Evaluating Alternative Operations Strategies to Improve Travel Time ...

t
SHRP 2 L11: Final Appendices
d
1
=
2
ln( VT
/ I) + ( r+ σ / 2)( T −t)
σ ( T − t)
Thus,
2
ln( VT
/ I) + ( r+ σ / 2)( T −t)
d1
=
σ ( T − )
The desired speed = 32.41 mph (2001 average speed)
The guaranteed speed (equivalent to the 2001 average speed) =
V
T
= I =
= 32.41 mph
Evaluate the standard normal distribution at d 1 and d 2.
N (d 1 ) = N (0.12256) = 0.4512
N (d 2 ) = N (-0.12255) = 0.5488
The certainty-equivalent value of reliability is
rT ( t)
PV ( ,) t Ie − −
= Nd ( ) −VNd
( )
T
2 T 1
= 3.16 mph
From this calculation, a commuter is willing to accept a reduction of 3.16 mph in his/her
average speed to eliminate travel-time variability.
E. Convert the certainty-equivalent value from miles per hour to minutes per mile.
The new average speed at which the commuter is willing to travel if unreliability is eliminated
= 32.41-3.16 = 29.25 mph
Time to cover 1 mile at the initial average speed =
Time to cover 1 mile at the new average speed =
∴The certainty-equivalent time per mile that the user is willing to “pay” to
eliminate unreliability is given by
Step 3 – Evaluate the Treatment that Reduces Unreliability
A. Calculate a new set of speed data parameters after implementation of the
treatment, which is reflected in the 2002 data.
B. Calculate the certainty-equivalent value for the after (2002) scenario.
SAMPLE PROBLEM-QUANTIFYING THE ECONOMIC BENEFIT OF IMPROVING TRAVEL-TIME RELIABILITY Page D-8