Queueing Systems

, Volume 20, Issue 3–4, pp 409–431 | Cite as

Deadlock properties of queueing networks with finite capacities and multiple routing chains

  • Jörg Liebeherr
  • Ian F. Akyildiz


Blocking in queueing network models with finite capacities can lead to deadlock situations. In this paper, deadlock properties are investigated in queueing networks with multiple routing chains. The necessary and sufficient conditions for deadlockfree queueing networks with blocking are provided. An optimization algorithm is presented for finding deadlock-free capacity assignments with the least total capacity. The optimization algorithm maps the queueing network into a directed graph and obtains the deadlock freedom conditions from a specified subset of cycles in the directed graph. In certain network topologies, the number of deadlock freedom conditions can be large, thus, making any optimization computationally expensive. For a special class of topologies, so-calledtandem networks, it is shown that a minimal capacity assignment can be directly obtained without running an optimization algorithm. Here, the solution to the minimal capacity assignment takes advantage of the regular topology of tandem networks.


Queueing networks blocking networks deadlocks deadlock prevention 


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Copyright information

© J.C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

  • Jörg Liebeherr
    • 1
  • Ian F. Akyildiz
    • 2
  1. 1.Department of Computer ScienceUniversity of VirginiaCharlottesvilleUSA
  2. 2.School of Electrical and Computer EngineeringGeorgia Institute of TechnologyAtlantaUSA

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