5.5. Consider a post office with two clerks. John, Paul, and Naomi enter simultaneously. John and Paul go directly to the clerks, while Naomi must wait until either John or Paul is finished before she begins service.

(a) If all of the service times are independent exponentially distributed random variables with the same mean 1/A, what is the probability that Naomi is still in the post office after the other two have left?

(b) How does your answer change if the two clerks have different service rates, say A, = 3 and A, = 47?

(c) The mean time that Naomi spends in the post office is less than that for John or Paul provided that max { A A2) > c min( A, , A, j for a certain constant

c. What is the value of this constant?