Heavy traffic convergence of a controlled, multiclass queueing system

L. F. Martins, S. E. Shreve, H. M. Soner

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


This paper provides a rigorous proof of the connection between the optimal sequencing problem for a two-station, two-customer-class queueing network and the problem of control of a multidimensional diffusion process, obtained as a heavy traffic limit of the queueing problem. In particular, the diffusion problem, which is one of "singular control" of a Brownian motion, is used to develop policies which are shown to be asymptotically nearly optimal as the traffic intensity approaches one in the queueing network. The results are proved by a viscosity solution analysis of the related Hamilton-Jacobi-Bellman equations.

Original languageEnglish (US)
Pages (from-to)2133-2171
Number of pages39
JournalSIAM Journal on Control and Optimization
Issue number6
StatePublished - Nov 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics


  • Brownian networks
  • Heavy traffic
  • Queueing
  • Stochastic control
  • Viscosity solutions


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