Question $1(20$ marks$)$:

There is a demand of $1000$ trips from zone A to zone B$.$ Two modes are available for travelling from zone A to zone B: transit and a single occupant automobile. A multinomial logit model has been developed that predicts mode choice between those zones with the following utility functions:

$V($ transit$)=-0\mathrm{.}22-{0\mathrm{.}07}^{**}$IVTT$($ transit$)-{0\mathrm{.}10}^{**}$TWALK $(transit)-{0\mathrm{.}12}^{**}$TWAIT

Where IVTT, TWALK and TWAIT are in$-$vehicle travel time, walk time and wait time, measured in minutes and COST is in dollars.

Transit route characteristics are as follows:

Transit in Vehicle Travel Time $=30$ minutes

Expected Transit walk time $=5$ minutes

Expected Transit wait time $=5$ minutes.

Fare $=$$$4$

The two zones are connected via a one lane highway.

IVTT$(auto)=(60\frac{\text{m}\text{i}\text{n}}{hr})**(\frac{L}{S})**(1+(\frac{V}{C}{)}^4)$

Where

IVTT $($ auto $)=in$ vehicle travel time $on$ the road

$L=$ road length $=20km$

$S=$ freeflow speed $=80\frac{km}{hr}$

$C=$ Lane Capacity $=900\frac{\text{V}\text{e}\text{h}}{\text{h}\text{o}\text{u}\text{r}}$

Assume that only vehicles travelling from A to B use the highway. Assume that all vehicles travelling along this highway have a cost of $$\frac{0\mathrm{.}40}{k}m$

a$)$ Determine transit frequency of service in vehicles per hour. $(1$ marks$)$ CLARIFY why you devided $60*60$sec$/80$min, was not supposed to devid $60$min$/80$min and I feel we shouldnt sum waiting and walking time?

b$)$ Determine the mode shares that would be predicted by the model assuming free flow roadway travel times $(2$ marks$)$

c$)$ Explain clearly why using expected transit walk times and expected transit wait times may give biased results when using a logit model $(7$ marks$)$

$2$

d$)$ Using your understanding of feedback between the traffic assignment and mode choice component, does an automobile flow of $723$ represent an "equilibrium state" within the four stage modelling paradigm? Justify your answer with calculations and a diagram of how the traffic assignment and mode choice steps of the modelling framework interact. $(10$ marks$)$

ANSWER WAS provided is wrong