Weak convergence limits for sojourn times in cyclic queues under heavy traffic conditions

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Autor/in:
Erscheinungsjahr:
2008
Medientyp:
Text
Schlagworte:
  • Bottleneck node
  • Central limit theorem
  • Customer stationary behaviour
  • Cycle times
  • Joint sojourn time distribution
Beschreibung:
  • We consider sequences of closed cycles of exponential single-server nodes with a single bottleneck. We study the cycle time and the successive sojourn times of a customer when the population sizes go to infinity. Starting from old results on the mean cycle times under heavy traffic conditions, we prove a central limit theorem for the cycle time distribution. This result is then utilised to prove a weak convergence characteristic of the vector of a customer's successive sojourn times during a cycle for a sequence of networks with population sizes going to infinity. The limiting picture is a composition of a central limit theorem for the bottleneck node and an exponential limit for the unsealed sequences of sojourn times for the nonbottleneck nodes. © Applied Probability Trust 2008.
Lizenz:
  • info:eu-repo/semantics/openAccess
Quellsystem:
Forschungsinformationssystem der UHH
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oai:www.edit.fis.uni-hamburg.de:publications/ffc9a751-5464-4204-af8a-7f2b500ecfc0