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CE 2710 Transportation Engineering

Homework 8 Solution

1. A vehicle stream is interrupted and stopped by a flag-person. The traffic volume

for the vehicle stream before the interruption is 1200 veh/hr and the concentration

is 100 veh/mi. Assume that the jam concentration is 240 veh/mi. After fiveminutes the flag-person releases the traffic. The flo condition for the release is a

traffic volume of 1!00 veh/hr and a speed of 20 mph.

Approach

Conditions:

q = 1200 veh/hr

u = 12 mi/hrk = 100 veh/mi

Platoon Conditions:

q = 0 veh/hr

u = 0 mi/hr

k = kj= 240 veh/mi

Shock ave at the rear o! the platoon"e#innin# at t = 0:

$s1= %0&1200'/%240 ( 100' = &)*+, mi/hr

Length of Queue after 5 minutes usw1* t !8"57 # $5%&0' 0"71( mi

)um*er of +ehi,les in -ueue L * k2 0"71( # 2(0 171"(

ApproachConditions:

q = 1200 veh/hru = 12 mi/hrk = 100 veh/mi

Platoon Conditions:q = 0 veh/hr

u = 0 mi/hrk = kj= 240 veh/mi

-elease Conditions:q = 1.00 veh/hr

u = 20 mi/hrk = )0 veh/mi

Shock ave at the !ront o! platoon

at t = + min it as de!ined eteen the jam and release conditions:

$s2= %1.00&0'/%)0&240' = &10 mi/hr

Time for "ueue of 0.#14 mi to dissipate$peed of dissipation % -10 & '-(.)#* % - 1.4+ mi/hr

Time Length % spee. 0"71( % 1"(/ 0"5 hour

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2. Traffic is traveling at 40 mph and a flo rate of 1000 veh/hr hen a tractor going

at 1) mph turns on to the road. The platoon that develops behind the tractor has a

density of !0 veh/mi. After 0.#) mile, the tractor turns off the main road. Therelease travel condition for the vehicles in the platoon is at a flo rate of 1200

veh/hr and a density of 40 veh/mi. alculate the length of the platoon that

develops and the time that it ill tae for it to dissipate after the tractor leaves.

Approach Conditions:

q = 1000 veh/hru = 40 mi/hr

k = 2+ veh/mi

Platoon Conditions:

q = 00 veh/hru = 1+ mi/hr

k = .0 veh/mi

Condition in Front of Truck:

q = 0 veh/hrk = 0 veh/mi

'ree-flo condition*

Length of latoon when tru,k turns off main roa.

The shoc ave at the rear of the platoon 'i.e., beteen the approach and

platoon conditions* ill have a speed of

$s1= %00&1000'/%.0&2+' = &2*). mi/hr

$hoc ave at front of truc has same speed as truc, $s1= 1+ mi/hr

Speed o! #roth o! platoon = 1+ ( % & 2*).'= 1,*). mi/hr

ime the truck takes to turn o!! = 0*,+ / 1+ = 0*0+ hr

Length of platoon after 0.05 hr ! 0.05*1".#$ ! 0.#%&'iles

Approach Conditions:

q = 1000 veh/hru = 40 mi/hr

k = 2+ veh/mi

Platoon Conditions:

q = 00 veh/hru = 1+ mi/hr

k = .0 veh/mi

(elease Conditions:

q = 1200 veh/hru = 30 mi/hr

k = 40 veh/mi

$hoc ave at the bac of platoon still has speed of -2.(! mi/hr

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$hoc ave at front of platoon ith truc gone,

$s2= %1200&00'/%40&.0' = &1+ mi/hr

$peed of dissipation of platoon, % - 1) & ' - 2.(!*% - 12.14 mi/hr

Time for platoon of 0"8/ miles to .issipate 0"8/ % 12"1( 0"07( hr ("(1 minutes

+. sing the distance - time plot given, a* estimate the speed, average spacingand

flo of the traffic at t % (0 seconds, b* the speed of the shoc ave 1 and 2 for thevehicles that has to slo don around time % 4) seconds, c* estimate the flo

conditions before, after and during the slo don.

3rom the plot

a* he speed t = )0 sec is aout 24 mphhe concentration t = )0 sec is aout +, veh/mi

here!ore %u5k' he !lo t = )0 sec is aout 13.) veh/hr

* he speed o! the !irst shock ave is aout &,*0 mphhe speed o! the second shock ave is aout &20*+ mph

c* Speed !or the approach condition u1= 31 mphhe concentration !or the approach condition k1= ++

here!ore the !lo !or the approach condition is aout q1= 1,0+

d* Speed !or the platoon u2= . mph

rom alculation

s1 % '"2 & "1* / '2 & 1*

$ubstitute non values gives, 2 % 1!1 veh/mi

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