# Special Topics: Overlaps By Michael P. Dixon, Ph.D.

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Special Topics: Overlaps By Michael P. Dixon, Ph.D.

Objectives Learn how overlaps are calculated Learn why they can be beneficial Learn how they are applied

Steps to Developing Overlaps Step 1: Determine values for each lane group Step 2: Determine location of overlaps Step 3: Sum the values for the critical lane groups Step 4: Calculate cycle length Step 5: Distribute green time

Step 1: Determine Lane Group Values Values can be in the form of: – V/s ratios, or – Adjusted volumes R1 R2 Ring Diagram: Four Phase with Overlaps  A1  A2  A3  B  C 37 158 386 453 263 232 246 281

Step 2: Determine location of overlaps R1 R2 Ring Diagram: Four Phase with Overlaps  A1  A2  A3  B  C Target phases with unbalanced flows 37 158 386 453 263 232 246 281

Step 3: Sum the Values for the Critical Lane Groups Follow the critical path R1 R2 Ring Diagram: Four Phase with Overlaps  A1  A2  A3  B  C 37 158 386 453 263 232 246 281 1155 vph

Step 4: Calculate Cycle Length C = (N*L*(v/c) des ) / [1 -  (v/s) ic ] or, C = (N*L) / [1 - V c / (3600/h*(v/c) des *PHF)] For our case C = 70 sec – V c = 1155 vehicle/hour – h = 2.2 seconds/vehicle – PHF = 1.0 – (v/c) des = 0.85 – N = 4 phases – t L = 3 seconds/phase

Step 4: Calculate Cycle Length (cont.) What would the cycle length be if their were no overlaps? R1 R2 Ring Diagram: Four Phase with Overlaps  A1  A2  A3  B  C 37 158 386 453 263 232 246 281 1155 vph

Step 4: Calculate Cycle Length (cont.) What would the cycle length be if the EB and WB through values were switched (with and without overlaps)? R1 R2 Ring Diagram: Four Phase with Overlaps Blue = w/o overlaps; Red = w/ overlaps  A1  A2  A3  B  C 37 158 386 453 263 232 246 281 1088 vph 1155 vph

Step 5: Distribute Green Time Step 5.a: Determine green times of phases that have no overlaps Step 5.b: Determine green times of phases on side(s) of barrier with overlaps R1 R2 Ring Diagram: Four Phase with Overlaps  A1  A2  A3  B  C 37 158 386 453 263 232 246 281

Step 5.b: Definition Values are categorized by the phases whose green times they define

Step 5.b: Determine green times of phases on side(s) of barrier with overlaps Calculate gA1: If phase A1 is defined by a lane group in the critical ring then Otherwise

R1 R2 Ring Diagram: Four Phase with Overlaps  A1  A2  A3  B  C 37 158 386 453 263 232 246 281 What are the volumes of interest? V A1 = 37 vph V A3 = 453 vph V A2+A3 = 386 vph V A1+A2 = 158 vph V c = 1155 vph Is phase A1 defined by a lane group that is in the critical ring? How much effective green time for A1?

Step 5.b: Determine green times of phases on side(s) of barrier with overlaps (cont.) Calculate gA3: If phase A3 is defined by a lane group in the critical ring then Otherwise

R1 R2 Ring Diagram: Four Phase with Overlaps  A1  A2  A3  B  C 37 158 386 453 263 232 246 281 What are the volumes of interest? V A1 = 37 vph V A3 = 453 vph V A2+A3 = 386 vph V A1+A2 = 158 vph V c = 1155 vph Is phase A3 defined by a lane group that is in the critical ring? How much effective green time for A3?

Step 5.b: Determine green times of phases on side(s) of barrier with overlaps (cont.) Calculate gA2: If phase A1 + A2 is defined by a lane group in the critical ring then – Where Otherwise – Where

R1 R2 Ring Diagram: Four Phase with Overlaps  A1  A2  A3  B  C 37 158 386 453 263 232 246 281 What are the volumes of interest? V A1 = 37 vph V A3 = 453 vph V A2+A3 = 386 vph V A1+A2 = 158 vph V c = 1155 vph How much effective green time for A2?