A model for the dynamics of large queuing networks and supply chains

Hans Armbruster, P. Degond, Christian Ringhofer

Research output: Contribution to journalArticlepeer-review

122 Scopus citations


We consider a supply chain consisting of a sequence of buffer queues and processors with certain throughput times and capacities. Based on a simple rule for releasing parts, i.e., batches of product or individual product items, from the buffers into the processors, we derive a hyperbolic conservation law for the part density and flux in the supply chain. The conservation law will be asymptotically valid in regimes with a large number of parts in the supply chain. Solutions of this conservation law will in general develop concentrations corresponding to bottlenecks in the supply chain.

Original languageEnglish (US)
Pages (from-to)896-920
Number of pages25
JournalSIAM Journal on Applied Mathematics
Issue number3
StatePublished - 2006


  • Asymptotics
  • Conservation laws
  • Supply chains

ASJC Scopus subject areas

  • Applied Mathematics


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