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Heterogeneous Commuters and Sustainable Transportation With Extending Usage-Dependent Peak-Load Pricing: Heterogeneous Commuters and Sustainable Transportation
Abstract
This study extends the bottleneck model of commuting by incorporating heterogeneous arrival windows to reflect the diverse professional and institutional schedules in modern urban environments. By expanding Vickrey's foundational framework, this analysis demonstrates how group-specific timing constraints dictate the formation of equilibrium queues. The resulting congestion follows a triangular–plateau–triangular profile: while excess demand generates early and late arrival “tails,” a central plateau emerges, representing the union of all group-specific penalty-free windows. By deriving closed-form expressions for tail length and plateau height, the model reveals that while schedule delays are technically unavoidable when demand exceeds system flexibility, queuing represents a pure waste of resources. To mitigate these inefficiencies, this study proposes two decentralization instruments—a time-dependent toll mirroring queue slopes and a simplified usage-based toll—both of which eliminate queuing without compromising travel feasibility. Ultimately, the findings highlight a critical efficiency-equity trade-off, as commuters with flexible windows avoid penalties by occupying the plateau, whereas those with rigid schedules are forced to absorb the majority of delay costs.
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