Models for the Optimal Control of Markovian Closed Queueing Systems with Adjustable Service Rates.
STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
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The report considers the problem of determining an optimal dynamic control policy for a closed queueing system in which the service facilities may be operated at more than one service rate. The optimality criterion is to minimize the long-run expected average cost per unit time. The author formulates a general control model whose cost structure includes 1 an operating cost for running each service facility 2 a switching cost for starting-up and shutting-down the facilities 3 a holding cost rate for customers waiting or in service 4 a service facility profit, earned whenever a service completion occurs. After reviewing some results from the theory of semi-Markov decision processes and proving that an optimal stationary deterministic policy exists for Markovian Closed Queueing Systems, analytical results are presented that specify the form of the optimal policy for several models of two-state closed queueing systems and investigate the behavior of the optimal policy as the number of customers in the system is increased. Several interesting future research topics are also identified in the dynamic control area, as well as in the static design area. Of particular interest are optimization problems that have applications to multiprogramming computer systems. Author
- Operations Research