Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
public without a mitigation strategy. The present value of the costs of installing the pumping
system is $101 million. The agency now has to ask the question, “Is it worth the (present value)
$101 million to mitigate the (present value) of $100 million in impact cost?” Given the current
state of disparity between the investment cost and the expected losses, traditional capital
investment models indicate that investment in the pumps would not be a rational decision by the
agency. This methodology, however, does not incorporate the uncertainty of the event in a formal
way.
The Solution
The options theoretic approach could be used to calculate the certainty-equivalent value of the
uncertainty regarding the occurrence and number of hurricanes.
Data Needs
• Information or data on the likelihood of hurricane events in the region to construct a
distribution of hurricane events.
Cautions
• By their very nature, it will be unlikely that the probability distribution for the rare event
can be estimated from historical data.
Procedure
The steps involved in the calculation are outlined below:
Step 1 – Characterize the Rare Event
The incidence of the disruptive hurricanes that cause these effects is infrequent, and not easily
predictable. Historical evidence suggests that in this particular region, hurricane incidence can be
characterized by a generalized extreme value (event) statistical distribution type known as the
Gumbel distribution.
A. Obtain data or information on the likelihood of future hurricane events in the region.
B. Estimate parameter values from the Gumbel distribution to describe the expected
probability distribution for hurricane events. Be certain that the rare event can be
characterized by the Gumbel distribution.
VALUATION OF TRAVEL-TIME RELIABILITY FOR RARE EVENTS Page C-14