Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
April) using data from a 13-year historical series of avalanche closures for the I-90 Eastbound
direction of Snoqualmie Pass.
With the parameters of the Gumbel EV distribution estimated from the closure data, one can
consider the certainty-equivalent value associated with strategies that offer various “guarantees” of
protection from rare-event closures (such as traffic management, staging of snow-removal
equipment, etc.). One such strategy might allow the agency to reduce the average monthly closure
duration by five hours. Another more-aggressive strategy might aim at reducing most of the rareevent
outcomes and the closure duration by 25 hours—effectively eliminating the closure duration
for all but the most-significant events. In a manner similar to the insurance analogy used to
illustrate valuing unreliability associated with recurring events, one could calculate the European
put option for various such “insurance” levels.
Figure C.2 illustrates how the European put option values vary with the closure delay guarantee
(duration reduction). This exhibit illustrates that the certainty-equivalent value of the uncertainty
about closure delay is highest when the closure reduction is greatest. The certainty-equivalent
value declines to zero when no reduction is provided by the strategy. At the 25 hour guarantee
level, the certainty equivalent value offered by the associated strategy is equivalent in value to 12
hours of monthly delay. At the 5 hour level, the certainty equivalent value is equal to
approximately 3 hours of monthly delay.
With information on the relationship between average monthly delay and the cost of unreliability
(the monetized cost of traffic delay), there is now a basis for valuing the severity of different
monthly closure durations and for evaluating remediation strategies. (The example in this figure
was developed to illustrate a principle and should not be used for policy guidance. There may be
other formulations of the data and associated options that should be considered.)
Figure C.2 - Illustrative Example of European Put Option for Avalanche Closure Delay
16
12
8
4
0
25
20
15
10
Closure Delay Guarantee, Hours per Month (I)
5
0
There often is an additional complexity of the reliability problem associated with rare events. That
complexity is that truly rare events play out over very long time periods and can occur at any time
VALUATION OF TRAVEL-TIME RELIABILITY FOR RARE EVENTS Page C-7