Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
B. Calculate the average speed and the standard deviation of the natural log of speed for
2001 conditions.
ΣSi
Average speed ( X )=
N
Where,
S = Speed during interval i
i
N =
Total number of intervals
For this, I = = 32.41 mph
Σ ln ( Si
)
Average ln speed ( µ )=
N
For this example, µ = 3.51
1
Standard deviation of ln speed or speed volatility ( α )= Σ(ln( S i
) −µ
)
N
α = 0.2451
C. Construct a log-normal distribution using the log mean and the log standard deviation of
the speed to confirm that the speed data are log-normally distributed.
2
Figure D.3 - Log-Normal Distribution of the 2001 Speeds
0.09
0.08
0.07
Probability Density Function
0.06
0.05
0.04
0.03
0.02
0.01
0
0 10 20 30 40 50 60 70
Speed (mph)
Note: Weekends were excluded from the data.
SAMPLE PROBLEM-QUANTIFYING THE ECONOMIC BENEFIT OF IMPROVING TRAVEL-TIME RELIABILITY Page D-6