V sf = e -1.89S 3.6 V sf = 25.5e -1.32S 3.1 V sf = S S 2 S Large Vehicles V sf = 89.2 S > 3 or V sf = S 20S 2 S 0.5 V sf = e -S S > 0.5 V sf = S 20S 2 S 1.5 V sf = e S S > Motorcycles or V sf = 51.4 S 1 e

8 4. TIME-MEAN FREE-FLOW SPEED Time-mean free-flow speed is the arithmetic mean of individual free-flow speeds. It can be determined as: V tf N u i i 1 N (2) where V tf = time-mean free-flow speed (km/h), N = number of sample vehicles, and = free-flow speed of vehicle i (km/h). u i Under free-flow conditions, the difference between harmonic-mean speed and time-mean speed is very small. Furthermore, as shown in Figure 7, observed time-mean free-flow speeds and harmonic-mean free-flow speeds have a very strong linear relationship. For ease of application, the following empirical relationship is recommended for estimating time-mean free-flow speed: Vtf V sf (3) where V tf and V sf are respectively time-mean and harmonic-mean free-flow speeds (km/h) and is 1.6 km/h for small vehicles, 1.3 km/h for large vehicles, and 3.5 km/h for motorcycles. 100 Time-Mean Free-Flow Speed, km/h Harmonic-Mean Free-Flow Speed, km/h Figure 7. Comparison of Harmonic-Mean and Time-Mean Free-Flow Speeds 1491

9 5. DISTRIBUTION OF FREE-FLOW SPEED Each individual free-flow speed of a segment can be normalized into a proportion of the time-mean free-flow speed. The cumulative distribution of the normalized free-flow speeds varies only slightly from one segment to another. Figures 8 through Figure 10 show respectively examples of such distributions for small vehicles, large vehicles, and motorcycles Cumulative Proportion segments Speed/Time-Mean Speed Ratio Figure 8. Cumulative Distributions of Normalized Free-Flow Speeds of Small Vehicles Cumulative Proportion segments Speed/Time-Mean Speed Ratio Figure 9. Cumulative Distributions of Normalized Free-Flow Speeds of Large Vehicles 1492

10 Cumulative Proportion segments Speed/Time-Mean Speed Figure 10. Cumulative Distributions of Normalized Free-Flow Speeds of Motorcycles The normalized free-flow speeds of small vehicles and large vehicles have a minimum value of about % of the mean and a maximum of about 1% of the mean. There is no significant difference between the normalized distributions of small vehicles and large vehicles. In contrast, the normalized free-flow speeds of motorcycles are more dispersed. And their distribution is significantly different from the normalized distribution for either small vehicles or large vehicles. Based on Figures 8 through 10, Table 2 presents the representative cumulative distributions of the respective normalized free-flow speeds of small vehicles, large vehicles, and motorcycles. 6. APPLICATIONS Taiwan s Institute of Transportation has developed a microscopic simulation model for analyzing the performance of signalized highway facilities. This model, referred to as Highway Traffic Systems Simulation Model, has incorporated the models as represented by Equation 3 and the distributions given in Table 2 to generate default time-mean free-flow speeds and the free-flow speeds of simulated vehicles. For capacity analysis of highways segments not affected by signalized intersections, the Institute of Transportation has established the representative flow-speed relationships as shown in Figure 11. To use this figure, one has to estimate first the harmonic-mean speed of the highway segment being analyzed. The Institute of Transportation plans to adopt the models given in Table 1 to provide the needed estimates. 1493

11 Table 2. Representative Distributions of Free-flow Speed Cumulative Free-flow Speed / Time Mean Free-flow Speed Ratio Percentage (%) Small Vehicles Large Vehicles Motorcycles Harmonic-Mean Speed, km/h km/h Free-Flow Speed Flow Rate, small cars/h/lane Figure 11. Representative Flow-Speed Relationships on Taiwan's Multilane Rural and Suburban Highways 1494

12 7. CONCLUSIONS Free-flow speed is an important parameter for capacity and level-of-service analysis of highways. To support the revision of Taiwan Area Highway Capacity Manual, this study uses data collected from 76 straight and level highway segments to develop models for estimating harmonic-mean and time-mean free-flow speed and to identify representative distributions of individual free-flow speeds. The study is focused on multilane rural and suburban highways. The results show that speed limit, vehicle type, and the spacing between signalized intersections are the major factors affecting free-flow speed. Mean free-flow speed, however, reaches a steady state once the spacing between signalized intersections is more than 3 km. On average, the mean free-flow speed of small vehicles is about 5 km/h higher than that of large vehicles if the speed limit is either km/h or km/h. At a speed limit of km/h, the difference increases to about 11 km/h. The difference between the mean free-flow speed of small vehicles and that of motorcycles is about 18 km/h if the speed limit is not greater than km/h. ACKNOWLEDGEMENT This study was sponsored by the Institute of Transportation, Ministry of Transportation and Communications, ROC. REFERENCES Agent, K. R., Pigman, J. G. and Weber, J. M. (1998) Evaluation of Speed Limits in Kentucky, Transportation Research Record No. 1640, Transportation Research Board, Washington, D. C., pp Akcelik, R. (1982) Traffic Signals: Capacity and Timing Analysis. Research Report No. 123, Australian Road Research Board, Victoria. Dixson, K. K., Wu, C-H, Sarasua, W. and Daniel, J. (1999) Posted and Free-Flow Speeds for Rural Multilane Highways in Georgia, ASCE Journal of Transportation Engineering, Vol.125, No.6. Dowling, R., Kittelson, W., Zegeer, J. and Skabardonis, A. (1997) Planning Techniques to Estimate Speeds and Service Volumes for Planning Applications, NCHRP Report 387, Transportation Research Board. Institute of Transportation (2001) Taiwan Area Highway Capacity Manual, , Ministry of Transportation and Communication, Taipei. Kyte. M., Khatib, Z., Shannon, P. and Kitchener, F. (2000) Effect of Environmental Factors on Free-Flow Speed, Transportation Research Circular E-C018: 4 th International Symposium on Highway Capacity. Teply, S., Allingham, D. I., Richardson, D. B. and Stephenson, B. W. (1995) Canadian Capacity Guide for Signalized Intersections. Institute of Transportation Engineers, District 7. Transportation Research Board (2000) Highway Capacity Manual. National Research Council, Washington, D. C. 1495

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