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

Trip Distribution

Gravity Model

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

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

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

Step 2- Find Denominator of Gravity Model Equation {AjFijKij} TAZ 1 2 3 4 Total Σ(AjFijKij) 0.17889 0.63246 0.1118 0.31623 1.23937 0.06325 1.78885 0.08 0.01 1.9421 0.02236 0.16 0.89443 0.02828 1.10507 0.02 1.00596

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

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

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

Example 2 UConn. UConn Buckland Hill Westfarm Mall Eastbrook Mall

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 = 2.0 Socioeconomic Adj. Factor K = 1.0

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=0.000625 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 trips 667 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 Tw Waiting time Tr Riding time C Out of pocket cost LRT -0.04 15 50 40 Auto -0.025 10 20 100

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

Utility Calculations uk = ak – 0.045 Ta – 0.03 Tw – 0.01 Tr– 0.005 C 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

Mode choice Estimation 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 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

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

Comparing Results

Example 2 Mode 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 - 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

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

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

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

Utility Calculations Mode 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 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