Trucks arrive at a grocery store at a rate of about 3 per hour according to a Poisson distribution. The worker who is in charge of unloading the trucks takes about 15 minutes to unload a truck. Unloading time is approximately exponentially distributed and the system operates on a first-in first-out basis.
(a) What is the probability that there will be more than 3 trucks either being loaded or waiting?
The grocery store manager is thinking of adding another unloader where both unloaders will work as a team so the queuing system will still operate as first-in first-out single server system. Because the two workers are now unloading trucks together, unloading rate doubles. The arrival rate of trucks does not change. The truck drivers who bring groceries to the store are paid $20 per hour and unloaders receive $12 per hour. Assume that trucks waiting to be unloaded and also being unloaded is a cost to the system.
(b) What is the hourly cost to the grocery store when two unloaders are employed, both working as a single server?
Now assume that the two loaders work independently. Each loader takes approximately 15 minutes to unload truck. The arrival rate of trucks does not change. Each truck is served on the first-in first-served basis. Assume that trucks waiting to be unloaded and also being unloaded is a cost to the system.
(c) Which of the three systems would you recommend?
Hint: the answer muse be based by comparing the cost of operation and relevant operational characteristics of the three queuing systems.