# zbMATH — the first resource for mathematics

Solving multi-regime feedback fluid queues. (English) Zbl 1148.60071
Summary: We study Markov fluid queues with multiple thresholds, or the so-called multi-regime feedback fluid queues. The boundary conditions are derived in terms of joint densities and for a relatively wide range of state types including repulsive and zero drift states. The ordered Schur factorization is used as a numerical engine to find the steady-state distribution of the system. The proposed method is numerically stable and accurate solution for problems with two regimes and $$2^{10}$$ states is possible using this approach. We present numerical examples to justify the stability and validate the effectiveness of the proposed approach.

##### MSC:
 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
##### Keywords:
feedback queues; Markov fluid queues; Schur decomposition
Full Text:
##### References:
 [1] Anick D., Bell. Syst. Tech. Jour. 61 pp 1871– (1982) [2] DOI: 10.1109/26.2773 [3] Kulkarni V.G., Frontiers in Queuing: Models and Applications in Science and Engineering (1997) [4] Ramaswami , V. Matrix analytic methods for stochastic fluid flows. Proc. of the 16th International Teletraffic Congress , Smith , D. , Key , P. , Eds. 1999 . [5] DOI: 10.1016/j.peva.2005.02.002 [6] DOI: 10.1080/15326349508807330 · Zbl 0817.60086 [7] DOI: 10.1214/aoap/1177005065 · Zbl 0806.60052 [8] DOI: 10.1239/jap/1082999086 · Zbl 1046.60078 [9] DOI: 10.1023/A:1019144400149 · Zbl 0916.90103 [10] Scheinhardt , W. Markov Modulated and Feedback Fluid Queues. Ph.D. dissertation , University of Twente , 1998 . [11] DOI: 10.1109/26.328980 [12] DOI: 10.1017/S0269964802164011 · Zbl 1038.90020 [13] DOI: 10.1016/j.orl.2004.11.008 · Zbl 1083.60076 [14] DOI: 10.1023/A:1025147422141 · Zbl 1030.60089 [15] DOI: 10.1016/S1389-1286(02)00415-2 · Zbl 1035.68010 [16] DOI: 10.1017/S0269964805050011 · Zbl 1063.90001 [17] Kankaya , H.E. ; Akar , N. Performance Evaluation and Traffic Modeling Tools.http://www.ee.bilkent.edu.tr/ pevatools/Electrical and Electronics Engineering Department, Bilkent University . [18] Golub G.H., Matrix Computations,, 3. ed. (1996) · Zbl 0865.65009 [19] LAPACK Users’s Guide , 1995 , 2nd Ed. [20] van Dooren , P.M. Numerical linear algebra for signals, systems, and control. Universite Catholique de Louvain, Belgium . 2003 . Draft notes prepared for the Graduate School in Systems and Control . [21] DOI: 10.1007/s002110050264 · Zbl 0876.65021
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.