Delay at a Fixed Time Traffic Signal---II: Numerical Comparisons of some Theoretical Expressions

Numerical comparisons of several expressions for the average delay to traffic passing a fixed time traffic signal have been made for a wide range of values of the arrival rate, saturation flow, cycle time, proportion of the cycle effectively green, and variance-to-mean ratio of the number of arrivals per cycle ( I -ratio). The values of average delay given by Miller's, Newell's, and Webster's simplified expressions, and by a new modification of the last incorporating the I-ratio are compared with the value given by Webster's full expression. The differences are not usually more than 10 per cent when I = 1, but the importance of the I -ratio is shown by the differences reaching about 50 percent at high degrees of saturation when I = 1.5. The differences between the values of the various expressions are also compared with the effects on the value of Webster's full expression of given errors in the parameters. These effects are found to be large enough to make it difficult to distinguish experimentally between the various expressions when the I-ratio is near to 1 except by extensive measurements. Because of this the choice between expressions is often a matter of convenience of computation, and this choice is briefly discussed.