Customers arrive to a local bakery with an average time between arrivals of 5 minutes. However, there is quite a lot of variability in the customers’ arrivals, as one would expect in an unscheduled system. The single bakery server requires an amount of time having the exponential distribution with mean 4.5 minutes to serve customers (in the order in which they arrive). No customers leave without service.

a. Calculate the average utilization of the bakery server.

b. Calculate how long customers spend on average to complete their transactions at the bakery (time in queue plus service time). What percentage of that time is spent queueing?

c. How many customers are in the bakery on average?

d. Calculate the probability a customer will spend more than an hour at the bakery

(time in queue plus service time).

e. What is the probability that there are fewer than two customers in the bakery?

f. Why are the estimated waits in this system so long? Are the assumptions behind them reasonable? Why or why not?