# Consider a ticket center with two clerks, whose service time S1 and S2 are expo- nentially distributed with parameter 1 and 2, respectively. The…

Consider a ticket center with two clerks, whose service time S1 and S2 are expo- nentially distributed with parameter μ1 and μ2, respectively. The service times are independent. Customer C arrives at the ticket center and finds S1 is serving customer A and S2 is serving customer B. No other customers are waiting in line.

1. (a) What is the probability that, of the three people, C is the last one to leave?
2. (b) Let t = 0 be the time instant that C arrives at the ticket center and T be the time instant that all three customers leave the system. Calculate E[T]. (Hint: Write E[T ] = E[T1] + E[T2] + E[T3], where Ti denotes the time length between the ith and the (i − 1)th customer leaving the ticket center.)

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