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A Cost-Equation Analysis of General-Input General-Service Processor Sharing System

In: Operations Research Proceedings 2011

Author

Listed:
  • Kentaro Hoshi

    (Waseda University)

  • Naohisa Komatsu
  • Yoshitaka Takahashi

Abstract

In the computer-communication field, we frequently encounter a situation in which the processor sharing (PS) rule is adopted for a time-shared server next to the first-come-first-serve (FCFS) rule. There has been much work on the Poisson-input general-service M/GI/1 (PS) system. However, there have been few results for a general-input general-service GI/GI/1 (PS) system. We deal with this general GI/GI/1 (PS) system. We show that the cost-equation analysis enables us to derive the relationship between the mean (time-average) unfinished work and the mean (customer-average) sojourn time. Our relationship is then applied to extend and generalize the previous results, e.g., Brandt et al.’s relationship between the mean (customer-average) sojourn times under the FCFS and PS rules, and Kleinrock’s conservation law for the M/GI/1 (PS) system.

Suggested Citation

  • Kentaro Hoshi & Naohisa Komatsu & Yoshitaka Takahashi, 2012. "A Cost-Equation Analysis of General-Input General-Service Processor Sharing System," Operations Research Proceedings, in: Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), Operations Research Proceedings 2011, edition 127, pages 515-520, Springer.
    • Handle: RePEc:spr:oprchp:978-3-642-29210-1_82
    DOI: 10.1007/978-3-642-29210-1_82
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