Analysis and Applications of the Delay Cycle for the M/M/c Queueing System

  • Authors:

  • K. Omahen;V. Marathe

  • Affiliations:

  • ECRM, Inc., 205 Burlington Road, Bedford, MA and Purdue University, West Lafayette, Indiana;Mount Sinai Hospital Services, City Hospital Center at Elmhurst, 79-01 Broadway, Elmhurst, NY and University of Illinois, Urbana, Illinois

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1978

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Abstract

The method of analysis employing decomposition of busy periodshas, in various forms, been applied to the M/G/1 queueing systemunder a variety of scheduling rules This paper extends thetechnique of decomposition of busy periods in order to deal withthe M/M/c queueing system. Particular attention is given to aspecial busy period referred to as a "delay cycle." The delay cyclecommences with a delay period (of general distribution) in whichjobs arrive but are not serviced, at the conclusion of the delayperiod, processing begins and continues until the system is empty.Closed form solutions are obtained for various entities such asdistribution of busy period length and expected waiting timeconditioned on the type of busy period in progress at the tmae ofjob arrival. These results are applied and extended to the analysisof six examples of multiprocessor systems.