Prove that the maximum flow using Greenberg Model can be computed using the following

formula:

$q_{\text{m}\text{a}\text{x}}=\frac{u_f*k_j}{e^1}$

A freeway with two lanes in one direction has a capacity of $2,100ve\frac{h}{h}\frac{?}{ln}$ under normal

operation $($i$.$e$.,$ under saturation$).$ One of these lanes is blocked for $15$ minutes on a particular

morning, beginning at $7$:$00$ AM$.$ The queue discharge capacity $($capacity under unstable

traffic conditions$)$ is only $1,950ve\frac{h}{h}\frac{r}{ln}.$ The arrival pattern of vehicles at this location is as

follows:

Conduct a deterministic queuing analysis to determine:

a$.$ The maximum size and length of the queue, assuming the average distance occupied

by vehicle is $50f\frac{t}{?}$ vehicle

b$.$ The time that the queue will fully dissipate

Using a linear car$-$following model, simulate the movement of two vehicles under the

following conditions:

The two cars were initially moving at a uniform speed of $60k\frac{m}{h}r,$ with the driver in

the following car attempting to maintain a safe distance of $30$ m $.$

The driver in the lead car rapidly decelerated at the rate of $4\mathrm{.}5\frac{m}{s^2}$ for $2$ sec $.$

The reaction time in the following vehicle equals $0\mathrm{.}8$ sec $.$