Problem
A truck safety inspection station is operated by a single inspector who can inspect at most one truck at a time. On average, 24 trucks arrive at the station in an hour, and an average inspection takes 1.5 minutes once the inspector begins examining the truck. The truck interarrival times and inspection times are both exponentially distributed.
1. What is the utilization of the inspection station?
2. How long on average does a truck spend waiting in line prior to its inspection (in minutes)?
3. The manager sets the requirement that at least 8 out of 10 arrivals should find waiting space for waiting trucks available. At least how many waiting spaces for waiting trucks (not including the one being inspected) does the station need to provide in order to meet the requirement?
4. After the inspector gains some experience, the inspection times become exactly 2 minutes, with no variability. If all else remains the same, we expect the system average inventory to (increase/decrease/stay the same).
5. The crew cost is approximately $300 per day. The cost associated with lost productivity from the breakdown is estimated at $150 per vehicle per day (or any fraction thereof). The mechanic crew can now repair 11 vehicles per day, which will lead to an average waiting time of Tq = 93.5 min. Assume the same arrival rate as before. Adding a second crew that works as fast as the old crew (still operating with one single queue) will make the total daily cost (increase or decrease) by ().