$1.$Assume the waiting line at the Panama Canal Agua Clara crossing lane follows an M$/$M$/1$ queue, with arrival rate $3$ ships per hour and service rate $5$ ships per hour.a$.$What is the crossing lanes utilization, avg. # in system, avg. # in queue, avg. time in system, and avg. time in queue?b$.$Is the system ever empty $($no ships in the lane or in queue$)?$ If it is$,$ can you estimate what percent of time the system is empty?c$.$In the long run, what do you expect the average flow rate per hour of this system to be$?$d$.$What if the arrival rate changes to $10$ ships per hour due to another port being closed? The queue length is increasing. What would be the average flow rate in this situation?