Freddy Krueger enters the police station to apply for the driver’s license where two applicants, Micheal Myers and Jason Voorhees are having service from two servers. Freddy will be the next one to be served. Each applicant leave the police station once his transaction has been completed in the server. Assume that serving time of each server is an exponential random variable with rate λ.
(a) Compute the probability that Freddy will be the last one to leave the police station among three applicants (Freddy, Micheal, and Jason).
(b) Compute the cdf of Freddy’s waiting time in the line. Hint: If J and M respectively denote serving time for Jason and Micheal, then Freddy’s waiting time should be expressed as a function of J and M.
(c) Compute the expected time that Freddy stays in the police station.
(a) Compute the probability that Freddy will be the last one to leave the police station among three applicants (Freddy, Micheal, and Jason).
(b) Compute the cdf of Freddy’s waiting time in the line. Hint: If J and M respectively denote serving time for Jason and Micheal, then Freddy’s waiting time should be expressed as a function of J and M.
(c) Compute the expected time that Freddy stays in the police station.