2.10) Consider the system of Conceptual Problem 2.9 (please see below). Now suppose the machine can...

2.10) Consider the system of Conceptual Problem 2.9 (please see below). Now suppose the machine can process two items simultaneously. However, it takes 2 minutes to complete the processing. There is a bin in front of the machine where there is room to store two nondefective items. As soon as there are two items in the bin, they are loaded onto the machine and the machine starts processing them. Model this system as a DTMC.

** please answer only question 2.10 **

2.9) Items arrive at a machine shop in a deterministic fashion at a rate of one per minute. Each item is tested before it is loaded onto the machine. An item is found to be nondefective with probability p and defective with probability 1-p. If an item is found defective, it is discarded. Otherwise, it is loaded onto the machine. The machine takes exactly 1 minute to process the item, after which it is ready to process the next one. Let Xn be 0 if the machine is idle at the beginning of the nth minute and 1 if it is starting the processing of an item. Show that {Xn , n>=0} is a DTMC, and display its transition probability matrix.

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orchestra answered 2 years ago

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