Question: A certain queuing system has two types of customers and two types of servers. Type A customers arrive according to a Poisson process with rate

A certain queuing system has two types of customers and two types of servers. Type A customers arrive according to a Poisson process with rate 3, and, independently, Type B customers arrive according to a Poisson process with rate 2. If Server A is free, then an arriving Type A customer begins service with Server A. If Server A is busy but Server B is free, then an arriving Type A customer will begin service with Server B. If an arriving Type A customer finds both servers busy, they will leave the system. If Server B is free, then an arriving Type B customer will be served by Server B, and otherwise will leave the system. Server A takes an exponential rate 2 time to finish a service, Server B takes an exponential rate 1 time to finish a service, and all service times are independent and independent of arrivals. state space = (0,0) both servers free, (0,1) server B busy, (1,0) server A busy, (1,1) both servers busy (a) Model the system as a four state Markov chain and write down its generator

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