A local café has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrival time an average of one every 2 minutes. The time to place their order and pay at the register is normally distributed with mean 90 seconds and standard deviation 20 seconds. Each customer’s order is then passed to one of the servers who take on average 5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order.
a) Calculate the capacity of the register and the servers. What is the bottleneck in this system?
b) Calculate the average utilizations of the register and the servers
c) What is the probability a customer is delayed at the register?
d) What is the expected time from a customer’s arrival to the order being passed on to the servers (including any queuing time)?
e) Estimate the probability that there is a delay between a customer placing his order and a server beginning to work on the order.
f) Estimate the squared coefficient of variation of arrivals of orders to the servers.
g) Estimate the expected time from the servers receiving an order to it being ready for the customer (including any queueing time).
h) If we add (d) and (g) we get the total time from a customer walking in to receiving their order. What assumptions have been made to compute this time? Which ONE of these assumptions is the least realistic for this system? Explain your answer.
i) List as many ways you can think of that would decrease the average time a customer spends waiting from placing their order to receiving their food.