Optimal-control of the M/G/1 queue with repeated vacations of the server

Optimal-control of the M/G/1 queue with repeated vacations of the server

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Article ID: iaor20001199
Country: United States
Volume: 38
Issue: 12
Start Page Number: 1766
End Page Number: 1775
Publication Date: Dec 1993
Journal: IEEE Transactions On Automatic Control
Authors: ,
Keywords: programming: dynamic
Abstract:

We consider a M/G/1 queue where the server may take repeated vacations. Whenever a busy period terminates the server takes a vacation of random duration. At the end of each vacation the server may either take a new vacation or resume service; if the queue is found empty the server always takes a new vacation. The cost structure includes a holding cost per unit of time and per customer in the system and a cost each time the server is turned on. One discounted cost criterion and two average cost criteria are investigated. We show that the vacation policy that minimizes the discounted cost criterion over all policies (randomized, history dependent, etc.) converges to a threshold policy as the discount factor goes to zero. This result relies on a nonstandard use of the value iteration algorithm of dynamic programming and is used to prove that both average cost problems are minimized by a threshold policy.

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