Question: Consider a two-server queueing system where all service times are independent and identically distributed according to an exponential distribution with a mean of 10 minutes.

Consider a two-server queueing system where all service times are independent and identically distributed according to an exponential with a mean of 10 minutes. Service is provided on a first-come-first-served basis. When a particular customer arrives, he finds that both servers are busy and no one is waiting in the queue.
(a) What is the probability (including its mean and standard deviation) of this customer’s waiting time in the queue?
(b) Determine the expected value and standard deviation of this customer’s waiting time in the system.
(c) Suppose that this customer still is waiting in the queue 5 minutes after its arrival. Given this information, how does this change the expected value and the standard deviation of this customer’s total waiting time in the system from the answers obtained in part (b)?

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