Ways to estimate the time-to-collision are explored. In the context of traffic simulation models, classical lane-based notions of vehicle location are relaxed and new, fast, and efficient algorithms are examined. With trajectory conflicts being the main focus, computational procedures are explored which use a two-dimensional coordinate system to track the vehicle trajectories and assess conflicts. Vector-based kinematic variables are used to support the calculations. Algorithms based on boxes, circles, and ellipses are considered. Their performance is evaluated in the context of computational complexity and solution time. Results from these analyses suggest promise for effective and efficient analyses. A combined computation process is found to be very effective.