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ex-10 - Spring 2011 OR3510/5510 Problem Set 10 When this is...

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Spring 2011 OR3510/5510 Problem Set 10 When this is due: We are back to the usual, non-crisis-prelim schedule. This problem set is due noon Monday April 25. Reading: We are just about finished with Chapter 6 and about to begin renewal theory in Chapter 7. (1) In the M/M/s queueing model, let R ( t ) be the number of busy servers at time t. If ρ < 1 show that a limit distribution exists lim t →∞ P [ R ( t ) = k ] = η k , 0 k s. Find it. What is the mean of the limit distribution? (2) Rework–Dissatisfied customers: The grill at Harry’s restaurant is modelled as an M/M/1 queue with a wrinkle. Harry has hired an inexperienced college student to do the grilling and customers may be dissatisfied with the item they receive and may ask to be served again. (This paradigm corresponds to rework in manufacturing settings.) The college student is only capable of working on one item at a time so dissatisfied customers are served again immediately until they are satisfied. Suppose on receiving an order, there is probability 1 - p (where 0
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