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Queueing Systems

Erschienen in:

06.02.2019

Exact tail asymptotics for fluid models driven by an M/M/c queue

verfasst von: Wendi Li, Yuanyuan Liu, Yiqiang Q. Zhao

Erschienen in: Queueing Systems | Ausgabe 3-4/2019

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Abstract

In this paper, we investigate exact tail asymptotics for the stationary distribution of a fluid model driven by the M / M / c queue, which is a two-dimensional queueing system with a discrete phase and a continuous level. We extend the kernel method to study tail asymptotics of its stationary distribution, and a total of three types of exact tail asymptotics are identified from our study and reported in the paper.

Vorheriger Artikel Discrete-time modified number- and time-limited vacation queues

Nächster Artikel Discrete-time queue with batch renewal input and random serving capacity rule:

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Adan, I., Resing, J.: Simple analysis of a fluid queue driven by an \(M/M/1\) queue. Queueing Syst. 22, 171–174 (1996)CrossRef

Banderier, C., Bousquet-Mélou, M., Denise, A., Flajolet, P., Gardy, D., Gouyou-Beauchamps, D.: Generating functions for generating trees. Discrete Math. 246, 29–55 (2002)CrossRef

Barbot, N., Sericola, B.: Stationary solution to the fluid queue fed by an \(M/M/1\) queue. J. Appl. Probab. 39, 359–369 (2002)CrossRef

Dai, H., Dawson, D.A., Zhao, Y.Q.: Kernel method for stationary tails: from discrete to continuous. In: Dawson, D., Kulik, R., Ould Haye, M., Szyszkowicz, B., Zhao, Y.Q. (eds.) Asymptotic Laws and Methods in Stochastics. Fields Institute Communications, vol. 37, pp. 54–60. Springer, New York (2015)

Dai, J.G., Miyazawa, M.: Reflecting Brownian motion in two dimensions: exact asymptotics for the stationary distribution. Stoch. Syst. 1, 146–208 (2011)CrossRef

Down, D., Meyn, S.P., Tweedie, R.L.: Exponential and uniform ergodicity of Markov processes. Ann. Probab. 23, 1671–1691 (1995)CrossRef

Fayolle, G., Iasnogorodski, R.: Two coupled processors: the reduction to a Riemann-Hilbert problem. Z. Wahrscheinlichkeitsth 47, 325–351 (1979)CrossRef

Fayolle, G., Iasnogorodski, R., Malyshev, V.: Random Walks in the Quarter-Plane. Springer, Berlin (1999)CrossRef

Flajolet, P., Odlyzko, A.: Singularity analysis of generating functions. SIAM J. Discrete Math. 3, 216–240 (1990)CrossRef

10.

Flatto, L., Hahn, S.: Two parallel queues created by arrivals with two demands I. SIAM J. Appl. Math. 44, 1041–1053 (1984)CrossRef

11.

Govorun, M., Latouche, G., Remiche, M.: Stability for fluid queue: characteristic inequalities. Commun. Stat. Stoch. Models 29, 69–88 (2013)CrossRef

12.

Knuth, D.E.: The Art of Computer Programming, Fundamental Algorithms, 2nd edn. Addison-Wesley, Reading (1969)

13.

Li, H., Tavakoli, J., Zhao, Y.Q.: Analysis of exact tail asymptotics for singular random walks in the quarter plane. Queueing Syst. 74, 151–179 (2013)CrossRef

14.

Li, H., Zhao, Y.Q.: Tail asymptotics for a generalized two-demand queueing model: a kernel method. Queueing Syst. 69, 77–100 (2011)CrossRef

15.

Liu, Y., Li, W.: Error bounds for augmented truncation approximations of Markov chains via the perturbation method. Adv. Appl. Probab. 50, 645–669 (2018)CrossRef

16.

Liu, Y., Li, W., Masuyama, H.: Error bounds for augmented truncation approximations of continuous-time Markov chains. Oper. Res. Lett. 46, 409–413 (2018)CrossRef

17.

Liu Y., Li Y.: \(V\)-uniform ergodicity for fluid queues. Appl. Math. A J. Chin. Univ. (2018, To appear)

18.

Liu, Y., Wang, P., Zhao, Y.Q.: The variance constant for continuous-time level dependent quasi-birth-and-death processes. Stoch. Models 34, 25–44 (2018)CrossRef

19.

Meyn, S.P., Tweedie, R.L.: A survey of Foster-Lyapunov technique for general state space Markov processes. Proceedings of Workshop Stochastic Stability and Stochastic Stabilization 1, 1–13 (1998)

20.

Miyazawa, M.: Tail decay rates in double QBD processes and related reflected random walks. Math. Oper. Res. 34, 547–575 (2009)CrossRef

21.

Nabli, H.: Asymptotic solution of stochastic fluid models. Perform. Eval. 57, 121–140 (2004)CrossRef

22.

Parthasarathy, P.R., Vijayashree, K.V.: An \(M/M/1\) driven fluid queue-continued fraction approach. Queueing Syst. 42, 189–199 (2002)CrossRef

23.

Sericola, B.: Transient analysis of stochastic fluid models. Perform. Eval. 32, 245–263 (1998)CrossRef

24.

Sericola, B., Parthasarathy, P.R., Vijayashree, K.V.: Exact transient solution of an \(M/M/1\) driven fluid queue. Int. J. Comput. Math. 82, 659–671 (2005)CrossRef

25.

van Doorn, E.A., Scheinhardt, W.R.W.: A fluid queue driven by an infinite-state birth-death process. In: Proceedings of the 15th International Teletraffic Congress: Teletraffic Contribution for the Information Age, pp. 467–475. Elsevier, Washington (1997)

26.

Virtamo, J., Norros, I.: Fluid queue driven by an \(M/M/1\) queue. Queueing Syst. 16, 373–386 (1994)CrossRef

Titel: Exact tail asymptotics for fluid models driven by an M/M/c queue
verfasst von: Wendi Li
Yuanyuan Liu
Yiqiang Q. Zhao
Publikationsdatum: 06.02.2019
Verlag: Springer US
Erschienen in: Queueing Systems / Ausgabe 3-4/2019
Print ISSN: 0257-0130
Elektronische ISSN: 1572-9443
DOI: https://doi.org/10.1007/s11134-019-09601-6

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