HW2 2010

HW2 2010 - Homework No. 2 (Due: 12 November 2010) 1. Find...

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Homework No. 2 (Due: 12 November 2010) 1. Find the UE flow and travel times for the network shown in the figure below, where tx 11 2 22 33 2 44 2 3 12 24 =+ 1 2 3 1 2 3 4 (The link numbers are shown on the respective links.) The O-D trip rate is 4 units of flow between nodes 1 and 3. 2. Figure 1 shows a network with two links connecting one O-D pair. 1 2 Link 1 Link 2 Figure 1 Link 1 performance: 2 1 1 2 Link 2 performance: t x 3 = + Demand function: q u =− 5 1 Flow conservation: q x x = + where t t , are the travel times on links 1 and 2, respectively. x x , are the flow on links 1 and 2. u is the O-D travel time, and q is the O-D flow. (a) Plot the demand function (b) Plot the performance function for the O-D pair: u as a function of q . (c) Solve for the equilibrium flows by locating the intersection between the demand and performance functions. 3. Formulate problem 2 as an equivalent minimization problem. State the first order conditions and solve for the equilibrium flows.
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HW2 2010 - Homework No. 2 (Due: 12 November 2010) 1. Find...

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