Suppose a certain industrial operation requires the use of m machines of a certain type. Suppose each machine has some probability of requiring maintenance at the end of the week, independently of how old the machine is. However, the chance of a machine requiring maintenance increases with the amount of work it does during the week, and the week's workload must be distributed over whatever machines are in service. Machines requiring maintenance are removed from service at the end of the week (Friday evening). Each Monday morning, an order is sent in to replace each machine that went out of service with a new machine, and this new machine will arrive the following Monday.

Please formulate a finite-state discrete-time Markov chain model (either by stochastic update rule or probability transition matrix, although both are preferred if possible) for the number of machines in operation each Monday. Make sure to explain any assumptions made and your reasoning. As an added objective, if possible it would be an added bonus to have the model constructed in such a way that it makes the computation of its stationary distribution (and therefore long-run average statistics) easy to do.