Problem $1$: $(15)$

Given: On a typical afternoon, $3$ solid waste vehicles arrive at a landfill per hour. It takes $15$

minutes to direct each vehicle to the appropriate site and discharge. Assume that a FIFO M$/$M$/1$

queuing discipline is used.

Find:

Average arrival rate, $.$

Average service rate, $.$

Utilization ratio, $.$ Ascertain whether a queue is expected to form at the landfill. Explain.

Average number of trucks waiting, $L_9$

Average time in the system, W$.$

Probability that more than $3$ solid waste vehicles will arrive in a one$-$hour time period.