Queuing Pricing with Time-Varying and Step Tolls: A Mathematical Framework for User Classification and Behavioral Analysis

Chen-Hsiu Laih ()
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Chen-Hsiu Laih: Department of Merchant Marine, National Taiwan Ocean University, No. 2 Beining Rd., Keelung 202, Taiwan

Mathematics, 2025, vol. 13, issue 13, 1-37

Abstract: This study investigates user behavior at a bottleneck under two queuing pricing schemes: the optimal time-varying toll and the optimal multi-step toll. A mathematical model is developed to classify users based on toll status and arrival timing, further distinguishing between normal compliance and deliberate avoidance behaviors. Under the optimal time-varying toll, queuing is fully eliminated, no avoidance behavior occurs, and the user distribution remains consistent with the non-toll equilibrium. In contrast, the optimal n -step toll induces regular avoidance intervals before each toll change, with each interval exhibiting a uniform duration. The analysis reveals a structured classification of users into 3 n + 2 behavioral groups, with predictable proportions in each category. These findings illustrate how step tolling affects user decision-making and temporal arrival patterns, offering valuable insights for the design of congestion pricing and traffic demand management strategies. Overall, the study highlights the practical applicability of queuing theory to transportation systems and contributes to the optimization of dynamic tolling mechanisms.

Keywords: bottleneck; queuing pricing; deliberate avoidance; optimal time-varying toll scheme; optimal step toll scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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