The variability of travel time modifies the rush hour traffic and the cost of commuting. The bottleneck model of road congestion with fixed peak-load demand is augmented of an additive random delay. When individuals have (α-β-γ) preferences, there exists a unique Nash equilibrium. The variability of travel time leads to departure rates that are spread more evenly over the rush hour than when travel times are deterministic. This equilibrium mechanism mitigates both congestion and the cost of unreliability. This implies that " single-traveler models, " which treat congestion as an exogenous phenomenon, overestimate the value of reliability for the rush hour. Application with two distributions, uniform and exponential, provides an appraisal of the extent of the overestimation.