Question: Consider a system with three parallel servers. Job arrivals are Poisson distributed at the rate of eight per hour unless all three servers are busy.

Consider a system with three parallel servers. Job arrivals are Poisson distributed at the rate of eight per hour unless all three servers are busy. Since there is no waiting space, the arrival rate is zero if all servers a busy. Normally, each server has service time that is exponentially distributed with mean 20 minutes. However, if all three servers are busy the servers speed up so that mean service time is 15 minutes. Find the steady state probability for each system state.

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