Heavy traffic limits for some queueing networks

Maury Bramson, J. G. Dai

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


Using a slight modification of the framework of Bramson [7] and Williams [54], we prove heavy traffic limit theorems for six families of multiclass queueing networks. The first three families are single-station systems operating under first-in-first-out (FIFO), generalized-head-of-the-line proportional processor sharing (GHLPPS) and static buffer priority (SBP) service disciplines. The next two families are reentrant lines that operate under first-buffer-first-serve (FBFS) and last-buffer-first-serve (LBFS) service disciplines; the last family consists of certain two-station, five-class networks operating under an SBP service discipline. Some of these heavy traffic limits have appeared earlier in the literature; our new proofs demonstrate the significant simplifications that can be achieved in the present setting.

Original languageEnglish (US)
Pages (from-to)49-90
Number of pages42
JournalAnnals of Applied Probability
Issue number1
StatePublished - Feb 2001


  • Brownian model
  • Diffusion approximation
  • Heavy traffic
  • Multiclass queueing network
  • Reflecting Brownian motion

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