The state of a particular continuous time Markov chain is defined as the number of jobs currently at a certain work center, where a maximum of two jobs are allowed. Jobs arrive individually. Whenever fewer than two jobs are present, the time until the next arrival has an exponential distribution with a mean of 2 days. Jobs are processed at the work center one at a time and then leave immediately. Processing times have an exponential distribution with a mean of 1 day.
(a) Construct the rate diagram for this Markov chain.
(b) Write the steady-state equations.
(c) Solve these equations for the steady-state probabilities.