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Queueing Systems

, Volume 79, Issue 3–4, pp 251–291 | Cite as

A law of iterated logarithm for multiclass queues with preemptive priority service discipline

  • Yongjiang Guo
  • Yunan LiuEmail author
Article

Abstract

A law of iterated logarithm (LIL) is established for a multiclass queueing model, having a preemptive priority service discipline, one server and \(K\) customer classes, with each class characterized by a renewal arrival process and i.i.d. service times. The LIL limits quantify the magnitude of asymptotic stochastic fluctuations of the stochastic processes compensated by their deterministic fluid limits. The LIL is established in three cases: underloaded, critically loaded, and overloaded, for five performance measures: queue length, workload, busy time, idle time, and number of departures. The proof of the LIL is based on a strong approximation approach, which approximates discrete performance processes with reflected Brownian motions. We conduct numerical examples to provide insights on these LIL results.

Keywords

Law of iterated logarithm Multiclass queues Priority queues Preemptive-resume discipline Non-Markovian queues Strong approximation 

Mathematics Subject Classification

60K25 90B22 60F15 60J65 

Notes

Acknowledgments

We thank Prof. Ward Whitt, Prof. Junfei Huang and the anonymous referees for providing constructive comments. Both authors were supported by NSFC grant 11471053. The first author also acknowledges support from NSFC grant 11101050. The second author also acknowledges support from NSF Grant CMMI 1362310.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of ScienceBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.Department of Industrial and Systems EngineeringNorth Carolina State UniversityRaleighUSA

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