CME 302 SAMPLE final_2005 Solutions

CME 302 SAMPLE final_2005 Solutions - 1 CME 302 Final Exam...

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1 CME 302 Final Exam, Fall 2005, Dec 1, 5pm – Dec 2, 5pm Name_________________________ Note: ± This is a take-home exam. In other words, it is open-book and open-note. You have 24 hours to complete the exam. ± I have meetings on Friday between 10am and 3pm. However, I will be available for clarification type of questions on Thursday after 5pm, Friday before 10am and after 3pm. ± The deadline is 5pm, Dec 2 nd 2005, due at my office in ERF 2089. No late submission is permitted . This rule will be strictly executed. I will lock my office door after 5pm, meaning that I won’t accept any submissions after that. ± Please provide your solutions as detailed as possible. Each step counts. ± Please complete the exam independently . I trust your honesty and I hope you respect my trust, and ± Good luck!
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2 1. Derive an analytical relationship between travel time and flow for each of the two networks depicted below on the basis of Wardrop’s first principle. Each network consists of two links with the following travel time-flow functions: 2 2 1 1 1 0 20 2 0 10 v . t v . t + = + = where, t a = travel time experienced by each vehicle on link a (minutes) v a = flow of vehicles on link a (vehicles/hour) State your results as equations defined for entering and exiting link flow v ranging from 0 to 2000 vehicles/hour. Draw figures illustrating the travel time-flow relationships ( t vs v ) for each network. (18 pts) v 2 v v 1 v v 1 v 2 v Solution. For sequential network: t = t 1 + t 2 = 10+0.2 v +20+0.1 v = 30+0.3 v 0 v 2000 For parallel network: At user equilibrium, = + = = + + = + = + = 3 0 10 2 0 3 0 1 0 10 1 0 20 2 0 10 2 1 2 1 2 1 2 1 2 1 . . . . . . v v v v v v v v v v v v t t Flow v 2 must be non-negative, i.e., v 2 0. So, v 50.
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CME 302 SAMPLE final_2005 Solutions - 1 CME 302 Final Exam...

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