Acyclic Fork-Join Queueing Networks

  • Authors:

  • Francois Baccelli;William A. Massey;Don Towsley

  • Affiliations:

  • -;-;-

  • Venue:
  • Acyclic Fork-Join Queueing Networks
  • Year:
  • 1987

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Abstract

IN THIS PAPER WE STUDY THE CLASS OF ACYCLIC FORK-JOIN QUEUEING NETWORKS THAT ARISE IN VARIOUS APPLICATIONS, INCLUDING PARALLEL PROCESSING AND FLEXIBLE MANUFACTURING. IN SUCH QUEUEING NETWORKS, A FORK DESCRIBES THE SIMULTANEOUS CREATION OF SEVERAL NEW CUSTOMERS WHICH ARE SENT TO DIFFERENT QUEUES. THE CORRESPONDING JOIN OCCURS WHEN THE SERVICES OF ALL THESE NEW CUSTOMERS ARE COMPLETED. WE DERIVE THE EVOLUTION EQUATIONS THAT GOVERN THE BEHAVIOR OF SUCH NETWORKS. FROM THIS, WE OBTAIN THE STABILITY CONDI- TIONS AND DEVELOP UPPER AND LOWER BOUNDS ON THE NETWORK RESPONSE TIMES. THESE BOUNDS ARE BASED ON STOCHASTIC ORDERING PRINCIPLES AND APPLY UNDER GENERAL WORKLOAD ASSUMPTIONS.