The operation of intersections when conditions are changing rapidly or if demand exceeds capacity has been a point of discussion for a long time. Most techniques for predicting delays and queue lengths have been based on the so-called coordinate transform approach. Discussed in this paper are the relationships from the coordinate transform method and their shortcomings. Also, the issues are explained and theoretical solutions described that are based on the diffusion theory by Newell, which provides an improved estimate of average queue length and, more importantly, gives the variance of the queue length. It is concluded that Newell's approach provides better estimates of the mean and variance of the queue length. Using the mean as well as the variance provides better methods to predict the performance of the system.