Short Communications

Queueing Systems

, Volume 5, Issue 4, pp 401-411

First online:

An extension to Norton's equivalent

  • Man-Tung T. HsiaoAffiliated withSchool of Electrical Engineering, Purdue University
  • , Aurel A. LazarAffiliated withDepartment of Electrical Engineering, Columbia University

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The aggregation method for queueing networks known as the Norton's equivalent is interpreted as a conditional estimate of the intensities of associated point processes. For multi-class Markovian queueing networks, it is shown that a first-order equivalent system of an isolated station can be obtained via the conditional estimates of intensities of the arrival and departure processes to and from that station. Based on these conditional estimates, separation results for optimal flow control problems in queueing networks can be obtained. Several examples which illustrate these concepts are given. The results obtained here generalize those which require the “product form” networks.


Norton's equivalent conditional estimates Markovian queueing networks