The commuters choose their departure times from home to work in the morning to maximize their own scheduling utility. Step tolling models with homogeneous and heterogeneous preferences are presented. The properties of the models and the optimal step toll schemes with constant and linear time-varying marginal activity utilities are analytically explored and compared. It was found that for a given number of toll steps the efficacy of a step toll in terms of queuing removal rate is higher in the activity-based bottleneck model with linear marginal utilities than in the conventional bottleneck model with constant marginal utilities, and ignoring the preference heterogeneity of commuters would underestimate the efficacy of a step toll.
- Activity-based bottleneck model
- Homogeneous and heterogeneous preferences
- Step tolling
- Time-varying marginal activity utility
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