A New Technique in the Optimization of Exponential Queueing Systems

Abstract

The problem of controlling M/M/c queueing systems with c = or > 1 is considered. By providing a new definition of the time of transition, we enlarge the standard set of decision epochs, and obtain a preferred version of the n- period problem in which the times between transitions are exponential random variables with constant parameter. Using this new technique, we are able to use the inductive approach in a manner characteristic of inventory theory. The efficacy of the approach is then demonstrated by successfully finding the form of an optimal policy for four quite distinct models that have appeared in the literature; namely, those of (i) McGill, (ii) Miller-Cramer, (iii) Crabill-Sabeti, and (iv) Low. Of particular note, one analysis establishes that an (s, S) or control-limit policy is optimal for an M/M/c queue with switching costs and removable servers.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1973
Accession Number
AD0769169

Entities

People

  • Steven A. Lippman

Organizations

  • University of California, Los Angeles

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  • Materials and Manufacturing Processes

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  • Air Force
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  • Markov Processes
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  • Mathematics

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  • Mathematical Modeling and Probability Theory.
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