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Control of Multiple Exponential Servers with Application to Computer Systems

Larsen, Ronald (1981) Control of Multiple Exponential Servers with Application to Computer Systems. Doctoral Dissertation, University of Maryland.

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A class of dynamic control policies is defined for scheduling customers from a Poisson source on a set of exponential servers with dissimilar service rates. A fastest-to-slowest ordering is imposed on the servers, and they are invoked in response to instantaneous system loading as measured by the length of the queue of waiting customers. Markov chain analysis is employed to analyze the performance of the control policies and to develop optimality criteria. It is shown for the two-server case, and believed to be true in general, that probabilistic control policies are suboptimal to minimize the mean number of customers in the system, and that the optimal policy is in a restricted class of policies referred to as "threshold queueing" policies. In a threshold queueing policy, specific queue lengths are identified as "thresholds" beyond which an additional (fastest idle) server is invoked. A new server remains busy until it completes service on a customer and the queue length is less than its invocation threshold. Optimality conditions are derived, and an approximation to the optimum policy is analyzed. For most operational applications, a very simple approximation of the optimal threshold value suffices.Extensions to the basic policy involving different objectives are considered, including a treatment of the n-server case, the finite queue situation, and inverse ordering (slowest-to-fastest) of servers. Several applications of threshold queueing policies in computer and communications systems are presented. It is concluded that threshold queueing policies with easily approximated thresholds provide near-optimal control of multiple exponential servers with dissimilar service rates, and that these policies can be readily applied to improve the performance of contemporary computer and communications systems


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Item Type: Other Thesis, Dissertation, or Long Paper (Doctoral Dissertation)
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Larsen, Ronaldrlarsen@pitt.eduRLARSEN
Date: 20 June 1981
Date Type: Publication
Institution: University of Maryland
Degree: ["degree_typename_PhD from University of Maryland" not defined]
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Queueing Theory, Resource allocation, Scheduling, Multiple servers, Applied Computing, Enterprise Computing, Business Process Management, Mathematics of Computing, Probability and Statistics
EditorsEmailPitt UsernameORCID
Date Deposited: 27 Oct 2021 15:21
Last Modified: 29 Oct 2021 04:55


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