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Proportional-Switch Adjustment Process with Elastic Demand and Congestion Toll in the Absence of Demand Functions

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  • Lie Han

    (Wuhan Textile University)

Abstract

This paper proposes a dynamic process to formulate the day-to-day evolution process of traffic flows, which is called “proportional-switch adjustment process with elastic demand (PSAP-ED)”. PSAP-ED extends Smith’s process (Smith in Transp Sci 18:259–304, 1984) from the case of fixed demand to the case of elastic demand and characterizes the process of approaching equilibrium states from non-equilibrium states in traffic networks. Several desirable properties of PSAP-ED are provided, such as the equivalence between user equilibrium and the stationary state of PSAP-ED, the existence and uniqueness of the stationary flow state, and the convergence of PSAP-ED. We also show that a proper fixed toll scheme can drive PSAP-ED to evolve towards system optimum states. When the demand functions are unknown, the trial-and-error procedure presented by Yang et al. (Transp Res B 38:477–493, 2004) can be modified and applied in the context of PSAP-ED. Furthermore, we develop a more efficient dynamic congestion toll scheme for PSAP-ED in the absence of demand functions. The properties of PSAP-ED and the effectiveness of toll schemes are demonstrated by a numerical example.

Suggested Citation

  • Lie Han, 2022. "Proportional-Switch Adjustment Process with Elastic Demand and Congestion Toll in the Absence of Demand Functions," Networks and Spatial Economics, Springer, vol. 22(4), pages 709-735, December.
    • Handle: RePEc:kap:netspa:v:22:y:2022:i:4:d:10.1007_s11067-022-09565-w
    DOI: 10.1007/s11067-022-09565-w
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