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HW5 solutions.docx - 1 CAE419 Introduction to...

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CAE419 Introduction to Transportation Engineering and Design Semester Fall 2017 Homework 5: Intersection Control and Signal Timing Design Solution 1 . PHF = 350 + 369 + 414 + 427 4 427 = 0.913 2. (a) Compute the ratios of the approach flows to saturation flow rates for each of the three phases, Phase A Phase B Phase C v 470 42 500 28 130 250 420 480 s 2400 1300 2400 1300 1300 1300 2400 2400 v/s 0.196 0.032 0.208 0.022 0.100 0.192 0.175 0.200 (b) Then, Y for each phase is determined as Y A = 0.208 Y B = 0.192 Y C = 0.200 Y = 0.208 + 0.192 + 0.200 = 0.6 The lost time per phase is 4 seconds, thus the total lost time is L = 3 × 4 = 12 sec Therefore, by the Webster model, the optimal cycle length can be get as C 0 = 1.5 L + 5 1 Y = 1.5 × 12 + 5 1 0.6 = 57.5 sec ,use 60 sec (c) Determine the effective green time for each phase, g A = V A V A + V B + V C ( C 0 L ) = 500 × ( 60 12 ) 500 + 250 + 480 = 19.51 19 sec g B = V B V A + V B + V C ( C 0 L )= 250 × ( 60 12 ) 500 + 250 + 480 = 9.76 10 sec g C = V C V A + V B + V C ( C 0 L )= 480 × ( 60 12 ) 500 + 250 + 480 = 18.73 19 sec 3. N-S E-W Critical lane flow 960 600 Saturation flow 2600 2600 Y 0.369 0.231 1
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The total lost time: L = 2 × 4 = 8 sec
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