On a Slow Server Problem
The slow server problem is generalized for the case of additional cost structure. With the help of special partial ordering of the system state space it is shown that the optimal policy for the problem has a monotone property consisting in the following: an additional server should be switched on only in the case if the queue length exceeds some level depending on the system state, and in this case the server with minimal service cost should be used.
KeywordsOptimal Policy Queue Length Sojourn Time Monotonicity Property Qualitative Property
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