Problem 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. Jobs are processed at the work center one at a time, at a mean rate of one per three days, and then leave immediately.

(a) Develop the rate 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.