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Consider an open Jackson network of two queueing stations, with one server at station 1 and two servers at station 2 . Assume that jobs

  Consider an open Jackson network of two queueing stations, with one server at station 1 and two servers at station 2. Assume that jobs arrive to stations 1 and 2 according to independent Poisson processes with rates 12 and 10 per hour, respectively. All jobs departing from station 1 will move to station 2, and \\(20\\%\\) of jobs departing from station 2 will go to station 1(the remaining \\(80\\%\\) of jobs departing from station 2 will leave the system). Assume furthermore that the service times at each station are independent and exponentially distributed with hourly rate 20. Specify the following quantities: (a) Steady-state probability that station 1 is empty (b) Steady-state probability that the entire network is empty (c) Long-run average number of jobs within the network (d) Long-run average time in the system per job

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