1. Introduction to Transportation Engineering
Instructor Dr. Norman Garrick
Hamed Ahangari
6th March 2014

2. Trip Distribution

3. Gravity Model

4. Example 1 P=800 A= 10 P=1500 P=200 A= 20 P=1200 A= 2 Zone 1 Zone 2
Calibration Factor, c = 1.5 Socio-economic factor, kij = 1.0

5. Target-Year Inter-zonal Impedances, {Wij}-Given
TAZ 1 2 3 4 5 10 20 25
100 50

6. Step 1- Calculate Friction Factors, {Fij}
TAZ 1 2 3 4
0.0894
0.0316
0.0112
0.0080
0.0010
0.0028

7. Step 2- Find Denominator of Gravity Model Equation {AjFijKij}
TAZ 1 2 3 4
Total
Σ(AjFijKij)
0.1118
0.08
0.01
1.9421
0.16
0.02

8. Step 3- Find Probability that Trip i will be attracted to Zone j, {pij}
AjFijKij
pij =
Σ(AjFijKij)
TAZ 1 2 3 4
Total
0.144
0.510
0.090
0.255
0.033
0.921
0.041
0.005
0.020
0.145
0.809
0.026
0.063
0.028
0.889

9. Step 4- Find Trip Interchanges, {Tij}
Tij = Pipij
TAZ 1 2 3 4
Total
173
612
108
306
1200 7
184 8
200 30
217
1214 38
1500 50 16 22
711
800

10. Zone 1
Zone 2
612 7
173 50 1 16
108 30
306
Zone 4
Zone 3 38 22

11. Example 2 UConn.
UConn
Buckland Hill
Westfarm Mall
Eastbrook Mall

12. Calibration Factor c = 2.0 Socioeconomic Adj. Factor K = 1.0
Uconn.
P1=2000
Eastbrook
A1: 10
t1: 10 min
Buckland Hill
A2: 60
t2: 20 min
Westfarm
A3: 80
t3: 40 min
Calibration Factor c = Socioeconomic Adj. Factor K = 1.0

13. Calculations-1 0.10 0.15 0.05 0.30 J Aj t1j F1j=tij^(-2) Aj*F1j 1 10
1/100=0.01
0.10 2 60 20
1/400=0.0025
0.15 3 80 40
1/1600=
0.05
Total
0.30

14. 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

15. Trip Distribution Results
UConn
Buckland Hill
Westfarm Mall
Eastbrook Mall
1000 trips
333 trips
667 trips

16. Mode Choice

17. Example 1
Calculate the mode shares for auto and light rail transit (LRT) using the utility function given.
uk = ak – Ta – 0.03 Tw – 0.01 Tr– C
where: Ta - access time, Tw - waiting time,
Tr - riding time, C - out of pocket cost

18. Modes Specifications Mode a(k) Ta Access time Tw Waiting time Tr
Riding time C
Out of pocket cost
LRT
-0.04 15 50 40
Auto
-0.025 10 20
100

19. Key formulas
𝑈 𝑚 = 𝑎 𝑚 −𝑎1∗ 𝑋 1 −𝑎2∗ 𝑋 2

20. Utility Calculations uk = ak – 0.045 Ta – 0.03 Tw – 0.01 Tr– 0.005 C
Mode
Calculations
Utility
LRT
= * * * *40
-1.865
Auto
= * * * *100
-1.190

21. Mode choice EstimationUk
e^(Uk)
Probability of selecting
LRT
-1.865
0.1548
0.337
Auto
-1.190
0.3042
0.663
Total
0.4841
1.000

22. Policy Analysis Which 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

23. Increase Train Frequencies
Scenario Analysis
Congestion Pricing
Increase Train Frequencies
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

24. Comparing Results

25. Example 2 Mode choice: Storrs to NYC
Available modes:
Auto (Private car )
Bus
Train (From New haven)
uk = ak – X1 – X2
X1: Travel Cost
X2: travel Time

26. Mode Characteristics - Auto
Cost Analysis
Gasoline Cost
(300 miles round trip)
35 $
Tool Cost
15 $
Parking Cost
40 $
Total Cost
80 $
Time Analysis
Round trip
150*2=300 min
Parking 20
Total time
320 min

27. Mode Characteristics - Bus
Cost Analysis
Ticket Cost
Round trip
25*2= 50 $
Time Analysis
Waiting time
15*2= 30 min
Round trip Travel time
210*2=420
Total time
440 min

28. Mode Characteristics - Train
Cost Analysis
Gasoline Price
12 $
Parking
8 $
Train Ticket
27 $
Total Cost
47 $
Time Analysis
Driving from Storrs to New Haven
55*2=110 min
Parking
20 min
Transfer time
2*15= 30 min
Train from New Haven to NYC
100*2=200 min
Total time
360 min

29. Modes Characteristics
Total Cost
Total Time
a(k)
Auto 80
320
-0.3
Bus 50
460
-0.5
Train 47
340
-0.2

30. Utility Calculations Mode Calculations Utility Auto
= * *320
-4.740
Bus
= * *450
-6.275
Train
= * *340
-4.873

31. Mode choice EstimationUk
e^(Uk)
Probability of selecting
Auto
-4.740
0.478
Bus
-6.375
0.103
Train
-4.773
0.418
Total
1.000

32. Scenario 2- New Utility Function (Sensitive to Out of Vehicle time)
uk = ak – X1 – X2 – X3
X1: Travel Cost,X2: in vehicle travel Time
X3:out of vehicle travel Time

33. Modal Choice in Scenario 2
Mode Uk
e^(Uk)
Probability of selecting
Auto
-5.22
0.627
Bus
-6.995
0.106
Train
0.267
Total
1.000