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Table 1 Previously developed regression-based operating speed models

From: Developing operating speed models for elevated multilane urban arterials using artificial neural networks

Author (s)

Model

R2

Eq.

Two-lane two-way highways

Lamm et al. [2]

\({V}_{85 C}=34.70-1.00 DC+2.081 LW+0.174 SW+0.0004 AADT\)

0.842

1

Krammes et al. [3]

\(\begin{array}{c}{V}_{85 C}=102.45-1.57DC+0.0037 Lc-0.1 \Delta \\ {V}_{85 C}=41.62-1.29 DC + 0.0049 Lc-0.12 \Delta + 0.95 V85T\end{array}\)

0.82

0.9

2

3

Voigt [4]

\(\begin{array}{c}{V}_{85}=102 - 2.08 DC + 40.33 e\\ {V}_{85 C}=99.6-1.69 DC + 0.014 L - 0.13 \Delta + 71.82 e\end{array}\)

0.81

0.84

4

5

Gong and Stamatiadis [5]

For inside lane:

\({V}_{85 IL}=51.520 + 1.567 ST - 2.795 MT- 4.001 PT - 2.15 AG + 2.22 ln (LC)\)

For outside lane

\({V}_{85 OL}=60.779 + 1.804 ST - 2.521 MT -1.071 AG - 1.519 FC + 0.00047 R+ 2.408 \frac{LC}{R}\)

0.647

0.432

6

7

Zuriaga et al. [6]

For all radii values:

\({V}_{85 C}=97.4254-\frac{3310.94}{R}\)

\({V}_{85 C}=\frac{1}{0.00948323+(0.00001501*CCR)}\)

For radii > 400 m

\({V}_{85 C}=102.048-\frac{3990.26}{R}\)

For Tangents

\({V}_{85 T}={V}_{85 C}+\left(1-{e}^{-\lambda L}\right)\times ({V}_{des}-{V}_{85C}\))

0.76

0.79

0.84

0.52

8

9

10

11

Passetti and Fambro [7]

\({V}_{85 C}=103.9 - 3020.5/R\)

0.68

12

Abbas et al. [8]

\({V}_{85 MC}=75.344-\frac{368.14}{\sqrt{R}}+0.307 {V}_{85 AT}\)

0.532

13

Mahmoud et al. [9]

Two-dimensional model:

\({V}_{85 C}=102.466-\frac{5003.426}{R}\)

Three-dimensional model:

\({V}_{85 C}=103.559-\frac{4951.51}{R}-{3012.795 G}^{2}\)

0.69

0.732

14

15

Islam and Seneviratne [10]

\({V}_{85 PC}=95.41 - 1.48 DC - 0.012 {DC}^{2}\)

\({V}_{85 MC}=103.3 - 2.41 DC - 0.029 {DC}^{2}\)

\({V}_{85 PT}=96.11 - 1.07 DC\)

0.99

0.98

0.98

16

17

18

Bird and Hashim [11]

\({V}_{85 C}=119.073-\frac{518.275}{\sqrt{R}}-\frac{125440}{{ATL}^{2}}+\frac{413.181}{{\Delta }^{2}}\)

0.88

19

Hashim et al. [12]

For point of curvature:

\({V}_{85}=99.885-\frac{3880.21}{R}\)

For center of the curve:

\({V}_{85}=101.564-3480.88/R\)

For point of tangency:

\({V}_{85}=101.18-\frac{3969.9}{R}\)

For tangents

\({V}_{85 T}=84.34+0.593\sqrt{{L}_{T}}\)

0.704

0.730

0.728

0.851

20

21

22

23

Arterials

Fitzpatrick et al. [13]

For all roadways

\({V}_{85 c}=7.675 + 0.98 PSL\)

For urban/suburban arterials

\({V}_{85 c}=8.666 + 0.963 PSL\)

For rural arterials

\({V}_{85}=36.453 + 0.517 PSL\)

0.904

0.86

0.81

24

25

26

Fitzpatrick et al. [14]

\({V}_{85 c}=43.5+0.38 IDS\)

\({V}_{85 T}=74.91+22.29/AD\)

0.83

0.71

27

28

Wang et al. [15]

\({V}_{85 T}=31.565 + 6.491 lane.num-0.101 roadside - 0.051 driveway - 0.082 intersection + 3.01 curb - 4.265 sidewalk - 3.189 parking + 3.312 land.use1 + 3.273 land.use2\)

0.67

29

  1. Where:
  2. V85 = predicted operating speed (mph or km/h)
  3. V85 C = predicted operating speed on horizontal curve (mph or km/h)
  4. V85 T = predicted operating speed on tangent (mph or km/h)
  5. V85 PC = predicted operating speed at point of curvature (km/h)
  6. V85 MC = predicted operating speed at midpoint of horizontal curve (km/h)
  7. V85 PT = predicted operating speed at point of tangency (km/h)
  8. V85 IL = predicted operating speed on horizontal curve inside lane (mph)
  9. V85 OL = predicted operating speed on horizontal curve outside lane (mph)
  10. R = horizontal curve radius (m)
  11. DC = degree of curvature (°) (equals to 1746.38/R)
  12. CCR = curvature change rate
  13. LC = length of horizontal curve (ft)
  14. LW = lane width (ft)
  15. SW = shoulder width (ft)
  16. AADT = average annual daily traffic (vehicles/day)
  17. \({L}_{T}\)= tangent length (m)
  18. Δ = deflection angle (°)
  19. e = superelevation rate (m/m)
  20. G = Grade on Horizontal Curve
  21. ST = shoulder type indicator (1 if the shoulder type is surfaced; 0 otherwise)
  22. MT = median type indicator (1 if no median barrier present; 0 otherwise)
  23. PT = pavement type indicator (1 if pavement type is concrete; 0 if asphalt)
  24. AG = approaching section grade indicator (1 if the absolute grade ≥ 0.5%; 0 otherwise)
  25. FC = front curve indicator (1 if the approaching section is a curve; 0 otherwise)
  26. Vdes = desired speed (km/h)
  27. PSL = Posted speed limit (km/h)
  28. \(\lambda\) = calibration factor to minimize mean square error (MSE)
  29. ATL = the average length of the preceding and following tangents of the curve
  30. AD = approach access density (number of access points per km)
  31. \(IDS\) = inferred design speed (km/h)
  32. roadside = density of roadside objects per mile / average offsets from roadside (ft)
  33. driveway = density of driveways (number of driveways per mile)
  34. lane.num = number of lanes
  35. curb = 0 if there is no curb; otherwise, curb = 1
  36. sidewalk = 0 if there is no sidewalk; otherwise, sidewalk = 1
  37. parking = 0 if there is no on-street parking; otherwise, parking = 1
  38. land.use1 = 0 and land.use2 = 0 if land use is commercial
  39. Intersection = intersection density per mile