In an inventory system for a single type of product the depletion of inventory is due to demand. The demand process for the product is a Poisson process with rate . A simple inventory control policy is exercised as follows. Each time the inventory level drops to zero, an order for Q units is placed. Assume that the order placed can arrive immediately. a. Model this stochastic process as a CTMC. Clearly define the state space, transition rates, and transition probability matrix (or equivalently, draw a transition graph with transition rates specified on the graph). b. Compute the expected inventory level and how often one needs to order new products for this system.