Off-Ramp Coupling Conditions Devoid of Spurious Blocking and Re-Routing

Salehi, Najmeh; Somers, Julia; Seibold, Benjamin · 2018 · Crossref

DOI: 10.1177/0361198118792997

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Summary

This paper addresses a critical modeling deficiency in macroscopic traffic flow simulations on highway networks, specifically regarding coupling conditions at off-ramp nodes. Standard First-In-First-Out (FIFO) models unrealistically predict zero traffic flow through a node if an off-ramp is clogged, ignoring the reality that vehicles on multi-lane highways can bypass exit queues. Conversely, existing non-FIFO models allow flow past clogged ramps but introduce "spurious re-routing," where vehicles intended for the exit are incorrectly accounted for as continuing on the highway, violating driver route choices. The authors propose a new coupling model, FIFOQ (FIFO with Queue), designed to preserve the realistic flow capabilities of non-FIFO models while strictly adhering to prescribed split ratios and preventing artificial re-routing. The study utilizes a single-class, lane-aggregated Lighthill-Whitham-Richards (LWR) model to describe traffic density evolution on network edges. The core innovation is the introduction of a "vertical queue" variable that tracks the excess accumulation of vehicles intending to exit versus those continuing straight. This queue ensures that when an off-ramp is blocked, the model accounts for the buildup of exiting vehicles without blocking the entire highway flow. The authors derive the mathematical formulation for FIFOQ, ensuring that at most one queue is active at any time to minimize computational overhead and avoid unrealistic congestion states. They also detail the implementation of this model within a Cell Transmission Model (CTM) framework, including specific algorithms for handling queue depletion during time-stepping. To validate the model, the authors conduct a comparative simulation involving a 1-in-2-out node representing a 4-lane highway and a single-lane off-ramp. The experiment simulates a scenario where the off-ramp is initially clogged and then cleared after nine minutes. Results demonstrate that the FIFO model severely underestimates total flow by blocking all traffic during the clogged period. The non-FIFO model maintains highway flow but fails to respect the split ratio, resulting in a distorted ratio of highway-to-ramp flow (7.81:1 instead of the prescribed 5:1) due to the loss of queued exiting vehicles. In contrast, the FIFOQ model achieves a nonzero highway flow during the blockage while correctly tracking the accumulation of exiting vehicles. Upon clearing the ramp, FIFOQ releases these stored vehicles, resulting in a total flow ratio that matches the historic split ratio (5:1) and a higher, more realistic total off-ramp flux than either competing model. The significance of this work lies in providing a robust, computationally efficient coupling condition for macroscopic traffic models that resolves the trade-off between realistic flow dynamics and route fidelity. By using vertical queues to track vehicle type imbalances, FIFOQ eliminates the need for complex multi-commodity models that require advance knowledge of individual vehicle destinations. This approach allows traffic engineers and researchers to simulate highway networks with greater accuracy, particularly in scenarios involving congestion at exits, without introducing unphysical artifacts like spurious re-routing or total node blockage.

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• traffic density