2. 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 next arrival occurs at a mean rate of one in two days (i.e., job arrival rate one at a time, at a mean rate of one per three days (i.e., job completion rate = 1/3), and then leave immediately.1/2). Jobs are processed at the work center (a) Develop the diagram for this Markov chain. (b) Write down time-dependent ordinary differential equations for this Markov chain. (c) Construct the steady-state equations. (d) Determine the the steady-state probabilities.

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