Diffusion limits for the queue length of jobs in multi-server open queueing networks
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DOI: 10.5277/ord170404
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References listed on IDEAS
- Sakalauskas, L. L. & Minkevicius, S., 2000. "On the law of the iterated logarithm in open queueing networks," European Journal of Operational Research, Elsevier, vol. 120(3), pages 632-640, February.
- Avishai Mandelbaum & Alexander L. Stolyar, 2004. "Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cμ-Rule," Operations Research, INFORMS, vol. 52(6), pages 836-855, December.
- Martin I. Reiman, 1984. "Open Queueing Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 441-458, August.
- Hong Chen & Hanqin Zhang, 2000. "Stability of Multiclass Queueing Networks Under Priority Service Disciplines," Operations Research, INFORMS, vol. 48(1), pages 26-37, February.
- Austin J. Lemoine, 1978. "State of the Art--Networks of Queues: A Survey of Weak Convergence Results," Management Science, INFORMS, vol. 24(11), pages 1175-1193, July.
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Keywords
performance evaluation; multiserver open queueing network; limit theorem; queue length;All these keywords.
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