Queue overflow is a critical issue in developing queue prediction technologies for applications in Advanced Transportation Management System (ATMS). Conventional queue prediction methods, however, are limited to incident-free queue length prediction where traffic arrivals can be readily obtained using detectors. Despite the problems posed by queue overflow, studies addressing queue-overflow issues, or for predicting queue overflows beyond detectors, appear inadequate. This paper describes an advanced methodology which uses a stochastic system modeling approach and random processes for predicting queue lengths beyond detectors in real time. Lane changing is taken into account in developing the queue-overflow prediction model because lane changing accompanies queue overflow in most cases. A discrete-time, nonlinear stochastic system is specified for modeling the queues and lane changes beyond detectors during queue-overflow occurrence. The noise terms of the recursive equations of the model account for the effects of queues and a variety of arriving volumes on vehicular lane-changing maneuvers during queue-overflow occurrence. The unknown traffic arrivals beyond detectors are predicted employing random processes. In addition, a recursive estimation algorithm for predicting real-time queue overflows is developed utilizing the extended Kalman filtering technique. Preliminary test results indicate that the proposed methodology is promising for real-time prediction of queue overflows. The predicted queue overflows can be used not only in understanding the phenomenon of lane traffic patterns during queue-overflow occurrence, but also in developing related advanced technologies such as real-time road traffic congestion control and management systems.