Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
Valuing Reliability for Recurring Events
Unreliability produced by recurring events is defined as the variability in travel time that occurs as
a result of events such as accidents, incidents, and poor traffic-signal timing. Over the course of a
year, travel times may display high volatility at the same time of day, on individual roadway
segments, and on specific paths or routes.
On a somewhat less frequent, but nonetheless recurring basis, weather and other random, natural
events can impair network performance. Normal rain events, for example, impair network capacity
and performance in a transitory fashion.
The certainty value of unreliability associated with recurring events can be derived by using
options valuation techniques that employ a log-normal frequency distribution. This is achieved by
recasting the question of reliability in terms of a speed insurance problem, which, in turn, can be
addressed using options theory.
The options theoretic approach answers the hypothetical question: “How large a reduction in
average speed should a traveler be willing to accept in return for a guaranteed minimum travel
speed?” The options formula determines the speed reduction premium a traveler would be willing
to pay for a minimum-speed guarantee insurance policy.
A simple speed insurance case is one in which the “coverage” of the insurance is relatively short
and the option can be invoked at the end of the life of the insurance period. Recast as a speedreliability
problem, this makes sense because we are interested in knowing the burden placed on
the traveler, who finds that the speed has been impaired by the volatility created by recurring
events.
A short-lived option that pays off at the end of its life is a European put option—that is, an option
of finite life that can be exercised at the end of the option’s life. Such an option compensates the
holder for any losses incurred if actual performance is poorer than the contracted performance
guarantee. If performance is greater than the expected performance guarantee, then the option has
no value.
A travel-time option, which is expressed as a certainty-equivalent of delay measured by speed or
additional travel time, can be monetized by using the dollar value of travel time. However, to
preserve the underlying distributional assumption of log-normality, it is better to compute the real
option in terms of speed.
Equation 1 - Speed Guarantee for Recurring Events
DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-9