Trip Distribution Application to Atlantis

A production$-$constrained parametric version of the gravity model has been calibrated. The results of this calibration effort reveal that the following friction factor function ensures that the gravity model fits the observed base year trip "length" frequency distributions reasonably well:

$f(c_{ij})=c_{ij}^{-b}$

where

$c_{ij},=$ travel time $(in$ minutes$),itoj$

$b,=,1\mathrm{.}5,$ for work trips

$b,=,2\mathrm{.}0,$ for non$-$work trips

Work trips and non$-$work trips should be distributed using the indices shown in the table below. Treat these indices as the "attractiveness" of each zone.

$\backslash$table$[[$Zone Number,Work Index,Non$-$work Index$],[1,1700,5\mathrm{.}0],[2,2000,6\mathrm{.}1],[3,2500,2\mathrm{.}1],[4,14,850,2\mathrm{.}4]]$

a$.$ Find the zone$-$to$-$zone travel times based on Atlantis Figure $2.$ The zone$-$to$-$zone travel time includes the travel time on the arterial and$/$or the freeway plus the travel time from the network node to the zone centroid. The intra$-$zonal $($e$.$g$.,$ zone $1$ to zone $1)$ travel times may be assumed to be the same as the time from the zone centroid to the network node $($i$.$e$.,$ the time shown on the dummy link$).$ For example, the zone $1$ to zone $1$ travel time is $3$ minutes. Present a matrix of the travel times.

b$.$ Assuming that travel times for the year $2055$ remain the same, distribute the total $($AM plus PM$)$ peak work person trip productions and total $($AM plus PM$)$ peak non$-$work person trip productions $($estimated in the previous assignment$)$ to obtain the total $($AM plus PM $)$ peak person trip production$-$attraction interchanges for each of the two purposes. Present a matrix for each trip type.

c$.$ Obtain the AM peak person trip origin$-$destination interchanges from the total $($AM plus PM$)$ peak person trip production$-$attraction interchanges for the work purpose and for the non$-$work purpose. You will need to assume the following: $1)$ All work trips in the AM peak are to work and all work trips in the PM peak are from work, $2)$ An individual who travels to work in the AM peak returns back from work in the PM peak and vice versa, $3)$ The person trip production$-$attraction interchanges for the non$-$work purpose are evenly split between the AM and PM peaks, and $4)$ An individual who leaves home in the AM peak to participate in a non$-$work activity returns home from that activity within the AM peak. Present an O$/$D matrix for each trip type.

d$.$ Convert the AM peak person trip origin$-$destination interchanges into equivalent AM peak vehicle trip origin$-$destination interchanges for the work and for the non$-$work purpose using the following estimates of average automobile occupancy: $1\mathrm{.}25$ for work trips and $2\mathrm{.}00$ for non$-$work trips. Present the two matrices.

e$.$ Finally, add the AM peak vehicle origin$-$destination interchanges for the work and nonwork purposes and determine the AM peak period traffic flow $($amount of vehicles$)$ using each link $($in each direction$)$ of the transportation system $($intra$-$zonal trips do not use the freeway or the arterial$).$ Present the link flows.