1. Critical Headways on Two-Lane Highways in New Zealand Christopher R. Bennett N.D. Lea International and Roger C.M. Dunn University of Auckland

2. Headways n Time difference between vehicles n < 2.5 s following n > 9.0 s free n 2.5 - 9.0 s either free or following (partially constrained)

3. Critical Headway n Headway below which a vehicle is following n Values adopted generally 4-6 s n Important since it governs the LOS

4. Data Collection n Part of study into developing free speed prediction model n Used ARRB VDAS data logger n Data collected at 58 sites in N.Z. around North Island n Over 300,000 vehicles measured

5. Determining Critical Headway n Considering significance surprisingly little research n Various techniques applied but the relative merits of each technique not addressed n This study used the same data with different methods

6. Averaging Interval n Necessary to average data over time interval n Researchers used 2 to 15 minutes n Adopted dynamic interval around 10 minute base

7. Relative Speeds n Speed difference between successive vehicles n Following vehicle has similar speed to lead vehicle n As headways increase, relative speed increases

8. Relative Speed Ratio n Normalises the relative speeds n 0 - following n 1 - free

9. Exponential Headway Model n Free flowing vehicles random and have negative exponential headway n Critical headway where headway distribution ceases to be exponential n Plotted prob(ln(h>T)): linear when negative exponential headway n Data showed volume effects

10. Relative Speed Distributions n Calculated headway distribution for free vehicles (> 9 s) n Calculated distributions for headways above 2 s in 0.5 s intervals n Used chi-squared test to establish critical headway n Very sensitive to sample size

11. Standard Deviations n Calculated standard deviation of speed ratio and relative speed ratio n Found that the data exhibited too much scatter

12. Critical Spacing n Tested spacing instead of headway n Gave results similar to those from headway analysis but less consistent

13. How Many Methods Fitted Data? n Exponential Headway Model - 54/58 n Mean Relative Speeds - 47/58 n Mean Relative Speed Ratio - 39/58 n Spacing - Mean Relative Speed Ratio 39/58 n Relative Speed Distribution - 35/58 n S.Dev. of Relative Speeds - 35/58 n Spacing - Mean Relative Speeds - 39/58

14. Which Method to Use? Exponential Headway n Theoretically correct n Less sensitive to sample size n Independent of vehicle speed n Fitted data at most sites

15. Critical Headway for N.Z. n Value between 3.0 and 4.5 s 87% of sites87% of sites 91% of traffic91% of traffic n Recommended value of 4.5 s for N.Z. n Conservative but ensures that few “following” vehicles mis-classified as “free”

16. Issues: n Autocorrelation analysis? n Distributions as opposed to single value n Volume effects n Geometry effects n Vehicle type effects