cee155-sp09-mt3-Cassidy-exam

cee155-sp09-mt3-Cassidy-exam - University of California M....

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Unformatted text preview: University of California M. Cassidy, Instructor Department of Civil Spring, 2009 " "'5‘. - 3.; Mldterm 3 April 23, 2009 I H 1 Point each (TOtal pages: 6) Try 'to answer all questions and problems in the allotted time of 50 minutes. .___\ if" ._ -. \ 45 points total DO NOT turn this page (and look at the exam) until instructed to do so. Good Luck!!! PART I: True or False [five questions; 1 point each Mark the corresponding column for each question. I actually arrives to the bottleneck; on both approaches. cost. 1. The abscissa (the “x” coordinate) of a point on the bottleneck signifies the time when the corresponding 2. When the total demand of two upstream of the capacity enveIOpe of a merge, queues will always-W163; 4. At Vickrey Equilibrium, the critical commuter experiences the same cost regardless of where they join the queue. 5. When the W—curve is non-linear S-shaped (as shown below), eVery commuter at Vickrey Equilibrium experiences the same we) Problem 1: (vehfmile) Figure 1 Figure 2 Consider the merge shown in Figure 1. Demand from Link 2 is 2,000 vehicles per hour (vph) all day long. Demand from Link 1 is 500 vph all day except for a 30-minute period when this demand rises to 3,500 vph. If queues were ever present on both links, vehicles from Links 1 and 2 would take turns merging, such that the ratio would be 1:] (One vehicle from Link 1' for every vehicle from Link 2). The fundamental diagram shown in Figure 2 describestraffic on Link 1, Link 2, and at all locations downstream of the merge. a. Sketch the queuing diagram for Link 1. In addition, calculate (and label on your diagram) the longest delay incurred by any driver on Link 1. [15 points] b. Modify your queuing diagram in part (a) so that it also displays the Back of the Queue at time t, BOQO‘). In addition, use this diagram to calculate the maximum physical distance (in units of miles!) over which the queue on Link 1 extends. To repeat: your solution is to be in units of miles (not number of vehicles). [15 points] (Part 0 is on the following page.) c. suppose that there is an off-ramp ups Demands for the merge (i.e., from the Ola-ramp, new there is an additional demand for the off that the rates that vehicles actually pass locations : Figure 3 Assume the delay incurred between locations x0 and 2:2 is negligible. We do not know the rates that pass location x0 while the queue spills back from Link 1. This is because the queued rate passing x0 will include vehicles destined for the off—ramp and this off-ramp departure flow will be affected by the queue. IMPORTANT: We can assume that the queue on Link 0 is FIFO, so if two vehicles join the queue at the same time, with one destined for the off-ramp and the other destined the merge, both vehicles incur the same delay. Keeping in mind that demand for the off-ramp from Link 0 is fixed at 500 Vph, and that Link 1’s queue is FIFO, you are to: (i) Sketch the queuing diagram for (only) those vehicles that are destined for the off- ramp, and label the V- and D-curves; (ii) Label 0n the diagram the longest delay incurred by any driver destined for the off- ramp. [15 points] Solu' n for Pr . 1; 0‘) Immm CGiJflCiTYO+ end {Pump ' ,u t = .375 hrs Ils'ré b L ‘ 37‘5- .€> = . §jfi§flgiiis nub} ' mi (alarm b= ‘1000 £ :0 ‘/?hr Va: - b 250020 E | | mat-HO“ ‘1 : — I6 an +5000 ’2’)‘ WITSO: .516 Ema: ! ‘ - - ' k; 9: H50 '3 mac 0» dc; Wei mafiflfim _ “Mame. '1'?“ (above nso gals—W d q 5 _ fimyh Solutiogs for Problem 1 (cont): /Mt3 ...
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cee155-sp09-mt3-Cassidy-exam - University of California M....

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