introduction to transportation engineering instructor dr. norman garrick hamed ahangari 6th march...
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Introduction to Transportation Engineering
Instructor Dr. Norman Garrick
Hamed Ahangari6th March 2014
Trip Distribution
Gravity Model
Example 1
• P=800• A= 10
• P=1500• A= 10
• P=200• A= 20
• P=1200• A= 2
Zone 1 Zone 2
Zone 4Zone 3
Calibration Factor, c = 1.5 Socio-economic factor, kij = 1.0
Target-Year Inter-zonal Impedances, {Wij}-Given
TAZ 1 2 3 4
1 5 10 20 10
2 10 5 25 100
3 20 25 5 50
4 10 100 50 5
Step 1- Calculate Friction Factors, {Fij}
TAZ 1 2 3 4
1 0.0894 0.0316 0.0112 0.0316
2 0.0316 0.0894 0.0080 0.0010
3 0.0112 0.0080 0.0894 0.0028
4 0.0316 0.0010 0.0028 0.0894
0894.0)5(
115.111 F
WF
cij
ij
Step 2- Find Denominator of Gravity Model Equation {AjFijKij}
TAZ 1 2 3 4 TotalΣ(AjFijKij)
1 0.17889 0.63246 0.1118 0.31623 1.23937
2 0.06325 1.78885 0.08 0.01 1.9421
3 0.02236 0.16 0.89443 0.02828 1.10507
4 0.06325 0.02 0.02828 0.89443 1.00596
Step 3- Find Probability that Trip i will be attracted to Zone j, {pij}
Σ(AjFijKij)pij =
AjFijKij
TAZ 1 2 3 4 Total
1 0.144 0.510 0.090 0.255 1
2 0.033 0.921 0.041 0.005 1
3 0.020 0.145 0.809 0.026 1
4 0.063 0.020 0.028 0.889 1
Step 4- Find Trip Interchanges, {Tij}
TAZ 1 2 3 4 Total
1 173 612 108 306 1200
2 7 184 8 1 200
3 30 217 1214 38 1500
4 50 16 22 711 800
Tij = Pipij
Zone 1 Zone 2
Zone 3 Zone 4
173
6127
108 30 30650
1 16
38
22
Example 2 UConn.
UConn
Buckland Hill
Westfarm Mall
Eastbrook Mall
Uconn.P1=2000
EastbrookA1: 10
t1: 10 min
Buckland HillA2: 60
t2: 20 min
WestfarmA3: 80
t3: 40 min
Calibration Factorc = 2.0
Socioeconomic Adj. FactorK = 1.0
Calculations-1
J Aj t1j F1j=tij^(-2) Aj*F1j
1 10 10 1/100=0.01 0.10
2 60 20 1/400=0.0025 0.15
3 80 40 1/1600=0.000625 0.05
Total 0.30
Calculations-2
J Aj*F1j P1j= Aj*F1j/(∑Aj*F1j) T1j= P1*p1j
1 0.10 0.1/0.30=0.333 2000*0.33=667
2 0.15 0.15/0.3=0.5 2000*0.5=1000
3 0.05 0.05/0.3=0.167 2000*0.167=333
Total 0.30 1.000 2000
Trip Distribution Results
UConn
Buckland Hill
Westfarm Mall
Eastbrook Mall
1000 trips
333 trips667 trips
Mode Choice
Example 1
Calculate the mode shares for auto and light rail transit (LRT) using the utility function given.
• uk = ak – 0.045 Ta – 0.03 Tw – 0.01 Tr– 0.005 C
where: Ta - access time, Tw - waiting time,
Tr - riding time, C - out of pocket cost
Modes Specifications
Mode a(k) Ta Access time
TwWaiting
time
TrRiding time
COut of
pocket costLRT -0.04 15 15 50 40
Auto -0.025 10 0 20 100
Key formulas
𝑈𝑚=𝑎𝑚−𝑎1∗𝑋 1−𝑎2∗𝑋 2
Utility Calculations
Mode Calculations Utility
LRT =-0.04-0.045*15-0.03*15 - .01*50- 0.005*40 -1.865
Auto =-0.025-0.045*10-0.03*0 - .01*20- 0.005*100 -1.190
uk = ak – 0.045 Ta – 0.03 Tw – 0.01 Tr– 0.005 C
Mode choice Estimation
Mode Uk e^(Uk) Probability of selecting
LRT -1.865 0.1548 0.337
Auto -1.190 0.3042 0.663
Total 0.4841 1.000
Policy AnalysisWhich policy may promote transit?
1-Applying congestion pricing for Auto mode( Increase the cost of auto to 120)
2- Improving transit by decreasing waiting time to 5 minute
Scenario Analysis
Mode Uk e^(Uk) Prob. of selecting
LRT -1.865 0.1548 0.360
Auto -1.290 0.2752 0.640
Total 0.4301 1.000
Mode Uk e^(Uk) Prob. of selecting
LRT -1.565 0.2091 0.407
Auto -1.190 0.3042 0.593
Total 0.5233 1.000
Congestion Pricing Increase Train Frequencies
Comparing Results
Base ca
se
Congestion Pric
ing
Increase
frequencie
s0
10
20
30
40
50
60
70
Mod
e Sh
are
%
LRT
Auto
LRT
Auto
LRT
Auto
Example 2Mode choice: Storrs to NYC
• Available modes:• Auto (Private car )
• Bus
• Train (From New haven)uk = ak – 0.0075 X1 – 0.012 X2
X1: Travel Cost
X2: travel Time
Mode Characteristics - AutoCost Analysis
Gasoline Cost(300 miles round trip)
35 $
Tool Cost 15 $
Parking Cost 40 $
Total Cost 80 $
Time AnalysisRound trip 150*2=300 min
Parking 20Total time 320 min
Mode Characteristics - Bus
Cost Analysis
Ticket CostRound trip
25*2= 50 $
Time AnalysisWaiting time 15*2= 30 min
Round trip Travel time 210*2=420Total time 440 min
Mode Characteristics - TrainCost Analysis
Gasoline Price 12 $
Parking 8 $
Train Ticket 27 $
Total Cost 47 $
Time AnalysisDriving from Storrs to New Haven 55*2=110 min
Parking 20 minTransfer time 2*15= 30 min
Train from New Haven to NYC 100*2=200 minTotal time 360 min
Modes CharacteristicsMode Total Cost Total Time a(k)
Auto 80 320 -0.3
Bus 50 460 -0.5
Train 47 340 -0.2
Utility CalculationsMode Calculations Utility
Auto =-0.3-0.0075*80-0.012*320 -4.740
Bus =-0.5-0.0075*50-0.012*450 -6.275
Train =-0.2-0.0075*47-0.012*340 -4.873
Mode choice Estimation
Mode Uk e^(Uk) Probability of selecting
Auto -4.740 0.008738 0.478
Bus -6.375 0.001883 0.103
Train -4.773 0.007654 0.418
Total 0.018275 1.000
Scenario 2- New Utility Function(Sensitive to Out of Vehicle time)
uk = ak – 0.0075 X1 – 0.012 X2 – 0.036 X3
X1: Travel Cost,X2: in vehicle travel Time
X3:out of vehicle travel Time
Modal Choice in Scenario 2
Mode Uk e^(Uk) Probability of selecting
Auto -5.22 0.005407 0.627
Bus -6.995 0.000916 0.106
Train -6.0725 0.002305 0.267
Total 0.008629 1.000