1. A calibration study resulted in the following utility equation for a mode cho

Question

1. A calibration study resulted in the following utility equation for a mode choice model: UK - AK0.057a_ 0.047w-0.027,-0.01C where access plus egress time, in minutes Ty waiting time, in minutes Tr -riding time in the vehicle, in minutes C- out-of-pocket cost, in cents The trip distribution forecast between two zones labeled "ODU" and "downtown" is 10,000 person-trips per day. During the target year, travelers between these two zones will have a choice between four different travel modes as shown in the table below. The target-year service attributes of the four competing modes are given in the table: Mode TaTw TrC Automobile: Drive alone Automobile: Shared ride (2 persons Automobile: Carpool (3 persons Transit: Local bus 5 0 60300 5 60200 5 1060 150 2010 75 100 Assume that the calibrated mode-specific constants (Ak) are 0.00 for all automobile modes and (a) Apply the multinomial logit model to estimate the target-year person-trips between ODUU and downtown by each of the four modes in the table. How many cars will travel per day 0.10 for the bus mode. between the two zones? (b) It is desired to examine the effect of introducing a light rail (LR) system between ODU and downtown. A related study has projected that the service attributes of the proposed light rail system between ODU and downtown will be: Ta (LR)-20 The mode-specific constant (Ak) for this new mode is -0.06. (LR) = 10 T(LR) 40 C (LR)-100 How many people will travel by light rail between ODU and downtown? How many cars per day will be reduced on the roads between the two zones (after introducing light rail)?

Explanation / Answer

Given:

Uk=Ak-0.05Ta-0.04Tw-0.02Tr-0.01C

For Automobile drive alone Uk1=-0.05(5)-0.02(60)-0.01(300)=-4.45

For Automobile share 2 person Uk2=-0.05(5)-0.04(5)-0.02(60)-0.01(200)=-3.65

For automobile share 3 person Uk3=-0.05(5)-0.04(10)-0.02(60)-0.01(150)=-3.35

For local bus Ukbus= -0.10-0.05(20)-0.04(10)-0.02(75)-0.01(100)=-4

The probability distribution is given by

Puk1=euk1/(euk1+euk2+euk3+eukbus)

Puk1=e-4.45/(e-4.45+e-3.65+e-3.35+e-4)=0.011/0.091=0.1208

Puk2=e-3.65/(e-4.45+e-3.65+e-3.35+e-4)=0.025/0.091=0.2856

Puk3=e-3.35/(e-4.45+e-3.65+e-3.35+e-4)=0.035/0.091=0.3855

Pukbus=e-4/(e-4.45+e-3.65+e-3.35+e-4)=0.0183/0.091=0.201

Trips by each of mode:

Single automobile=0.1283x10000=1283

Shared by 2 persons=0.2856x10000=2856

Shared by 3 persons=0.3849x10000=3849

Local bus=0.2013x10000=2012

Estimate the number of cars:

12.83% of cars are driven alone=12.83(10000)/100=1283 cars

28.56% of cars are shared by 2 persons=28.56(10000)/100=2856/2=1428 cars

38.49% of cars are shared by 3 persons=38.49(10000)/100=3849/3=1283 cars

Total number of cars=3994 cars are the total number of cars travelledin the trip

(b)

After introduction of LR system

Ukrail=-0.06-0.05(20)-0.04(10)-0.02(40)-0.01(100)=-3.26

PukLR=e-3.26/(e-4.45+e-3.65+e-3.35+e-4+e-3.26)

PukLR=0.2968

29.68% of the people will travel by metro=0.2968x10000=2968 persons

Estimate for number of cars

Puk1=e-4.45/(e-4.45+e-3.65+e-3.35+e-4+e-3.26)=9.03%

9.03% of single driven cars=903 cars

Puk2=e-3.65/(e-4.45+e-3.65+e-3.35+e-4+e-3.26)=20.1%

20% of cars shared by 2 persons=1005 cars

Puk3=e-3.35/(e-4.45+e-3.65+e-3.35+e-4+e-3.26)=27.13%

Cars=2713/3=904 cars

Total cars=2812 cars

Reduction in cars=3994-2812=1182 cars

Introduction of LR reduces 1182 cars on the road between two zones

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