Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
The formula in Equation 4 is then solved for F( ) for various values of V (the mitigation value) and
K (the project cost).By reviewing Equation 6, it can be determined that the project value function,
F( ) varies in the following way with the parameters:
• The greater is V, the greater is the project value
• The greater is K, the lower is the project value
• The greater is the uncertainty, s, about the value V, the greater is the project value
• The greater is the number of events, x, that can occur at one point in time, the lower the
project value. This is because the probability of many simultaneous rare events is low.
This method has been applied to the previously used case of avalanche mitigation in the
Snoqualmie Pass in Washington. Using data from a 13-year history of avalanche events in the area,
a Generalized EV-Gumbel (GEV-Gumbel) distribution was fit and the location and scale
parameters obtained. Figure C.3 shows the (GEV-Gumbel) probability density function for the
number of avalanche closures per month for the months of December through March for the
eastbound direction. The estimated (GEV-Gumbel) distribution is displayed in Figure C.4.
Figure C.3 - Gumbel Probability Function for Avalanche Closures per Year, I-90
Eastbound
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0 2 4 6 8 10 12 14 16 18 20
Avalanche Closures per Month (December-March)
VALUATION OF TRAVEL-TIME RELIABILITY FOR RARE EVENTS Page C-10