Macroscopic calculation of delay for diverging diamond interchanges

Diverging diamond interchanges (DDI) have been proved to outperform other types of diamond interchanges in terms of safety, cost-effectiveness and efficiency, but most of those research efforts were based on case studies using simulation or empirical analysis. Few research efforts have been done to conduct the analytic calculation of delay, with which optimization of timing plans can be acquired more efficiently. This paper first develops the control strategies based on the introduction of overlap and offset analysis, which provide a uniform representation of sequences for DDI signal control. Considering the difference of delay calculation between DDI and isolated intersections, as the inflows will serve either as saturated flow or arrival rate from either upstream ramp or arterial, delay equations were developed to calculate the delay on the internal lanes of DDI, which can be used for all different undersaturated traffic. Finally, 39 different traffic patterns that each with 10 decision variables created from JMP are used to check the accuracy of the calculations using VISSIM software. The results show the calculation fit simulation very well with R-Square to be 0.9968 for delay calculation of westbound internal lane, 0.9914 for eastbound internal lane, and 0.9949 for total delay of those two directions. By changing the pre-determined parameters such as the length of internal lanes, saturated flow rate of upstream approach, desired speed, all-red and amber time, the equations proposed in the paper are actually able to take all kinds of configurations of DDI into consideration and get the optimized timing plan easily with commercial solvers.