Question: Consider a system in which individual jobs in a stream of Poisson arrivals with a rate of 10 jobs per second are routed to one

Consider a system in which individual jobs in a stream of Poisson arrivals with a rate of 10 jobs per second are routed to one of two queues as follows. A job is routed with probability 0.4 to a single-server queue with a service rate of 8 jobs per second. Otherwise, it is routed to a single-server queue with a service rate of 14 jobs per second. Both queues have exponentially distributed service times and unlimited waiting room capacities.

(a) Determine the expected delay in each of the individual queues (including service time) as well as the overall expected delay of a job (including service time) in the complete system.

(b) What is the steady-state probability that there are two jobs in the entire system?

(d) What is the utilization of each server?

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