Additive measures of travel time variability

Abstract

This paper derives a measure of travel time variability for travellers equipped with scheduling preferences defined in terms of time-varying utility rates, and who choose departure time optimally. The corresponding value of travel time variability is a constant that depends only on preference parameters. The measure is unique in being additive with respect to independent parts of a trip. It has the variance of travel time as a special case. Extension is provided to the case of travellers who use a scheduled service with fixed headway.

The cost of travel time variability: Three measures with properties

“…The following theorem is stronger than the results established in Engelson and Fosgerau (2011). The earlier paper demonstrated first that additivity required ℎ to be constant.…”

“…Proof. Engelson and Fosgerau (2011) prove that the scheduling measure is additive when ℎ, are as stated in the theorem. Thus the "if" part of the theorem has already been established.…”

“…From Theorem 4, additive scheduling measures have constant ℎ and ( ) = ℎ + � − 1� with ≠ 0, or ( ) = ℎ + . Engelson and Fosgerau (2011) show that then…”

“…Theorem 2 in Engelson and Fosgerau (2011) establishes that then ℎ is constant. We do not repeat this proof here.…”

“…The use of this model to value travel time variability is due to Fosgerau and Engelson (2011) who used linear utility rates to find a cost measure that is linear in the mean and variance of the travel time distribution when ℎ is constant. In this case, the cost measure is additive over independent travel time components, and the additivity property was characterized in Engelson and Fosgerau (2011). Engelson (2011) explored exponential and quadratic utility rates.…”