Develop the system equations for the steady-state probabilities for a single operator servicing three machines. What type of difficulties will have to be overcome to solve this system of equations for n → ∞, where n denotes the number of machines for which the operator is responsible.
Consider an infinite capacity 3-machine 2-operator service system where an operator is required to setup a job on a machine before processing can begin. Develop the node-arc diagram for 5 or less jobs in the system. That is, develop the diagram explicitly for 0 to 5 jobs in the system with the understanding that the complete diagram would contain an infinite number of nodes. All processes, (arrivals, setups and processing) are assumed to be exponentially distributed with mean rates λ, γ, and μ, respectively.
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