Sub-problem 3a: Actuated Signal Detection and Signal Timing

If we look back at the analysis completed in Sub-problem 1b, page2, we assumed the default value of unit extension (3.0 seconds) and a g/c ratio of 0.33 for Reitz Union. However, from the discussion on the last two pages, we found that the phase length varies as a function of the signal timing parameters and thus, depending on the parameters the g/c ratio, may change accordingly. Essentially, the phase length is a function of the unit extension; once traffic is served, the controller times the gap setting as extra time looking for an additional vehicle to cross the detector.

Step 2. Results

How do signal timing parameters affect the phase length and the volume to capacity ratio in the HCM methodology? Let's assume our minimum green time is 5 seconds, our maximum green time is 40 seconds (as was used in the HCS analysis from Sub-problem 1b, page2), and our unit extension is three seconds. If we reduce the unit extension, we would expect the actuated side street movement  (Reitz Union) to receive less green time. HCS calculates that a shorter unit extension reduces the delay for the entire intersection because there is potentially less time wasted at the intersections.

If we make this change in our HCS file, now assuming that the unit extension is one second, (because we have detection on the north and south approaches that allows shorter unit extension time) (Reitz3a4 - ask PJK) we find that changing the unit extension does not change the g/c ratio assumed in the analysis for the north/south approach. This is due to the procedures within HCS represent analyses of fixed lengths of intervals and sequences of phases. In other words, there is no direct link between the g/c ratio assumed and signal timing parameters such as unit extension. The reduced unit extension does result in a reduction in delay for the intersection and each individual movement in the calculation.

Is this representative of what happens in the field? This may not be representative of what occurs in the field and for a detailed analysis, measured green time for each approach may be used to refine the analysis.  Reducing the unit extension would reduce the g/c ratio for the north/south movement. The coordinated phase, Museum Road through (east/west) would receive the additional time that is unused from the Reitz Union approaches.

Report results from analysis here...

Discussion:
Take a few minutes to consider how much more the phase times could vary if we assumed equally spaced random arrivals at the intersection. What conditions would make the 50th-percentile phase length the same as the average phase length? How significant is this difference in phase length?