1) Tom Jones, the mechanic at Golden Muffler Shop, is able to install new mufflers at an average rate of 3 per hour (or about 1 every 20 minutes), according to a negative exponential distribution. Customers seeking this service arrive at the shop on the average of 2 per hours, following a Poisson distribution. They are served on a first-in, first-out basis and come from a very large (almost infinite) population of possible buyers. Based on the information that you have, obtain the operating characteristics of Golden Muffler’s queuing system.
2) The owner of the Golden Muffler Shop estimates that the cost of customer waiting time, in terms of customer dissatisfaction and lost goodwill, is $10 per hour of time spent waiting in line. The average car has a 2/3-hour wait (Wq). There are approximately 16 cars serviced per day (2 arrivals per hour times 8 working hours per day). The only other major cost that Golden's owner can identify in the queuing situation is the salary of Jones, the mechanic, who earns $7 per hour, or $56 per day. What is the total expected costs?
3) Garcia-Golding Recycling, Inc., collects and compacts aluminum cans and glass bottles in New York City. Its truck drivers currently wait an average of 15 minutes before emptying their loads for recycling. The cost of driver and truck time while they are in queues is valued at $60 per hour. A new automated compactor can be purchased to process truckloads at a constant rate of 12 trucks per hour (that is, 5 minutes per truck). Trucks arrive according to a Poisson distribution at an average rate of 8 per hour. If the new compactor is put in use, the cost will be amortized at a rate of $3 per truck unloaded. Evaluate the costs versus benefits of the purchase.