This research was motivated by the belief that it is possible to develop improved algorithms for the computer control of urban traffic. Previous research suggested that the computer software, and especially the filtering and prediction algorithms, is the limiting factor in computerized traffic control. Since the modern approach to filtering and prediction begins with the development of models for the generation of the data and since these models are also useful in the control problem, this paper deals with the modeling of traffic queues and filtering and prediction. It is shown that the data received from vehicle detectors is a discrete-time point process. The formation and dispersion of queues at a traffic signal is then modeled by a discrete-time time-varying Markov chain which is related to the observation point process. Three such models of increasing complexity are given. Recent results in the theory of point-process filtering and prediction are then used to derive the nonlinear minimum error variance filters/predictors corresponding to these models. It is then shown that these optimal estimators are computationally feasible in a micro-processor. All three algorithms were tested against the UTCS-1 traffic simulator and, in one case, against an algorithm in current use called ASCOT. Some results of these tests are shown. They indicate good performance in every case and better performance than ASCOT in the comparable case.