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Light traffic heuristic for anM/G/1 queue with limited inventory

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Abstract

Motivated by solving a stylized location problem, we develop a light traffic heuristic for anM/G/1 queue with limited inventory that gives rise to a closed form expression for average delay in terms of basic system parameters. Simulation experiments show that the heuristic works well. The inventory operates as follows: the inventory level drops by one unit after each service completion and whenever it drops to a pre-specified levelu, an order is placed with replenishment time ∼ exp(γ). Upon replenishment the inventory is restocked to a pre-specified levels and any arrivals when there is no inventory are placed in queue. Suggestions are given to cover the more general case of a New Better than Used (NBU) replenishment time distribution. Applications to inventory management problems are also discussed.

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Authors and Affiliations

  1. Department of Industrial Engineering and Operations Research, Columbia University, 10027, New York, NY, USA

    Karl Sigman & David Simchi-Levi

Authors
  1. Karl Sigman
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  2. David Simchi-Levi
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Additional information

The research was supported in part by ONR Contract N00014-90-J-1649, NSF Contract DDM-8922712 and the Center for Telecommunications Research under NSF grant CDR 84-21402.

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Sigman, K., Simchi-Levi, D. Light traffic heuristic for anM/G/1 queue with limited inventory. Ann Oper Res 40, 371–380 (1992). https://doi.org/10.1007/BF02060488

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  • DOI: https://doi.org/10.1007/BF02060488

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