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The flow congestion model provides a realistic form of depicting congestion by considering the spatial dynamic characteristics of traffic flow. For reducing the complication of analysis, previous studies adopted the α − β − γ preference of travel time, arrival early and late penalties. This handling method destroys the continuity of user equilibrium (UE) inflow rate as pointed out by Li and Huang (2017). In this paper, we investigate the single-entry traffic corridor with continuous scheduling preference (CSP) and develop a customized method to find the computational solution of UE flow pattern. Analytical and numerical results show that the introduction of CSP lets inflow rate of early arrivals first increase then decrease. This extends the knowledge given by classical bottleneck model and flow congestion model with α − β − γ preference. Another finding is that, even though the introduction of CSP can smooth inflow rate at departure time of the punctual commuter and make the UE flow pattern more stable, a series of shock waves still exist. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of staggered shifts on the user equilibrium (UE) state in a single-entry traffic corridor with no late arrivals from the analytical and numerical perspective. The LWR (Lighthill–Whitham–Richards) model and the Greenshields’ velocity–density function are used to describe the dynamic properties of traffic flow. Propositions for the properties of flow patterns in UE, and the quasi-analytic solutions for three possible situations in UE are deduced. Numerical tests are carried out to testify the analytical results, where the three-dimensional evolution diagram of traffic flow illustrates that shock and rarefaction wave exist in UE and the space-time diagram indicates that UE solutions satisfy the propagation properties of traffic flow. In addition, the cost curves show that the UE solutions satisfy the UE trip-timing condition. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to extend the work of DePalma and Arnott (2012) by investigating the solutions for social optimum (SO) and user equilibrium (UE) assignment in a single-entry traffic corridor with consideration of both early and late arrivals. The LWR model and the Greenshields’ relation are used to describe the dynamic properties of traffic flow. The closed-form SO solution and quasi-analytic UE solution are developed and well illustrated by numerical examples. It is shown that the SO assignment is associated with a smooth cumulative outflow curve, while the UE assignment will result in recursively generated cumulative inflow and outflow curves. In UE, however, the system finally becomes a free flow state. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of coarse toll on the user equilibrium (UE) state in a single-entry traffic corridor with early and late arrivals from analytical and numerical perspective. Unlike previous studies on traffic tolls, the flow congestion model is used to take into account the dynamic propagation of traffic flow. The LWR (Lighthill–Whitham–Richards) model and the Greenshields' velocity–density function are used to describe the dynamic properties of traffic flow. The quasi-analytic solutions of the three possible cases in UE due to different charges are derived. Both analytical and numerical results indicate that rarefaction waves and shock waves appear in the corridor under the coarse toll. The three-dimensional evolution diagrams of traffic flow and space–time diagrams illustrate that the introduction of course toll lets flow patterns more complicated. This extends the knowledge given by the classical bottleneck model. • Effects of coarse toll on user equilibrium state are studied in traffic corridor. • Quasi-analytic UE solutions are derived and numerical examples are presented. • Three possible situations of course toll under UE principle are discussed in detail. • Shock and rarefaction wave exist in UE state. [ABSTRACT FROM AUTHOR]