Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
effect of the strategy on improving reliability and then perform the same options-theoretic
computation under the improved conditions.
The policy may, of course, affect both the average travel time and its volatility. For simplicity,
assume that the policy does not affect average travel times, but rather reduces the variance
(volatility) of travel times. For example, a traveler information system, incident management
system, or some other treatment may reduce the travel-time variance such that the options value of
unreliability is now only 30 seconds per mile on the roadway segment described above. There is
now a savings of approximately $3.5 million per year for each hour of the day that is affected by
the treatment.
Thus, a treatment that costs less than $3.5 million per year would be worthwhile (cost-effective) to
implement due to its impact on improving reliability. In a real-world application, an improvement
to traffic information systems might generate improvements in reliability over many years. As
traffic grows, values of time evolve and the computation of the options value of reduced volatility
are repeated for each period of time during the life of the improvement. These future savings can
be reduced to a present value in the planning year by discounting the stream of annual options
values. The advantage of the certainty-equivalent approach is that user benefits from
improvements in travel-time reliability can be treated deterministically, just as they are in other
traditional user benefit categories in standard transportation investment or policy evaluations.
Characterizing Reliability for Recurring Events
Travel-time reliability options formulations have been developed to correspond to the valuation of
reliability related to recurring and rare events. The stochastic nature of rare events (such as bridge
failures, road closures due to flooding, and other events) is quite different than the uncertainty that
characterizes recurring events. Whereas recurring events (like crashes, weather-related events, and
other common sources of travel-time variation) can generally be characterized using a log-normal
distribution, the stochastic nature of rare events necessitates adapting the more traditional options
formula. For rare events, an application of stochastic variables displaying a generalized extreme
value (GEV) distribution has been adopted and is presented in Appendix C.
Since both recurring and rare events cause unreliability, recurring and rare events are distinguished
only by differences in the frequency distributions that characterize them. Unreliability produced by
recurring events is assumed to display statistical behavior best represented by normal distributions
(often, log-normal distributions).
In the case of unreliability caused by recurring events, it often is possible to observe the effect of
these events on network performance by directly observing the variability of speeds or travel time.
This is because normal distributions often best describe high-frequency phenomena, so the chances
of having useful network performance data improves.
In the case of unreliability caused by rare events, variability in speeds or travel time may not be
measured directly. For example, the numbers of bridge failures may so low that changes in
performance measures may be difficult to study directly. (In cases such as major accidents, for
example, there may be a way to directly measure the influence of these rare events on speed
variability.) The next section describes the options theoretic approach for valuing reliability for
recurring events.
DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-8