  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.
