Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
from available data or extrapolated from other studies. In the case of an a.m. peak-hour study,
travel times or speed data could be assembled for that time of day for a year of data. The log-mean
and log-standard deviation would then be computed from this data sample. In the case in which the
average travel time for the entire weekday is of interest, daily average travel times could be
constructed for each of 250 weekdays in a year.
The life of the option is determined differently in each of these two cases. In the case of the a.m.
peak-hour study, the life of the option would be set to one hour and the time period would be
examined. In the case of the study of weekday performance, a 24-hour life would be assumed. In
all cases, these lives would be expressed in years for consistency with the standard interest rate
term.
The interest rate parameter in the calculation is provided to respect the yield on risk-free
alternative uses of the travelers' resources. In short-life options, such as those used to represent
recurring unreliability problems, the effect of different interest-rate assumptions is not particularly
material. Nevertheless, it is important to place the analysis properly in its surrounding, economic
conditions. Hence, for short-life options, short-term interest rates (expressed on a per annum basis)
should be used to represent these opportunity costs.
The approach developed for recurring events can be generalized, such that the value of
unreliability is calculated based on the speeds and travel times experienced on the facility. This
approach does not necessarily rely on specific information about the source of the unreliability, so
long as the source and the speeds are log-normally distributed. Thus, system performance data
determine the underlying stochastic nature of unreliability on a facility. Table B.3 summarizes the
disruption data identified in the SHRP2 L03 project for use by agencies in reporting reliability
performance measures.
Reliance on the normal or log-normal distribution is standard in options theory, and a requirement
for the use of the Black-Scholes formulation. The Black-Scholes model is based on the normal (or
log-normal) distribution of the underlying asset. In the real option for travel time reliability, the
assumed asset is speed, and so the assumption of the log-normality of speed (e.g., to compute the
certainty-equivalent measure in minutes of travel time) is an assumption for the options theoretic
approach.
The log-normal has been shown to be the most appropriate distribution for high frequency speed
data collected from roadways. Traffic engineering research has confirmed the validity of the use of
log-normal distribution for travel time and speed. The lower bound of zero and longer right tail of
the distribution make the log-normal particularly appropriate for the typically skewed speed data.
SHRP2 L03 cites Rhaka et al (2006), which confirms the use of the log-normal assumption for
speeds and travel times in the context of travel time reliability. Other recent papers include El
Faouzi and Maurin (2007), Emam and Al-Deek (2006), Leurent et. al. (2004), and Kaparias et. al.
(2008).
DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-16