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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 alwaysW163; 4. At Vickrey Equilibrium, the critical commuter experiences the same cost regardless of where they join the queue. 5. When the W—curve is nonlinear Sshaped (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 30minute 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 offramp ups Demands for the merge (i.e., from the Olaramp,
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 offramp
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 offramp and the other destined the merge,
both vehicles incur the same delay. Keeping in mind that demand for the offramp 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 Dcurves; (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

 matHO“ ‘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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 Spring '09
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