Prediction of Arrival Profiles and Queue Lengths along Signalized Arterials by using a Markov Decision Process

Geroliminis, Nikolaos; Skabardonis, Alexander · 2005 · Crossref

DOI: 10.1177/0361198105193400112

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Summary

This paper addresses the need for robust analytical models to estimate queue lengths and travel times on signalized urban arterials, particularly when loop detector data is incomplete, inaccurate, or aggregated. Existing models, such as Pacey’s and Robertson’s, often fail to accurately estimate spatial queue extents or require site-specific calibration. The authors propose a methodology based on a two-step Markov Decision Process (MDP) combined with kinematic wave theory to predict platoon arrival profiles and queue lengths downstream from a known starting flow. The model treats traffic dynamics between successive signals as a recursive process. First, platoon dispersion is modeled using the Lighthill-Whitham-Richards (LWR) kinematic wave theory, assuming a quadratic flow-density ($q-k$) relationship. This allows for the calculation of how vehicle platoons spread due to speed variations and interactions. The model accounts for heterogeneous driver behavior by applying different $q-k$ diagrams to the head and tail of platoons, capturing the slower dispersion of trailing vehicles. Second, the dispersed platoon interacts with the downstream traffic signal, modeled as a "signal filter." This interaction determines whether vehicles stop (forming queues) or pass through, generating a new departure profile that serves as the input for the next downstream segment. The MDP formulation ensures that future states depend only on current arrivals, allowing for stochastic handling of variable signal settings. The proposed methodology was applied to two real-world test sites and validated against microscopic simulation results. The study demonstrates that the model can accurately estimate queue lengths and predict travel times even without precise detector data. Specifically, the inclusion of driver heterogeneity improved the estimation of platoon tail dispersion, which standard kinematic wave models often overlook. The results showed close agreement between the analytical model’s queue estimates and those from microscopic simulations, confirming the model's ability to capture complex traffic dynamics, including platoon merging and queue formation. The significance of this work lies in providing a computationally efficient, analytical tool for arterial performance monitoring and signal timing optimization. Unlike simulation-based approaches, this model can operate with limited or faulty surveillance data, making it suitable for online estimation systems. By accurately predicting queue lengths and arrival profiles, the model supports better assessment of signal coordination needs and traffic management strategies on urban arterials.

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• mental model of traffic

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• Theoretical Contribution: computational model