The marginal social cost of travel time variability

• We study the marginal social cost of travel time variability (MSCTTV) of car users.
• We amend the bottleneck model of road congestion by adding a random delay.
• We derive the Nash equilibrium and the MSCTTV for users with (α, β, γ) preferences.
• The MSCTTV is strictly lower than the VTTV, which assumes exogenous congestion.
• Data for the Paris area suggests that in practice, the gap is substantial.

This paper investigates the cost of travel time variability for car users at the peak hour. In particular, we derive the marginal social cost of travel time variability, which takes the feedback of travel time unreliability on the congestion profile into account. This is in contrast with the value of travel time variability, which treats congestion as an exogenous phenomenon. Congestion is modeled using the standard bottleneck model of road congestion, which we amend by adding a random delay. For individuals with (α, β, γ) preferences and uniformly distributed delays, the marginal social cost of travel time variability is strictly lower than the value of travel time variability. Moreover, we show that the former tends toward the latter when σ, the standard deviation of the random delay, tends toward +∞. For normally distributed delays, numerical application leads to similar conclusions. Analysis of data from the Paris area suggests that given the plausible range of σ, the marginal social cost of travel time variability is markedly lower than the value of travel time variability. When appraising the economic benefits of reliability improvements, one should prefer the marginal social cost of travel time variability for the peak period, and the value of travel time variability for the off-peak period.