Bureau of Public Roads $($BPR$)$ function $($shown below$)$ is a travel time function used in urban transportation planning to calculate travel time on a link given volume on the link:

$t=t_0(1+(\frac{v}{C}{)}^{})$

Where,

$t=$ travel time $on$ the link

$t_0=$ free$-$flow travel time $on$ the link

$v=$ volume $on$ the link

$C=$ capacity $of$ the link

$,=$ parameters $of$ the model estimated for local condition

Demand between a given origin$-$destination $($OD$)$ pair in a transportation network is $10,100$ vehicles$/$hour$.$ There are three independents links connecting the OD pair, whose travel times can be represented using the BPR function. Parameters of the BPR function for the three links are given below.

$\backslash$table$[[$BPR parameter,Link $1,$Link $2,$Link $3],[$Free$-$flow travel time, $t_0($minutes$),17\mathrm{.}0,15\mathrm{.}5,12\mathrm{.}5],[$Capacity$,$ C $($vehicles$/$hour$),3800,4200,6600],[,0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}4],[,2\mathrm{.}8,3\mathrm{.}7,4\mathrm{.}3]]$

Perform three iterations of the method of successive averages $($MSA$)$ to find user equilibrium assignment flows between the given OD pair. Show hand calculations for each iteration. At the end, summatize your calculations in a table by showing link flows and travel times at the end of each iteration. It's OK if flow on a link exceeds its capacity $($this method allows for such scenarios, but penalizes such routes through rapidly increasing travel times$).$