a8_cee3604_2011_sol

a8_cee3604_2011_sol - CEE 3604: Introduction to...

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Unformatted text preview: CEE 3604: Introduction to Transportation Engineering Fall 2011 Assignment 8: intersection Analysis and Queueing Theory Solution Instructor: Trani Problem 1 The intersection shown in Figure 1 is to be studied for level of service characteristics. The intersection has a cycle length of 55 seconds. After consulting with the traffic engineer in town, you are told the green time for University Avenue traffic is 35 seconds. The intersection has two phases: 1) phase 1 allows green time for the traffic on University Avenue and 2) phase 2 allows green time for traffic on Elmo Street. The traffic flows recorded in a recent survey are shown in Figure 1. Assume that the D/D/1 queueing system adequately describes each lane for each approach at the intersection . In other words, in your analysis assume that each lane is independently studied as a D/D/1 queueing system. Assume no time loss in the cycle. The saturation flows for straight approaches (i.e., when cars move in straight line through the intersection) are 1,900 vehicles per hour. The saturation flows for turning movements are 1,600 veh/hr. Figure 1. Intersection for Problem 1. a) Estimate the average delay per vehicle for every approach and every lane. Show a set of sample calculations by hand if using a Matlab or Excel. The nomenclature to calculate intersection delays is presented in Figure 2. CEE 3604 A8 Trani Page 1 of 8 Figure 2. Basic Queueing Diagram to Estimate Intersection Delays. Equations to estimate total delay ( d ) and the average delay ( d ) are presented below. Example calculation: For the approach with 800 veh/hr on University Avenue moving from West to East we know: g = 35 seconds c = 55 seconds λ = 800 veh/hr = 0.222 veh/s μ = 1900 veh/hr = 0.528 veh/s ρ = λ μ = 0.222 0.528 = 0.42 λ c = (0.222 veh/s)(55 seconds) = 12.2 vehicles CEE 3604 A8 Trani Page 2 of 8 μ g = (0.528 veh/s)(35 seconds) = 18.5 vehicles Since λ c ≤ μ g U ndersaturated conditions apply Using equations 17 through 21 in the notes, Arrival flow = 800 veh/hr Saturation flow = 1900 veh/hr...
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This note was uploaded on 12/31/2011 for the course CEE 3604 taught by Professor Katz during the Fall '08 term at Virginia Tech.

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a8_cee3604_2011_sol - CEE 3604: Introduction to...

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