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

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Trip Distribution

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Gravity Model

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Example 1 P=800 A= 10 P=1500 A= 10 P=200 A= 20 P=1200 A= 2 Zone 1Zone 2 Zone 4Zone 3 Calibration Factor, c = 1.5Socio-economic factor, k ij = 1.0

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Target-Year Inter-zonal Impedances, {Wij}-Given TAZ1234 15102010 2 525100 32025550 410100505

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Step 1- Calculate Friction Factors, {Fij} TAZ1234 1 0.08940.03160.01120.0316 2 0.08940.00800.0010 3 0.01120.00800.08940.0028 4 0.03160.00100.00280.0894

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Step 2- Find Denominator of Gravity Model Equation {AjFijKij} TAZ1234Total Σ(A j F ij K ij ) 1 0.178890.632460.11180.316231.23937 2 0.063251.788850.080.011.9421 3 0.022360.160.894430.028281.10507 4 0.063250.020.028280.894431.00596

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Step 3- Find Probability that Trip i will be attracted to Zone j, {pij} Σ(A j F ij K ij ) p ij = A j F ij K ij TAZ1234Total 1 0.1440.5100.0900.255 1 2 0.0330.9210.0410.005 1 3 0.0200.1450.8090.026 1 4 0.0630.0200.0280.889 1

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Step 4- Find Trip Interchanges, {Tij} TAZ1234Total 1 173612108306 1200 2 718481 200 3 30217121438 1500 4 501622711 800 T ij = P i p ij

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Zone 1 Zone 2 Zone 3 Zone 4 173 612 7 10830 306 50 116 38 22

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Example 2 UConn. UConn Buckland Hill Westfarm Mall Eastbrook Mall

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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

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Calculations-1 JAjt1jF1j=tij^(-2)Aj*F1j 110 1/100=0.01 0.10 260201/400=0.0025 0.15 380401/1600=0.000625 0.05 Total 0.30

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Calculations-2 JAj*F1jP1j= Aj*F1j/(Aj*F1j)T1j= P1*p1j 10.100.1/0.30=0.3332000*0.33=667 20.150.15/0.3=0.52000*0.5=1000 30.050.05/0.3=0.1672000*0.167=333 Total0.301.0002000

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

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Mode Choice

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Example 1 Calculate the mode shares for auto and light rail transit (LRT) using the utility function given. u k = a k – 0.045 T a – 0.03 T w – 0.01 T r – 0.005 C where: T a - access time, T w - waiting time, T r - riding time, C - out of pocket cost

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Modes Specifications Modea(k)Ta Access time Tw Waiting time Tr Riding time C Out of pocket cost LRT-0.0415 5040 Auto-0.02510020100

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Key formulas

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Utility Calculations ModeCalculationsUtility 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 u k = a k – 0.045 T a – 0.03 T w – 0.01 T r – 0.005 C

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Mode choice Estimation ModeUke^(Uk)Probability of selecting LRT -1.8650.15480.337 Auto -1.1900.30420.663 Total 0.4841 1.000

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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

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Scenario Analysis Mode Uke^(Uk) Prob. of selecting LRT -1.8650.15480.360 Auto -1.2900.27520.640 Total 0.4301 1.000 Mode Uke^(Uk) Prob. of selecting LRT -1.5650.20910.407 Auto -1.1900.30420.593 Total 0.5233 1.000 Congestion PricingIncrease Train Frequencies

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Comparing Results

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Example 2 Mode choice: Storrs to NYC Available modes: Auto (Private car ) Bus Train (From New haven) u k = a k – 0.0075 X 1 – 0.012 X 2 X1 : Travel Cost X2: travel Time

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Mode Characteristics - Auto Cost Analysis Gasoline Cost (300 miles round trip) 35 $ Tool Cost15 $ Parking Cost40 $ Total Cost80 $ Time Analysis Round trip150*2=300 min Parking20 Total time320 min

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Mode Characteristics - Bus Cost Analysis Ticket Cost Round trip 25*2= 50 $ Time Analysis Waiting time15*2= 30 min Round trip Travel time210*2=420 Total time440 min

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Mode Characteristics - Train Cost Analysis Gasoline Price12 $ Parking8 $ Train Ticket27 $ Total Cost47 $ Time Analysis Driving from Storrs to New Haven55*2=110 min Parking20 min Transfer time2*15= 30 min Train from New Haven to NYC100*2=200 min Total time360 min

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Modes Characteristics ModeTotal CostTotal Timea(k) Auto80320-0.3 Bus50460-0.5 Train47340-0.2

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Utility Calculations ModeCalculationsUtility 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

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Mode choice Estimation ModeUke^(Uk)Probability of selecting Auto -4.7400.0087380.478 Bus -6.3750.0018830.103 Train -4.7730.0076540.418 Total 0.0182751.000

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Scenario 2- New Utility Function (Sensitive to Out of Vehicle time) u k = a k – 0.0075 X 1 – 0.012 X 2 – 0.036 X 3 X1 : Travel Cost,X2: in vehicle travel Time X3:out of vehicle travel Time

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Modal Choice in Scenario 2 ModeUke^(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

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