Exercise 1 12 pts]. Two alternative routes connect one origin to one destination
ID: 1867155 • Letter: E
Question
Exercise 1 12 pts]. Two alternative routes connect one origin to one destination Assume the travel time on the two routes can be expressed approximately by a linear function, whose coefficients are: ta+b,(/ci); a 12 [minutes b 20 [minutes]; c4,000 [veh/h]; t- atb(q/c); a 25 [minutes]; b 10 minutes]; c 4,000 [veh/h]; where q and q denote the flows on the routes 1 and 2 respectively The total demand on both routes, measured upstream the bifurcation of the routes, is 6,000 veh/h A traveler information system can be applied to reroute a fraction of drivers from the congested route after the capacity reduction to an alternative less congested route An accident occurs on the first route and reduces its capacity to 2,000 veh/h, while the coefficients of the performance functions are unchanged. Determine a) the flows and travel times on both routes at the user equilibrium state standard conditions when the whole capacity is available. (2 Points) b) the increase of the total travel time due to the capacity reduction in case of no information to drivers. (2 Points) c) the new equilibrium point that a driver information system should pursue. (2 Points) d) the gain obtained by the driver information system, in terms of reduction of the total travel time increase. (2 Points) if a strategy that reroute a fraction of drivers proportional to the capacity reduction (that is 50%) from route 1 to route 2 is beneficial or if the traveler information system produces an overreaction. Specify which theoretical principle explains the solution (2 point) e) f) the system optimal solution in incident conditions (2 points)Explanation / Answer
a) t1 = a1 +b1 ( q1/c1)
a1 = 12 min = 0.2 hrs
b1 = 20 min = 0.33 hrs
q1 =q2 = 12
t1 = 0.2 +0.33 ( 12/4000)
t1 = 0.2hrs
t2 = a2 +b2 ( q2/c2)
a2 = 0.416hrs
b2 = 0.166hrs
t2 = 0.416 + 0.166 ( 12/4000)
t2 = 0.416 hrs
b) t1 = a1 +b1 ( q1/c1)
t1 = 0.2 +0.33 ( 12/6000) = 0.2006 hrs
t2 = 0.416 + 0.166 ( 12/6000) = 0.416 hrs
total travel time = 0.616 hrs
e ) ATIS is benefical. The information elements should be provided by advanced driver information systems in cars of the future, and a rational for selecting them. The systems engineering approach provide a method for determining which features to select for further analysis and which information elements comprise those features.
f) The problem is solved for fixed origin -destination (OD) flows (demands) over a relatively long time period, such as an hour or a peak period; during this period the flows are regarded as constant. The flows are real-valued, and may be divided among more than one route.
Choice of route by drivers is assumed to depend only on travel time, ignoring travel distance.
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