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Comments on: Light tail asymptotics in multidimensional reflecting processes for queueing networks. (English) Zbl 1291.60192

Comment to [M. Miyazawa, Top 19, No. 2, 233–299 (2011; Zbl 1280.60051)].

MSC:

60K25 Queueing theory (aspects of probability theory)
90B15 Stochastic network models in operations research
60G50 Sums of independent random variables; random walks
60F10 Large deviations

Citations:

Zbl 1280.60051
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References:

[1] Asmussen S (2003) Applied probability and queues, 2nd edn. Springer, New York · Zbl 1029.60001
[2] Cohen JW, Boxma OJ (1983) Boundary value problems in queueing systems analysis. North-Holland, Amsterdam
[3] Debicki K, Dieker A, Rolski T (2007) Quasi-product form for Lévy-driven fluid networks. Math Oper Res 32:629–647 · Zbl 1341.60111 · doi:10.1287/moor.1070.0259
[4] Doetsch G (1974) Introduction to the theory and application of the Laplace transformation. Springer, Berlin · Zbl 0278.44001
[5] Guillemin F, van Leeuwaarden JSH (2011) Rare event asymptotics for random walk in the quarter plane. Queueing Syst, Theory Appl 67:1–32 · Zbl 1210.60100 · doi:10.1007/s11134-010-9197-7
[6] Müller A, Stoyan D (2002) Comparison methods for stochastic models and risks. Wiley, Chichester · Zbl 0999.60002
[7] Miyazawa M, Rolski T (2009) Exact asymptotics for a Levy-driven tandem queue with an intermediate input. Queueing Syst 63:323–353 · Zbl 1209.90117 · doi:10.1007/s11134-009-9146-5
[8] Miyazawa M Rolski T (2011) Unpublished work
[9] Robert Ph (2003) Stochastic networks and queues. Springer, Berlin
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