USE MATLAB:

$3.$ Traffic Flow Simulation $($traffic$.$m$)$Before running the programs for each part, increase the simulation time from $8$ to $16$ minutes by doubling the number of intervals $($i$.$e$.$ changing n$=48$ to n$=96).($a$)$ Simulation shows that for a $0\mathrm{.}3$ probability of car arrival in any one second, a $20$ second green and $40$ second red cycle $($i$.$e$.$ p$=0\mathrm{.}3,$ GREEN$=2,$ RED$=4)$ appears to lead to traffic congestion. Run this case for the $16$ minute total time to see if the congestion gets worse or eases.$($b$)$ Investigate the flow for lighter traffic cases where p$=0\mathrm{.}2$ and $0\mathrm{.}25.$ You may want to extend the time intervals further to see if a steady state condition is reached.$($c$)$ For p$=0\mathrm{.}3,$ change the cycle to have green and red for equal time $($i$.$e$.$ set GREEN$=3$ and RED$=3).$ For each run, only submit the print$-$out of the last $15$ to $20$ red$/$green intervals$($not all $96$ intervals$).$ Discuss your results. For part $($d$),$ run the program gui$\_$slider$\_$traffic$\_$simulation$1.$m $($d$)$ Instead of setting green and red lights to a fixed interval, for the dynamic approach the green interval is extended only if the traffic builds up$.$ This approach may be more practical if there is concern about perpendicular traffic density at the intersection. This change will effectively add another $10$ second green light interval when there are at least MIN cars at the end of the current green interval. The slider in the GUI program controls the value of MIN. The display will still show the status after each $10$ second interval. Investigate this approach for the case in $($a$).$ Try to relieve the congestion without making MIN smaller than necessary. Assume that congestion means more than about $15$ cars are waiting during the last few light cycles. Submit the resulting slider and graph. Extra credit if you can come up with any other novel approaches to relieving the congestion.