Evaluating Alternative Operations Strategies to Improve Travel Time ...

SHRP 2 L11: Final Appendices
Thus,
2
⎛32.67 ⎞ ⎡ ⎛39.12
⎞⎤
ln ⎜ ⎟+ ⎢0.05+ ⎜ ⎟⎥×
0.0000863
⎝32.67 ⎠ ⎝ 2 ⎠
d1
=
⎣
⎦
= 0.18176
39.12×
0.0000863
d2 = d1 −σ
( T −t)
= 0.18176 − 39.12 0.0000863 =−0.18173
Evaluate the standard normal distribution at d 1 and d 2.
Nd (
1) = N(0.18175) = 0.4279
Nd (
2) = N( − 0.18174) = 0.57211
−rT
( −t)
PV ( ,) t = Ie Nd ( ) −VNd
( )
T
2 T 1
−0.05(0.0000086)
= 32.67 e (0.57211) − 32.67(0.4279)
= 4.71 mph
A commuter is willing to accept a reduction of 4.17 mph in his/her average speed
to eliminate the travel-time variability.
E. The new average speed at which the commuter is willing to travel if unreliability
is eliminated = 32.67-4.71 = 27.96mph
1
Time to cover 1 mile at old average speed = minutes
32.67 ×60
1
Time to cover 1 mile at new average speed = minutes
27.96 ×60
∴The certainty-equivalent time per mile that the user is willing to “pay” to
eliminate unreliability is given by
⎛ 1 1 ⎞
PV (
T
, t) = ⎜ − ⎟× 60 = 0.31 minutes per mile
⎝27.96 32.67 ⎠
DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-44