Consider a queuing system with two servers whose service times are independent and are exponentially distributed with a mean of 1 hour. The servers do not assist each other.

Assume customers arrive into the system according to a Poisson rate of 20 per hour. Assume that if a prospective customer enters the system and sees two people waiting in line, the prospective customer immediately balks. (That is, the prospective customer immediately leaves; it is as if the prospective customer did not enter the system.)

(a) Analyze the queue using the state transition diagrams discussed during lectures. For each possible number k of customers in the system, determine the steady-state probability that k customers are in the system.

(b) What is the steady-state probability that a prospective customer will balk?

(c) What is the steady-state average number of customers in the system?