Multinomial Choice Models $[21]$

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:

$V_{DA}=(()DA)DA()SR(()TR)TR$

Where,

$V_{DA}$ is the utility for the drive $-$ alone mode

$V_{SR}$ is the utility for the shared $-$ ride mode

$V_{TR}$ is the utility for the transit mode

Cost ${?}_i$ is the cost for mode $i,)=(DA,SR,TR$

Time ${?}_i$ is the travel time by mode $i,)=(DA,SR,TR$

WalkTime is the walk time associated with transit mode

LongDist $=1$ if the commute trip 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.

$\backslash$table$[[,$Type $1,$Type $2,$Type $3,$Type $4],[$Modes available,DA$,$SR$,$TR$,$DA$,$SR$,$TR$,$DA and SR$,$DA and SR$],[$Commute distance,short,long,short,long$],[$Cost$,$ DA$,0\mathrm{.}94,3\mathrm{.}99,1,4\mathrm{.}23],[$Time$,$ DA$,16\mathrm{.}5,60,18,62],[$Cost$,$ SR$,0\mathrm{.}53,2\mathrm{.}23,0\mathrm{.}56,2\mathrm{.}29],[$Time$,$ SR$,29\mathrm{.}5,74,31,75],[$Cost$,$ TR$,0\mathrm{.}33,1\mathrm{.}8,$NA$,$NA$],[$Time$,$ TR$,27\mathrm{.}5,126,$NA$,$NA$],[$Walk time,$10,20,$NA$,$NA$]]$

$($a$)$ Compute the money value of travel time $($VOTT$)$ for a traveler for this commute trip using the above empirical specification. $[1]$

$($b$)$ For each type of commuter, compute the probability of choosing each of the available modes $[12]$

$($c$)$ The urban region has $4300$ commuters of type $1,2100$ commuters of type $2,3500$ commuters of type $3$ and $2900$ commuters of type $4.$ Determine

$($i$)$ The total number of person$-$trips $($home$-$to$-$work commute trips$)$ by car and by transit in the urban area.

$($ii$)$ The number of vehicle trips by car $($Assume that the average occupancy of shared$-$ride trips is $2\mathrm{.}5)$