Problem 3. Multinomial Choice Models (15) A multinomial logit model with three alternatives (drive-alone, shared-ride, and transit) has been developed for forecasting mode choice for home-to-work commute trips. The utility functions have been estimated to be the following: VDA = -1.14 Cost DA -0.0461-Time DA VSR -0.8814-1.14. Cost SR -0.0461-Time SR +0.1737. Long Dist VTR Where, 0.17-1.14 Cost TR -0.0461- Time TR -0.114. Walk Time VDA is the utility for the drive - alone mode VSR is the utility for theshared-ride mode VTR is the utility for the transit mode Cost, is the cost for modei, (i=DA, SR, TR) Time, is the travel time by modei, (i = DA, SR, TR) Walk Time is the walk time associated with transit mode Long Dist = 1 if the commutetrip is long distance, 0 otherwise The urban region has four types of commuters classified based on the commute distance and the available modes. The transportation level-of-service characteristics for each of the four types of commuters are presented below. Type 1 Modes available DA,SR,TR Type 2 DA,SR,TR Type 3 DA and SR Type 4 DA and SR Commute distance short long short Cost, DA 0.94 3.79 1.05 long 4.33 Time, DA 18 61 17 67 Cost, SR 0.47 2.12 0.56 2.16 Time, SR 29.5 74 31 75 Cost, TR 0.33 1.8 NA NA Time, TR 27.5 126 NA NA Walk time 12 24 NA NA (a) For each type of commuter, compute the probability of choosing each of the available modes (b) The urban region has 4000 commuters of type 1, 2000 commuters of type 2, 3700 commuters of type 3 and 3100 commuters of type 4. Determine 1. The total number of person-trips (home-to-work commute trips) by car and by transit in the urban area. 2. The number of vehicle trips by car 3. The transit revenue 4. If transit improvements result in a 10% decrease in transit travel times and all else remains the same, (i) How many short distance (Type 1) commuters and long distance (Type 2) commuters will switch to transit?

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