Travel cost budget based user equilibrium in a bottleneck model with stochastic capacity

•Commuters are assumed to choose departure time by minimizing their travel cost budget.•Consideration of travel cost budget yields seven possible equilibrium patterns.•Closed form solutions to all possible equilibrium patterns are derived.•The rationality of the patterns has been investigated.•Dependence of travel cost and the duration of peak hours on the commuters' risk attitude has been derived.