Heavy-traffic approximations for a layered network with limited resources

Angelos Aveklouris, Maria Vlasiou, Jiheng Zhang, Bert Zwart

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)


Motivated by a web-server model, we present a queueing network consisting of two layers. The first layer incorporates the arrival of customers at a network of two single-server nodes. We assume that the inter-arrival and the service times have general distributions. Customers are served according to their arrival order at each node and after finishing their service they can re-enter at nodes several times (as new customers) for new services. At the second layer, active servers act as jobs which are served by a single server working at speed one in a Processor-Sharing fashion. We further assume that the degree of resource sharing is limited by choice, leading to a Limited Processor-Sharing discipline. Our main result is a diffusion approximation for the process describing the number of customers in the system. Assuming a single bottleneck node and studying the system as it approaches heavy traffic, we prove a state-space collapse property. The key to derive this property is to study the model at the second layer and to prove a diffusion limit theorem, which yields an explicit approximation for the customers in the system.
Original languageEnglish
Pages (from-to)497-532
Number of pages36
JournalProbability and mathematical statistics
Issue number2
Publication statusPublished - 30 Dec 2017
Externally publishedYes


  • Diffusion approximation
  • Fluid model
  • Heavy traffic
  • Layered queueing network
  • Limited processor sharing


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