Consider a customer service facility that is staffed with 2 representatives. We assume that the amount of time a customer spends with a representative is exponentially distributed with an average service time of 5 mins.
a) Let X be the amount of time a customer spends with a representative. What is the PDF FX(x) of the variable X?
b) During lunch time, there will be only one representative serving customers. Suppose Andrew enters the facility during lunch time and finds the representative is busy serving another customer. If there is no other customer waiting for service, what is the expected wait time for Andrew?
c) Again, suppose Andrew enters the facility during lunch time and finds the representative is serving another customer. If there is already one other customer waiting for service, what is Andrew's expected wait time?
d) Andrew enters the facility(not during lunch time) and finds that both representatives are serving customers. If there is NO customer waiting for service, what is Andrew's expected wait time? Compare your answer to part b. What can you conclude?
e) Andrew enters the facility (not during lunch time) and find that both representatives are serving customers. If there is already one other customer who is waiting, what is Andrew's expected wait time? Compare answer to part c.
f) Consider the case described in part (e). What is the probability that Andrew will leave the facility before the other customer who was already waiting for service leaves the facility?