Introduction to Transportation Engineering Instructor Dr. Norman Garrick Hamed Ahangari 6th March 2014
Feb 24, 2016
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 c
ijij
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
10203040506070
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 AnalysisTicket 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