Cycle-by-Cycle Queue Length Estimation for Signalized Intersections Using Sampled Trajectory Data

to be constant and the input and output flows reach equilibrium (2, 10). Further improvement includes providing queue length in small time stamps on the basis of vehicle arrival and departure profiles, first applied in the software TRANSYT (11). This approach was later extended and named the incremental queue accumulation method (12, 13). Stochastic analysis is also introduced to address the stochastic and dynamic nature of arterial traffic (10, 14). Several recent studies formulate traffic queuing as a Markov chain renewal process (15–18); the queue length is thus estimated on the basis of the condition of previous time steps. The other category of models is based on shock waves of the queue formation and dissipation. These shock wave models can provide detailed temporal and spatial information for the queuing process (6, 7, 19). Queue length estimation methods leading to practical applications are limited. One of the major difficulties that input–output models encounter is the occurrence of long queues. When the rear of the queue exceeds the advance vehicle detector that provides the arrival traffic volume, the inflow cannot be accurately obtained; the result is large estimation errors (8, 9). This limitation is significant because long queues are common on congested arterial links. Although analysis based on shock waves is able to address the problem of long queues (9), detailed information about traffic conditions is required to detect the necessary shock waves; this information is difficult to obtain through existing arterial traffic data collection systems. Recent studies indicate an increasing interest in providing realtime estimates of queue length (3, 9, 20, 21). These studies show the benefit and importance of using new data sources, such as highresolution loop detector data (aggregated in small time intervals or individual vehicle counts) and probe vehicle data. As a new format of probe data, vehicle trajectory data is a topic attracting researchers’ interest. Several studies use trajectory data for shock wave detection (22, 23), whereas a few focus on intersection performance. Comert and Cetin (24) studied the conditional probability distribution of the queue length at an isolated intersection given the locations of probe vehicles in the queue. They found that only the location of the last probe in the queue is necessary for queue length estimation. However, the assumption that the actual percentage of probe vehicles among the traffic stream is known limits the application of this method. A simulation study by Shladover and Kuhn (25) investigated the feasibility of using probe trajectories, but it also follows the sampled travel time approach. An impressive study about freeway travel time estimation was conducted by Claudel et al. (26), in which the probe trajectory measurement was converted to density estimation using the Moskowitz function (27, 28). Using probe trajectory data for arterial performance measurement is more complicated because of the periodic turbulence from signals Cycle-by-Cycle Queue Length Estimation for Signalized Intersections Using Sampled Trajectory Data