Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
SWY (2005) use a mixed logit model with both RP and SP data from the unique setting of
California’s SR-91 express lanes. This setting is unique because a driver using the congested
general-purpose lanes can pay a toll and enjoy both a faster speed of travel and (an assumed) zero
variability in travel speed. This allows SWY to estimate both the value of travel time savings and
the value of unreliability. Using the revealed preference data, SWY measure the value of travel
time at $21.46/hour (93 percent of the average wage rate). The study was conducted under 4-hour
AM peak conditions, which expose general-purpose lane users to considerable volatility in speeds
and travel times. Under the conditions in place, their model yields a value of unreliability of
$19.56 per hour. When applied to the 10-mile segment of SR-91, the value of unreliability is then
measured to be $0.52 (for the 10-mile segment).
The SWY paper provides enough information to enable measuring the volatility of speeds in a
manner compatible with the options theoretic approach. Specifically, the median speed on the
general-purpose (free) lanes is reported to be 53 mph. The corresponding 20th percentile speed
(imputed from the 80th percentile travel time, in minutes) is 46 mph. This speed data, combined
with the assumption of a log-normal distribution of speeds, yields a log-mean speed of 3.9703 and
the log-standard deviation of speed of 0.1683. Using the log-standard deviation and the
assumption of a 5% discount rate (to which the calculations are very insensitive), the put option
value can be calculated for an option whose life lasts long enough for the traveler to traverse the
10-mile facility.
All that remains to be done is to hypothesize the "speed guarantee" appropriate to this setting. In
our characterization of unreliability, the average speed experience of travelers, measured over
time, is taken as the speed against which they measure unreliability and, thus, is the desired
"guaranteed" speed. Unfortunately, SWY do not know the average speed experience at the various
times their RP sample travels. All they know is the median speed over across the entire 4-hour
AM peak (53 mph). However, we can test various speed guarantees in the options formula and see
what speed guarantee corresponds to SWY's revealed $0.52 value of reliability over the 10-mile
facility. That speed is 57 miles per hour.
Alternatively, using the 53 mph peak period median value as the guaranteed speed (though not the
correct datum for the options approach), the value of reliability calculated via the options approach
is $0.29. Measured either way, it is clear that the options approach and the RP/SP approach yield
quite consistent values. Indeed, SWY also estimate a stated preference model, which ends up
producing a value of reliability that is much smaller than the revealed preference-based estimate.
Given the computational cost and flexibility of the options approach, it is clear that it is a valuable
method of evaluating travel unreliability.
Conclusions for the Options Theoretic Approach
This appendix presents an options theoretic approach for the valuation of travel-time reliability.
Options theory is a well-established methodology from the field of financial economics used for
the valuation of assets in the presence of uncertainty. Whereas options theory in finance deals with
the dollar value of financial instruments, real options deal with stochastic variables when quantities
are measured in terms of real units, such as time or actual commodities.
Given the novel approach developed in this research, an extensive review of the options theoretic
approach was performed by a number of expert reviewers. Experts on options theory and finance
were consulted, providing multiple rounds of review of the appropriateness and validity of the
approach. Expert reviewer comments largely focused on the mapping of the travel time reliability
DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-31