Please answer problem $1$ using the material provided:

Problem $1$

An accident occurs at $4$:$00$pm on a four$-$lane highway closing two lanes for $30$ minutes. At

$4$:$30$pm$,$ one of the closed lanes is reopened and the second lane remained closed for

another $30$ minutes. The demands for the freeway section where the accident occurred are as

follows:

The capacity of a lane of the freeway during queuing conditions is $1800$ vehicles per hour and

$2000$ vph under free$-$flow conditions. Use the cumulative curve procedure to determine: $(1)$ the

length of time queuing conditions exists; and $(2)$ the number of vehicles affected by queuing

conditions.

Problem $1$

An accident occurs at $4$:$00$ pm on a four$-$lane highway closing two lanes for $30$ minutes. At $4$:$30$ pm$,$ one of the closed lanes is reopened and the second lane remained closed for another $30$ minutes. The demands for the freeway section where the accident occurred are as follows:

The capacity of a lane of the freeway during queuing conditions is $1800$ vehicles per hour and $2000$ vph under free$-$flow conditions. Use the cumulative curve procedure to determine: $(1)$ the length of time queuing conditions exists; and $(2)$ the number of vehicles affected by queuing conditions.

Answer in this fo

Time

$4$:$00-4$:$15$ PM

$4$:$15-4$:$30$ PM

$4$:$30-4$:$45$ PM

$4$:$45-5$:$00$ PM

$5$:$00-5$:$15$ PM

$5$:$15-5$:$30$ PM

$5$:$30-5$:$45$ PM

$5$:$45-6$:$00$ PM

$6$:$00-6$:$15$ PM

$6$:$15-6$:$30$ PM

$6$:$30-6$:$45$ PM

$6$:$45-7$:$00$ PM

Formulas to use:

Capactiy: Hourly Capacity by lane x number of lanes

Cumulative Demand: Demand $+$ cumulative demand from previous time period

Cumulative Capacity: Capacity $+$ cumulative capacity from previous time period

Excess Demand $=$ Cumulative Demand $-$ Cumulative Capacity

Total Time of Queuing

$\backslash (\backslash$mathrm$\{$T$\}1=(\backslash$mathrm$\{$QT$\}-1)/(\backslash$mathrm$\{$CT$\}-\backslash$mathrm$\{$VT$\})\backslash )$

$\backslash (\backslash$mathrm$\{$T$\}1=\backslash )$ Time to dissipate queue during the last period

QT $-1=$ Excess demand in the period before the queue ends

$\backslash (\backslash$mathrm$\{$CT$\}=\backslash )$ Capacity in the period when the queue ends

$\backslash (\backslash$mathrm$\{$VT$\}=\backslash )$ Demand in the period when the queue ends