A discrete choice model of travel mode to work includes two alternatives: driving alone (alternative 1) and taking transit (alternative 2) The model is based on the following utility functions: U1 = \phi 1 − t + \xi 1 U2 = \phi 2 - t^ + \xi 2 where \phi 1 and \phi 2 are model parameters. Both error terms \xi 1 and \xi 2 follow a uniform distribution between -b and b (a) Develop an analytical expression for P1 as a function of\ phi 1, \phi 2, t. t^, and b.. (b) Assume that \phi 1-\phi 2 = = 1 and plot P1 versus t^- t for several values of b. Discuss the effect of b on the choice probability and draw general conclusions.
A discrete choice model of travel mode to work includes two alternatives: driving alone (alternative 1) and taking transit (alternative 2) The model is based on the following utility functions: U1 = \phi 1 − t + \xi 1 U2 = \phi 2 - t^ + \xi 2 where \phi 1 and \phi 2 are model parameters. Both error terms \xi 1 and \xi 2 follow a uniform distribution between -b and b (a) Develop an analytical expression for P1 as a function of\ phi 1, \phi 2, t. t^, and b.. (b) Assume that \phi 1-\phi 2 = = 1 and plot P1 versus t^- t for several values of b. Discuss the effect of b on the choice probability and draw general conclusions.
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.11P
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Transcribed Image Text:A discrete choice model of travel mode to work includes two
alternatives:
driving alone (alternative 1) and taking transit (alternative 2)
The model is based on
the following utility functions:
U1 =
\phi 1 − t + \xi 1
U2
=
\phi 2 - t^ + \xi 2
where \phi 1 and \phi 2 are model parameters. Both error
terms \xi 1 and \xi 2 follow a uniform
distribution between -b and b
(a) Develop an analytical expression for P1 as a function of\
phi 1, \phi 2, t. t^, and b..
(b) Assume that \phi 1-\phi 2 =
= 1 and plot P1 versus t^- t
for several values of b. Discuss
the effect of b on the choice probability and draw general
conclusions.
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