CHAPTER $5,$ part $2-$ Problem $2$:

The Port of Virginia at Portsmouth is upgrading all of its entries to electronic scanning and processing of trucks entering the port. The final upgrade is on the single entry booth at the secondary gate on Harper Ave. The average service time at this gate is one truck every $30$ seconds, which will not change. The only change is the fact that processing will become uniform instead of random. Based on current operating statistics, the highest hourly demand is $115$ tractor$-$trailers arriving during the peak hour. The upgrade will result in a change in the queue processing from random departures following a Poisson distribution $($M$)$ to being uniformly distributed $($D$).$ Assume that before and after the upgrade, trucks arrive at the port according to the same random $($Poisson$)$ distribution $($M$).$

Determine the length of queue, average time waiting in the queue, and average time spent in the system for $($a$)$ before and $($b$)$ after implementation as well as $($c$)$ the reductions in trucks, waiting time, and time in the system.