Delay at Controlled Intersections: The Old Theory Revised

The calculation of delays at an intersection is an old problem that has been studied and solved by many researchers. This paper reanalyzes the problem by using a Markov chain model for the probability distribution of queue length. From the dynamics of the expectation value of the queue length, the authors derive a formula for the delay in fixed time traffic control. The effect of the overflow queue is made explicit. The result is a new formula, but even more important, a clear understanding of the role of the overflow queue