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Queueing Systems

, Volume 70, Issue 1, pp 45–79 | Cite as

Dynamic server allocation for unstable queueing networks with flexible servers

  • Salih Tekin
  • Sigrún Andradóttir
  • Douglas G. Down
Article

Abstract

This paper is concerned with the dynamic assignment of servers to tasks in queueing networks where demand may exceed the capacity for service. The objective is to maximize the system throughput. We use fluid limit analysis to show that several quantities of interest, namely the maximum possible throughput, the maximum throughput for a given arrival rate, the minimum arrival rate that will yield a desired feasible throughput, and the optimal allocations of servers to classes for a given arrival rate and desired throughput, can be computed by solving linear programming problems. We develop generalized round-robin policies for assigning servers to classes for a given arrival rate and desired throughput, and show that our policies achieve the desired throughput as long as this throughput is feasible for the arrival rate. We conclude with numerical examples that illustrate the points discussed and provide insights into the system behavior when the arrival rate deviates from the one the system is designed for.

Keywords

Multi-class queueing networks Stability Fluid model Maximum throughput Jackson networks 

Mathematics Subject Classification (2000)

60K25 90B22 90B15 68M20 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Salih Tekin
    • 1
  • Sigrún Andradóttir
    • 2
  • Douglas G. Down
    • 3
  1. 1.Industrial Engineering DepartmentTOBB Economy and Technology UniversityAnkaraTurkey
  2. 2.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Department of Computing and SoftwareMcMaster UniversityHamiltonCanada

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