A probabilistic approach for queue length estimation using license plate recognition data: Considering overtaking in multi-lane scenarios

Multi-section license plate recognition (LPR) data has emerged as a valuable source for lane-based queue length estimation, providing both input–output information and sampled travel times. However, existing studies often rely on restrictive assumptions such as the first-in-first-out (FIFO) rule and uniform arrival processes, which fail to capture the complexity of multi-lane scenarios, particularly regarding overtaking behaviors and traffic flow variations. To address this issue, we propose a probabilistic approach to derive the stochastic queue length by constructing a conditional probability model of no-delay arrival time (NAT), i.e., the arrival time of vehicles without experiencing any delay, based on multi-section LPR data. First, the NAT conditions for all vehicles are established based on upstream and downstream vehicle departure times and sequences. To reduce the computational dimensionality and complexity, a dynamic programming (DP)-based algorithm is developed for vehicle group partitioning based on potential interactions between vehicles. Then, the conditional probability of NATs of each vehicle group is derived and a Markov Chain Monte Carlo (MCMC) sampling method is employed for calculation. Subsequently, the stochastic queue profile and maximum queue length for each cycle can be derived based on the NATs of vehicles. Eventually, we extend our approach to multi-lane scenarios, where the problem can be converted to a weighted general exact coverage problem and solved by a backtracking algorithm with heuristics. Empirical and simulation experiments demonstrate that our approach outperforms the baseline method, demonstrating significant improvements in accuracy and robustness across various traffic conditions, including different V/C ratios, matching rates, miss detection rates, and FIFO violation rates. The estimated queue profiles demonstrate practical value for offset optimization in traffic signal control, achieving a 6.63% delay reduction compared to the conventional method.