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Queueing networks with dependent nodes and concurrent movements

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Abstract

Classical queueing network processes are useful for modeling the movement of discrete units in a network in which the nodes operate independently, the routing of units is independent of the congestion, only one unit moves at a time and its equilibrium distribution is a well-understood product form. Actual networks, however, typically have dependent nodes and concurrent movement of units. Imagine the dependencies associated with the network movements of telephone calls, manufacturing material, computer data packets, messages in a parallel-processing simulation, etc. A second generation of queueing network processes is beginning to evolve for modeling such “intelligent” networks with dependent nodes and concurrent movements. This paper describes the following fundamental processes that have been developed in this regard:

  • • A basic queueing network process for dependent nodes and single-unit movements. Examples include the classical Jackson, BCMP, Kelly and Kelly-Whittle networks and networks with interacting subpopulations.

  • • Reversible queueing network processes for dependent nodes and concurrent movements. An example is a multivariate, compound birth-death process.

  • • Miscellaneous partially balanced queueing networks. Examples include extensions of the basic network processes and weakly coupled and quasi-reversible networks.

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This research was supported in part by the Air Office of Scientific Research under contract 89-0407 and NSF grant DDM-9007532.

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Serfozo, R.F. Queueing networks with dependent nodes and concurrent movements. Queueing Syst 13, 143–182 (1993). https://doi.org/10.1007/BF01158932

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Keywords

  • Markovian network process
  • queueing processes
  • Jackson network
  • birth-death process
  • reversibility