New Optimum Cycle Length Equations for Pretimed Isolated Intersections with Modification of Webster’s Equation Based on HCM 2000

When the degree of saturation at intersection approaches one, Webster’s optimum cycle length equation becomes inapplicable, because the cycle length will becomes very big when the degree of saturation approaches one and will be fully unrealistic when the degree of saturation becomes greater than one. This is not a problem for HCM2000 method. But optimum cycle length calculation in this method has not specific equation and based on try and error to minimize delay time. Also this method requires many input parameters that made it expensive. In this paper new modified Webster’s optimum cycle length equations for some specific situation of geometric and phasing based on HCM2000 method have been presented that have not described problem. The purpose of this paper is ability to use of “total lost time within the cycle (L)” and “the sum of critical phase flow ratios (Y)” parameters and creation new minimum cycle length equation based on HCM2000 method. Regarding to this fact that intersection geometry and phasing is related to the optimum cycle length, four situations of intersection have been considered. After this stage the following step by step procedure was used:
- having low traffic volume and low “L”
- using “HICAP2000” software to calculate optimum cycle length
- also using Webster’s equation to calculate optimum cycle length
- increasing traffic volume and repeating the above steps
- the above steps continue until degree of saturation at intersection approaches one
- increasing “L” and repeating above steps
- with renewed increased “L” and repeating above steps we have optimum cycle length for many of “L” and traffic volume at specific intersection
After this method we used “SPSS” software to modeling new relationship between “L” and “Y” and finally new equations are presented for four situations of intersection. This method can be expanded for other geometry and phasing intersections.