Old MathJax webview

Old MathJax webview

054 last 3 digits

Network is already shown please look it carefully

this topic

1 10 A simple network is given as shown in the Figure below with link a, b, c, and d. Suppose total traffic demand from 0 to D is six hundred (x = 600 vehicles). Xa, Xb, Xc, and xd denote the link flows for the link a, b, c and d and ta, tb, tc, and ta denote the link travel times (link costs) for each traveler for the link a, b, c and d, respectively. The link-cost function for each link is defined as below; ta(x) = 4950 + abc + Xa th(x) = 10 x t.(x) = 10 x ta(x) = 4950 + abc + Xd where, abc = the last three digits of your student ID. Note that the link flow Xa and xc are the same and equal to Xa-c, which is the route flow for the route a-c, the link flow Xb and xd are the same and equal to Xb-d, which is the route flow for the route b-d, and total traffic demand x = Xa-c + Xb-d. o D b d Part 1: For user equilibrium condition, calculate the route flow for the route a-c (through link a and c) and the route b-d (through link b and d). Calculate the route travel time (for each traveler) for these two routes, and take the summation of all travelers' costs (i.e., the total cost'). Part 2: Assume a new road construction as shown in the Figure below. The link-cost function between link cost (te) and link flow (xe) for the newly constructed link e is te(x)= 1000 + Xe. Calculate each route flow, the route travel time, and total cost for this network. Note that there is one additional route b-e-c (through link b, e and c), the flow on the link b is the summation of the route flow b-d and b-e-c, and the flow on the link c is the summation of route flow a-c and b-e-c. Part 3: Compare the total travel times (total cost) obtained for both part 1 and 2, and explain the resulting paradox, if exists. Note: total cost = total travel time