Q5  Queuing

The BUS670 store is a small facility that sells all sorts of supplies, snacks, etc.  It has one checkout counter where one employee operates the cash register.  Once customers select their items for purchase, they line up at the counter in a first-come-first-served basis to pay for their selections.

You monitored the store for a few days and found that customers arrive on the waiting line to pay for the selections at an average of 24 customers per hour (assume Poisson distribution) and the cashier seems to be able to serve an average of 30 customers per hour (assuming exponential distribution).

The owner of the store has hired you to answer the following questions:

Part 1 In a typical 8 hour work day, how much time in total will the cashier be idle?

Part 2 How many customers on average are waiting in line to pay?

Part 3 What is the average amount of time a customer is waiting in line?

Part 4 What is the probability a customer will have to wait in the line before being able to pay?