<abstract><p>The accurate estimation of time delays is crucial in traffic congestion analysis, as this information can be used to address fundamental questions regarding the origin and propagation of traffic congestion. However, the exact measurement of time delays during congestion remains a challenge owing to the complex propagation process between roads and high uncertainty regarding future behavior. To overcome this challenge, we propose a novel time delay estimation method for the propagation of traffic congestion due to accidents using lag-specific transfer entropy (TE). The proposed method adopts Markov bootstrap techniques to quantify uncertainty in the time delay estimator. To the best of our knowledge, our proposed method is the first to estimate time delays based on causal relationships between adjacent roads. We validated the method's efficacy using simulated data, as well as real user trajectory data obtained from a major GPS navigation system in South Korea.</p></abstract>

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