Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
the degradation of network performance due to rare events (such as bridge failures, flooding, and
other natural disasters, presented in Appendix C).
Although recurring and rare phenomena arise out of processes with very different stochastic
properties, the challenge for analyzing these different sources of reliability is similar and the
solutions have a common approach. In both cases, the uncertainty that these two processes impose
upon the cost of travel may be converted to a certainty-equivalent measure to enable the use of
conventional evaluation methods for determining the value of reliability.
In the case of rare events, the facts are different, but the virtue of the certainty-equivalence notion
is the same. For example, if our knowledge of the processes that cause a bridge failure can be
characterized by an assignment of a probability distribution to the bridge-failure event, then the
uncertainty about the occurrence of a bridge failure can be used to derive a certainty-equivalent
measure of the number of such events. This quantity can then be associated with the resulting
impacts on network performance and valued using conventional techniques for measuring network
performance. These techniques involve measuring the incremental delay associated with the bridge
failure and the time period over which the delay persists.
The ultimate goal of valuing network unreliability is to guide investments into policies or technical
solutions that reduce the economic burden of unreliability. Thus, the methodology for valuing
unreliability naturally incorporates considerations of present valuation (the time value of money)
and the discount rates associated with considering event timing.
Measuring the value of reliability involves five considerations:
• Options Theory
• A Real Option for Travel Time
• Measuring the Economic Cost of Unreliability
• Evaluating Reliability Management Policies
• Characterizing Reliability for Recurring Events
Options Theory
The field of economics that provides a mechanism for converting uncertainty into a certaintyequivalent
value is options theory. Options theory provides insights into the value of current and
future opportunities whose value is not known with certainty, but whose opportunities can be
characterized probabilistically. The classic application of options theory in a financial context is to
answer such questions as "How much should I be willing to pay to be able to buy (or sell) a
security at a given point in the future at a specific, pre-arranged price?" An option to buy at a fixed
price is a "call option" and an option to sell at a fixed price is a "put option."
Economists have determined that many financial arrangements that involve valuing uncertainty
(such as insurance contracts, prepayment penalties on mortgages, or car lease terms) can be
analyzed as financial options of one sort or another. In insurance, for example, we might ask how
large an insurance premium I should be willing to pay to avoid the risk associated with the loss
from a fire. The option can provide an opportunity to buy or sell (“exercise the option”) at a
specific point in time or any time up to a specific time.
The opportunity to buy or sell at a specific point in time is a “European option” and the
opportunity to buy or sell at anytime up to a specific time is an “American option.” Simple
examples of the application of a European and an American option are described below:
DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-4