A truck safety inspection station on Interstate 73 is operated by a single operator who can inspect at most one truck at a time. Trucks arrive at the station every 2.5 minutes on the average and an inspection takes 1.5 minutes on the average once the inspector begins examining the truck. The truck interarrival and inspection times are both exponentially distributed.

(a) What is the utilization of the inspection station? (6 pts)

(b) How long on the average does a truck spend waiting in the line prior to inspection (in minutes)? (7 pts)

(c) What is the largest arrival rate (in trucks/minute) such that there are no more than 3 trucks at the station on the average (including those in line and those being inspected) (6 pts)

(d) After the inspector gain some experience, the inspection times become exactly 1.5 minutes, no variability. Is all else remains the same, we expect the system cycle time to (choose one-6 pts)

i. increase

ii. decrease

iii. stay the same

iv. not enough information