Heavy-traffic Analysis of the Generalized Switch under Multidimensional State Space Collapse

Daniela Hurtado-Lange*, Siva Theja Maguluri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Stochastic Processing Networks that model wired and wireless networks, and other queueing systems, have been studied in heavytraffic limit under the so-called Complete Resource Pooling (CRP) condition. When the CRP condition is not satisfied, heavy-traffic results are known only in the special case of an input-queued switch and bandwidth-sharing network. In this paper, we consider a very general queueing system called the 'generalized switch' that includes wireless networks under fading, data center networks, input-queued switch, etc. The primary contribution of this paper is to present the exact value of the steadystate mean of certain linear combinations of queue lengths in the heavy-traffic limit under MaxWeight scheduling algorithm. We use the Drift method, and we also present a negative result that it is not possible to obtain the remaining linear combinations (and consequently all the individual mean queue lengths) using this method. We do this by presenting an alternate view of the Drift method in terms of an (under-determined) system of linear equations. Finally, we use this system of equations to obtain upper and lower bounds on all linear combinations of queue lengths.

Original languageEnglish (US)
Pages (from-to)33-34
Number of pages2
JournalPerformance Evaluation Review
Issue number1
StatePublished - Jul 8 2020


  • drift method
  • generalized switch
  • heavy-traffic
  • input-queued switch

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications


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