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"v I? ,c )A/ ,1 A Transportation Engineering "1' ‘
Exam 1 Fall 2007 Name PROBLEM 1. A freeway in Wausau is known to follow Greenshield’s (linear speeddensity
relation). The free speed is 72 mph and the jam density is 120 vehicles per lanemile. What is
the capacity for a single lane? What are the volume and average headway for a single lane when
the speed is 40 miles per hour? (8 points) ' i , , AM” iféé wheey P“ W
72“ Coyacl‘L? : _ /" PROBLEM 2. A two lane road has an average daily trafﬁc of 11,200 vehicles. Estimate the
directional design hourly volume for this road, using the 100th highest hour standard
(Wisconsin) and a directional spit of 60/40. (4 points) V lg PROBLEM 3. A one—way road is near a school. The volume on that road is 120 vehicles per
hour, Poisson distributed, during times children are present. A minimum acceptable headway for
children crossing the road is 30 seconds. What is the probability that any given headway is acceptable? (4 points) ' v 1/) '_ 3‘
V: {20 ; pl: ( 50m” '11:; run _
f PROBLEM 4. What is the LOS for a My with an hourly digggtjonal volume of 3600 v h? What is the'density in passenger cars per mile? The prevailing conditions are listed
below. State all assumptions. (8 points) ll foot lanes E7 ‘~ l1g
> 6 foot shoulders, both sides ( T— O ‘7 g
Experienced drivers 1‘ 51‘?" I“) 1C 2 '
‘ﬂ/ 1‘ ( .5 '1) k 0
0% RV’s I f o / .
10% trucks PeakhOur factor=0.90 \f w M 7—“ [V03.5I Pc//I\ /L/\ @ Urban area, Base Free F lowjjlﬂimph f o .0) 0195 1‘ 0‘)
Level terrain
g, 1 interchange per mile I  —J; is,  it?
/ F F5 ,. ge: PS Lw Lo #0
Lo.)
1% :2. 701%!“ " Ital 3’0_ 2’6. L ‘1‘" o. 0 PROBLEM 5. Estimate the percent time spent following (using the HCM procedure) for a two W (Class I) with an anticipated peak hour volume of 1260 vehicles per hourain
both directions and 40% no passing zones and a 60/40 directional split. Otherwise, assume ideal conditions (no trucks, level terrain, etc.). The base free ﬂow speed is 60 mph and the peak hour
factor @090. If the average travel speed in 34 mph, What is the level of service? (8 points) in V9 . l p9 T/WZ 56/41” 7' Faucywiva Q5 " [,0 VF: [290 £9. . $€T§P~apﬂ0<gw e 772ch) [9'00 6’“ h new web
V raw!” re ..
P 04"! (IX A $9,040!) u. 370 9th §\ 2 {$10 {3:}; "52.2 m“ >> a?" 30:32: ‘ /”‘ \
' \ PROBLEM 6. A toll booth on a singlelane onramp can process vehicles at an average rate of
120 per hour, Poisson distributed. Vehicles arrive randomly at an average rate of 80 per hour,
Poisson distributed. (a) What is the average waiting time in the system? (b) What is the average
length of the queue? Hint: This is an M/M/l queue. (6 points) i [4 : i291.) V?\\
)3 7— 80 wok \— W L
/"*>x 310;; cal.» 4 IW 0% ii = e, 73 “Ir/m + Min/we ‘; Be: 2
«ff;
1’? \ u... 'J“ 1’ 6AM"? lw *gh l _’ \ \
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8? f" 2 r
,3, (357 a‘ w. A .——__. ’/“’ $50 vf’o
yam main» ..~ / (QM/cal"? gfo, 017 hALbi I mr‘n/vekm/}rﬂ3 iv”? o.. (I t.‘ :1; (Doc h/VLL. : 54;“ (I
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TEM +104" IV] \
M PROBLEM 7. A freeway with three lanes in one direction has one of its lanes blocked for a long
term work zone. The capacity W. Outside of a peak twohour period (4 to
_6 pm), trafﬁc is very liéhtfﬁétween 4 and 5 pm, the upstream trafﬁc volume is a constant 4500
vehicles per hour. Between 5 and 6 pm, the upstream trafﬁc is a constant 3000 vph. Sketch a
cumulative ﬂow (queuing) diagram showing both the arrival and departure curves for these two
hours. What is the maximum length of the queue? For how long does the queue exist? What is the longest time a vehicle must wait within the queue? Hint: you can easily read all the numbers
off a carefully drawn diagram. (8 points) Extra Credit V/
PROBLEM A. Previously the toll only took exact change. Then, the averageservice rate was
140 vehicles per hour and service times were constant. How much did theperformance of the
toll both change as compared to present circumstances? (2 points) //’
Ilt/t PROBLEM B. Refer to PROBLEM 6. What is the aver/age delay across all vehicles that arrive
during the two hours? (2 points) 7 I/ 1/.
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fir/f
PROBLEM C. Refer to PROBLEM l. A better modelof trafﬁc ﬂow for this road is:
2 “<5
S=S 1——D— =~7Z [’ ‘ [Way ‘
f D j if” .
What is the capacity with this model? (3 points)
{in a
x/L/r’. I
/ / PROBLEM D. Refer to PROBLEM I. A detector on this freewayhasran;:effectiye length of 10
feet and an average vehicle is 20 feet long. What is the “apparent”’6‘ccupancvxat/this detector w when the speed is 40 mph? (2 points)
f I [J +zo
75% e "277" Tl‘ 0V4‘V+I'CM ES udng '
gm 4. M50535; mi 07 m aw” . 5Q 95/4 = mum/ff mac; 1)”: LzoO~40/7;); 53.3 «L/Mm'.
one»: Saga+0 =' 7433', h S Sew/ma — \6°£ aer— C13 WW .2 “7.0.54? o.é 9‘ 0,95 = 8450 “A,
® 7’65: 0‘3 MC") }: lath/WM; ?Y* #53: é‘)*°: C,” 05462 = 0.37 (4) PH =7o~\ﬁ=—3 ~25 = 42.4; “any Aw“ (MM “5,0 s 035
\‘p~‘ 3900/(5d‘05’l54‘036Il‘1) = )Vtos', 5=/ 6.1.6} Cb. 14t23/52.6: 124 oc/M/m'n MW £N,=\ ‘) £QQ= ) \l‘} '' \ZGO/O.°\ "1 W07); Siffsvr \OD(\ 60.00097q4§\40¢)=1b.8 VTSF‘ = away—x: 76,27») 5=34r a has he: 11m = «L; map = 4a; keg; = \1
Man = 31.5 QM,—
‘AM# .7 7.3 MW
qmwas (19! (to ma“ ...
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 Fall '07
 Horowitz

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