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A small computer store has room to display up to three computers for sale. Customers come at…


A small computer store has room to display up to three computers for sale. Customers come at times of a Poisson process with rate 2 per week to buy a computer and will buy one if at least 1 is available. When the store has only one computer left it places an order for two more computers. The order takes an exponentially distributed amount of time with mean 1 week to arrive. Of course, while the store is waiting for delivery, sales may reduce the inventory to 1 and then to 0. (a) Write down the matrix of transition rates Qij and solve πQ = 0 to find the stationary distribution. (b) At what rate does the store make sales?