×

zbMATH — the first resource for mathematics

Fluid flow models and queues – a connection by stochastic coupling. (English) Zbl 1021.60073
Summary: We establish in a direct manner that the steady state distribution of Markovian fluid flow models can be obtained from a quasi birth and death queue. This is accomplished through the construction of the processes on a common probability space and the demonstration of a distributional coupling relation between them. The results here provide an interpretation for the quasi-birth-and-death processes in the matrix-geometric approach of Ramaswami and subsequent results based on them obtained by Soares and Latouche.

MSC:
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1016/S0166-5316(00)00020-1 · Zbl 1017.68011 · doi:10.1016/S0166-5316(00)00020-1
[2] Anick D., Bell Syst. Tech. J. 61 pp 1871– (1982) · doi:10.1002/j.1538-7305.1982.tb03089.x
[3] DOI: 10.1080/15326349508807330 · Zbl 0817.60086 · doi:10.1080/15326349508807330
[4] DOI: 10.1080/15326349908807170 · Zbl 0744.60108 · doi:10.1080/15326349908807170
[5] DOI: 10.1080/15326349708807417 · Zbl 0871.60070 · doi:10.1080/15326349708807417
[6] DOI: 10.2307/1426216 · Zbl 0212.49601 · doi:10.2307/1426216
[7] DOI: 10.1287/opre.33.5.1107 · Zbl 0576.60083 · doi:10.1287/opre.33.5.1107
[8] DOI: 10.2307/3213214 · Zbl 0443.60086 · doi:10.2307/3213214
[9] DOI: 10.1080/15326348708807055 · Zbl 0622.60077 · doi:10.1080/15326348708807055
[10] DOI: 10.1137/1.9780898719734 · Zbl 0922.60001 · doi:10.1137/1.9780898719734
[11] DOI: 10.2307/3214773 · Zbl 0789.60055 · doi:10.2307/3214773
[12] DOI: 10.1287/opre.40.3.S257 · Zbl 0825.90344 · doi:10.1287/opre.40.3.S257
[13] Neuts M. F., Matrix-Geometric Solutions in Stochastic Models, An Algorithmic Approach (1981) · Zbl 0469.60002
[14] Ramaswami V., Opsearch 19 pp 238– (1982)
[15] DOI: 10.1080/15326349908807141 · Zbl 0699.60091 · doi:10.1080/15326349908807141
[16] Ramaswami, V. 1999. ”Matrix analytic methods for stochastic fluid flows. InTeletrafic Engineering in a Competitive World”. Edited by: Smith, D. and Key, P. 1019–1030. Elsevier. Proc. of the 15th International Teletraffic Congress
[17] Ramaswami V., Mathematics for the New Millennium (2000)
[18] da Silva Soares A., Matrix-Analytic Methods, Theory and Applications (2002)
[19] DOI: 10.1287/opre.30.2.223 · Zbl 0489.60096 · doi:10.1287/opre.30.2.223
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.