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