Obtain the steady-state probabilities for a GE2/GE2/1/1 system where an arrival to a full system blocks the arrival process, and with inter-arrival time distribution parameters (α, p,β)=(1.5,1/3,3) and service time distribution parameters (μ,q, γ)=(2,1/6,4). (Notice that the maximum number of jobs allowed in the system is 2.) Also assume that a blocked arrival stops the arrival process. Note that this system has 8 probability states.
(a) What are the probabilities that there will be 0, and 1 jobs in the system?
(b) What is the probability that the arrivals to this system are blocked?
(c) Counting a blocked arrival as an extra job in this system, what are the probabilities that there will be 0, 1, and 2 jobs in the system?