This paper introduces a spatial queueing model for a single bottleneck during morning peak hours. Utilizing the logistic function and after appropriate calibration, it articulates the arrival and departure flows in continuous, differentiable terms. By validating the model across different peak periods and locations, the demand model’s robustness is superior to other commonly used functions. This model also incorporates constant or varying capacity scenarios. It effectively captures key aspects of morning peak traffic, including the emergence of hysteresis loops in fundamental diagrams (FDs) of density and flow. The model’s multi-stage approach recognizes three distinct phases in traffic flow: freeflow, transition, and queued segments, ensuring spatial consistency in flow and density across these stages. It accounts for the growth of the queued segment and vehicle spillback under various bottleneck intensities, with the resulting FDs for speed and density also displaying hysteresis loops. The calibration of model parameters utilizes time-series data of traffic flow and density space–time maps derived from real-world data. The validation results accurately reflect real traffic scenarios, emulating the counterclockwise hysteresis loops observed in density and its heterogeneity, and provide both planar and three-dimensional FDs at different points along the traffic link, each mirroring real-life traffic patterns. Additionally, a comparison with the cell transmission model (CTM) reveals that the proposed model exhibits superior generalization and robustness.

中文翻译：

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符合微观基本图和滞后性的物流到达和离开的多阶段空间排队模型


本文介绍了早高峰时段单一瓶颈的空间排队模型。利用逻辑函数并经过适当的校准后，它以连续、可微分的方式阐明到达和出发流程。通过在不同的高峰时段和地点验证模型，需求模型的稳健性优于其他常用函数。该模型还包含恒定或变化的容量场景。它有效地捕获了早高峰交通的关键方面，包括密度和流量基本图 (FD) 中出现的磁滞回线。该模型的多阶段方法识别交通流的三个不同阶段：自由流、过渡和排队路段，确保这些阶段的流量和密度的空间一致性。它解释了在各种瓶颈强度下排队段和车辆溢出的增长，由此产生的速度和密度 FD 也显示出磁滞回线。模型参数的校准利用交通流的时间序列数据和从现实世界数据导出的密度时空图。验证结果准确反映了真实的交通场景，模拟了在密度及其异质性中观察到的逆时针磁滞回线，并提供了交通链路沿线不同点的平面和三维 FD，每个点都反映了现实生活中的交通模式。此外，与细胞传输模型（CTM）的比较表明，所提出的模型表现出优异的泛化性和鲁棒性。