The interactions with human drivers is one of the major challenges for autonomous vehicles. In this study, we consider urban crossroads without signals where driver interactions are indispensable. Crossroads are parameterized to be used in studying how drivers pass the crossroad while maintaining a desired speed without collision. We define a probability of yielding for each car as a function of vehicle speed and the distance-to-intersection for both vehicles, while the interactions between vehicles are characterized by a point of action for incoming vehicles from different directions. Driver behaviors in terms of acceleration/deceleration given current circumstances are also modeled probabilistically. The method is then analyzed and validated by data collected from human drivers in the simulated environments. The result shows comparable prediction accuracy to the state-of-the-art method, where characteristic parameters of drivers are also shown to be critical for the behavior predictions. We also extend our model to two real-world urban crossroads applications : crash analysis and traffic characteristic parameters identification. In both cases, our prediction results are analogous to those acquired in virtual environments. For autonomous vehicle, our method can help building a computer-driving logic that matches human behaviors, such that interactions between different drivers will be more intuitive.