Question: An agent in a train station sells tickets and provides information to travelers. An average of two travelers approach the agent for assistance each minute.

An agent in a train station sells tickets and provides information to travelers. An average of two travelers approach the agent for assistance each minute. Their arrival is distributed according to a Poisson distribution. The agent is able to meet the travelers’ needs in approximately 20 seconds, distributed exponentially.
(a) What is the probability that there are more than two travelers in the system? More than three? More than four?
(b) What is the probability that the system is empty?
(c) How long will the average traveler have to wait before reaching the agent?
(d) What is the expected number of travelers in the queue?
(e) What is the average number in the system?
(f) If a second agent is added (who works at the same pace as the first), how will the operating characteristics computed in parts (b), (c), (d), and (e) change? Assume that travelers wait in a single line and go to the first available agent.

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