Question

Question 1: Trip makers can choose one of the following four modes of travel - automobile, bus, rail and bike. The utility functions for each mode are as follows: Vi=-0.075 * ATi -0.05 * WTi-0.04 *RT:-0.002 * TCH where Vi = observable utilities for mode iz AT; = access time for mode i (minutes) (e.g., walk time to the bus stop, rail station or destination); WT; = waiting time for mode i (minutes); RT; = riding time for mode i (minutes); TC; = out-of-pocket travel cost for mode i (cents). The values of each mode attribute are shown below. Mode Access time Waiting time (minutes) (minutes) Auto be Bus 10 152 Raile 7e 102 Bike le 02 ܒ:1 Riding time (minutes) 252 40- 302 60 Out-of-pocket cost (cents 3002 60 75e (a) Calculate the share of each mode using the multinomial logit model. (b) The city will construct bike paths to encourage people to use bikes. The city expects that the paths will reduce riding time by bike to 40 min. Assume that the values of all other mode attributes remain the same as above. What will be the new share of each mode? (c) Describe the effects of access time, waiting time, riding time and out-of-pocket cost on modal splits. Are they realistic?

Answer 1

Paget Given utility function Vi = -0.075XAT: -0.05 ⓇWT; -0.04X RT; -0.002 x TC; V А =-0.075* 6 -0.05*1-0.04%25 -0.0028300 -2.1 BE -0,075 * 10 - 0:05X15-0.04x40 -0.002 x 60 -3.22 VR E-0.075 X 7 -0.05 x 10 -0.04x30 -0.002 x 75 - 2.375 v Bi = -0.075X1 -0.05% 0 -0,04x60 0.002x0 -2.475 NA e »% share of Auto = PX 100 UBI e A e B te te VR

Page 2 -2.475 -3.22 te te percentage share of Bus te-2.475 -2.1 xor 2.375 36.06 %. -3.22 e X 100 -2.1 -3.22 -2.375 1.77% -2.375 x 100 -2) -2.475 te + е + percentage share of Rail 11 -2.375 m3:22 te té 27.39% percentage share of Bike -2.475 X100 -2.475 te -20/40-3.2e ne* 2375 24.78%

6 Page 3 Reduced riding time for bike = homin (VBike ) -0.075 X 1 -0.05X0 -0.04x40 Men -0.002X0 -1.675 -2.1 % share of Auto = € 2.1 100 -1.675 -2.375 e-21-3.22 te te t 27066 4 similarly, s share of Bus = 9.02% % share of Rail = 21000% % share of Bike = 42.38% For on given utility function, increase of access time, waiting time, riding time and out-of-pocket cost results decrease of utility factor value by that decrease of share of model is occuring. they are realistic in practical. so,