# hw7 - n queues and there is one server At each time we must...

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EE 292E Analysis and Control of Markov Chains Spring 2008 Prof. Ben Van Roy May 22, 2008 Homework Assignment 7: Due May 29 Queueing with Constraints Consider the Queueing problem from Homework 6, but suppose that the objective is to minimize average cost, and there is an additional requirement that the queue can have more than 10 customers waiting no more than 5% of the time. Provide an optimal policy. Uniformization Provide transition probabilities, a per-stage cost function, and a discount factor that deﬁne a discrete-time problem equivalent to the following queueing system. There are
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Unformatted text preview: n queues and there is one server. At each time, we must allocate the server to one of the queues. When serving the i th queue, the service time is exponential with expected completion time 1 /ν i . There is a cost c i per unit time per customer waiting in queue i . After a customer is served, he leaves the system with probability q . Otherwise, he joins another queue; the probability he chooses each i th queue is q i , and ∑ n i =0 q i = 1. The objective is to minimize expected discounted cost, with a discount rate β > 0....
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