Hw6 - EE 292E Analysis and Control of Markov Chains Spring 2008 Prof Ben Van Roy Homework Assignment 6 Due May 22 Queuing Consider a queue with a

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Unformatted text preview: EE 292E Analysis and Control of Markov Chains Spring 2008 Prof. Ben Van Roy May 15, 2008 Homework Assignment 6: Due May 22 Queuing Consider a queue with a finite buffer of length of 100. At the beginning of each time period, a customer arrives with probability 0 . 75. If there are already 100 customers, he leaves immediately, and the system incurs a cost of 1000. There is a server that, when on, serves one customer per unit time. There is a cost of 10 to switching the server on and a cost of 1 per time period while the server is switched on. There is no cost to switching the server off. There is a cost of 1 per time period per waiting customer. The objective is to minimize expected discounted cost, with a discount factor of 0 . 98. Compute an optimal policy (for switching on and off) using value iteration and policy iteration. Describe the policy concisely, and discuss how the compute times for the two algorithms compare....
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This note was uploaded on 02/15/2011 for the course EECS 6.231 taught by Professor Bertsekas during the Spring '10 term at MIT.

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Hw6 - EE 292E Analysis and Control of Markov Chains Spring 2008 Prof Ben Van Roy Homework Assignment 6 Due May 22 Queuing Consider a queue with a

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