## Markov-modulated and Feedback Fluid Queues (1998)

Venue: | In: Proceedings 14th ITC-specialists seminar on access networks and systems, 215 -- 220 |

Citations: | 8 - 2 self |

### BibTeX

@INPROCEEDINGS{Scheinhardt98markov-modulatedand,

author = {W. R. W. Scheinhardt and N. D. Van Foreest and M. R. H. Mandjes and Werner Scheinhardt},

title = {Markov-modulated and Feedback Fluid Queues},

booktitle = {In: Proceedings 14th ITC-specialists seminar on access networks and systems, 215 -- 220},

year = {1998},

pages = {25--27}

}

### OpenURL

### Abstract

CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a theme-oriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms.

### Citations

2054 | Handbook of Mathematical Functions - Abramowitz, Stegun - 1965 |

527 | Applied probability and queues - Asmussen - 2003 |

524 | An Introduction to Orthogonal Polynomials - Chihara - 1978 |

447 | Asymptotics and special functions - Olver - 1974 |

336 |
Sondhi: Stochastic Theory of a Data-Handling System with Multiple Sources
- Anick, Mitra, et al.
(Show Context)
Citation Context ...luid input rate r(t) at time t is then given by ri at times when X(t) =i. Ofparticular importance are Markov-modulated fluid models in whichthe background process {X(t)} is a Markov process, see e.g. =-=[2, 11]-=-. More general models, known as feedback fluid queues, were introduced in [1] and [16]. Here, the behavior of the fluid buffer content is determined by the background process as before, but in turn th... |

223 | The Feynman lectures on physics - Feynman, Leighton, et al. - 1963 |

165 |
Markov Models and Optimization
- Davis
- 1993
(Show Context)
Citation Context ...(y) = lim t→∞ Fi(y, t), i ∈ X ,y∈ [0,B]. Remark 2.1. The model is such that the joint process {X(t),C(t),t ≥ 0} can in principle be viewed as a piecewise-deterministic Markov process, as described in =-=[6]-=- (as is indeed also the case for more traditional fluid queueing processes). For the special case of a two-state background process, [4] presents an approach as in [6], i.e. using the (extended) gener... |

113 |
Broadband Integrated Networks
- Schwartz
- 1996
(Show Context)
Citation Context ...s. AMS Subject Classifications (2000) — 60K25 1 Introduction In the area of modern telecommunication systems fluid queues are often used as burst scale models for multiplexers, see e.g. [15, Ch. 17], =-=[18]-=-. In such models the content process {C(t),t≥ 0} of a fluid buffer changes at a rate determined by some autonomous modulating stochastic process {X(t), t≥ 0}. The net fluid input rate r(t) at time t i... |

60 | Models for analysis of packet voice communication systems - Daigle, Langford - 1986 |

57 | Analysis and design of rate-base congestion control of high speed networks, I:stochastic fluid models, access regulation”, Queueing Systems 9 - Elwalid, Mitra - 1991 |

53 | Analysis, approximations and admission control of a multi-service multiplexing system with priorities - Elwalid, Mitra - 1995 |

49 | Effective bandwidth and fast simulation of ATM intree networks - Chang, H, et al. - 1994 |

49 | Analysis of separable Markov-modulated rate models for information-handling systems - Stern, Elwalid - 1991 |

48 | Congestion Control Through Input Rate Regulation - Sidi, Liu, et al. - 1989 |

42 | The superposition of variable bit rate sources in an ATM multiplexer - Norros, Roberts, et al. - 1991 |

41 | The Differential Equations of Birth-and-Death Processes - Karlin, McGregor - 1957 |

40 | Stochastic theory of data-handling systems with groups of multiple sources - Kosten - 1984 |

38 | Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains - Rogers - 1994 |

35 |
Statistical multiplexing with loss priorities in rate-based congestion control of high speed networksll
- Elwalid, Mitra
(Show Context)
Citation Context ...ess is allowed to have jumps. Also in the context of fluid queues, where the input process is gradual, some models were studied where the input and/or output rates are state-dependent. The authors of =-=[7]-=- allow the net input rates, i.e., the difference between theinput and the output rates, to be piecewise constant functions of the buffer content. In [10] the case is solved in which these rates are pi... |

35 | An introduction to numerical transform inversion and its application to probability models
- Abate, Choudhury, et al.
- 1999
(Show Context)
Citation Context ...place transform variable. Moreover, once such solutions are known for various well-chosen values of ×, the transient solution �� Ý� Ø can be obtained by standard numerical Laplace inversion, see e.g. =-=[1]-=-. Thus, let us define for fixed ×� the Laplace transforms with respect to time, � �� Ý , � �� and � �� � , where ��� Ý � Ê �s×Ø�� Ý� Ø �Ø, etc.; note that we suppress the dependence on × in the transf... |

31 | Accurate method for analysis of a packet-speech multiplexer with limited delay - Tucker - 1988 |

30 | Superimposed renewal processes and storage with gradual input - Cohen - 1974 |

29 | Fluid models for the analysis and design of statistical multiplexing with loss priorities on multiple classes of bursty traffic - Elwalid, Mitra - 1992 |

24 | Stationary distributions for fluid flow models with or without Brownian noise - Asmussen - 1995 |

23 |
Stochastic theory of a multi-entry buffer. I,DelftProgr.Rep.1
- Kosten
- 1974
(Show Context)
Citation Context ...luid input rate r(t) at time t is then given by ri at times when X(t) =i. Ofparticular importance are Markov-modulated fluid models in whichthe background process {X(t)} is a Markov process, see e.g. =-=[2, 11]-=-. More general models, known as feedback fluid queues, were introduced in [1] and [16]. Here, the behavior of the fluid buffer content is determined by the background process as before, but in turn th... |

23 | A storage model with a two-state random environment - Kella, Whitt - 1992 |

22 | Stochastic Storage Processes - Prabhu - 1998 |

21 | A tandem fluid network with l'evy input - Kella, Whitt - 1992 |

21 | A mathematical theory for transient analysis of communication networks - Kobayashi, Ren - 1992 |

20 | Performance Analysis of the Dual Cell Spacer in ATM Systems - Ritter - 1994 |

18 | Steady state rare events simulation in queueing models and its complexity properties - Asmussen, Rubinstein - 1995 |

18 | Fluid models for single buffer systems - Kulkarni - 1997 |

17 | Fluid and diffusion limits for queues in slowly changing environments - Choudhury, Mandelbaum, et al. - 1996 |

17 | The Single Server queue, North-Holland Publ - Cohen |

17 | Parallel and tandem fluid networks with dependent Lévy inputs - Kella - 1993 |

16 |
Two-point boundary value problems, shooting methods
- ROBERTS, SHIPMAN
- 1972
(Show Context)
Citation Context ...the state of affairs may be less agreeable as the problem (31) is principally ill-conditioned. When Æ is large, the two-point boundary value problem can be solved by a more efficient method, see e.g. =-=[23]-=-. Still, for relatively small buffer sizes and a small number of source states the above method can be successful. 17s8.2 Three Discouraged Sources We applied the method above to compare a model with ... |

13 | Fluid Model Driven by an Ornstein-Ühlenbeck Process - Kulkarni, Rolski - 1994 |

12 | Fluid queue driven by an M/M/1 queue. Queueing Systems: Theory and Applications - Virtamo, Norros - 1994 |

11 |
The stationary distribution and first exit probabilities of a storage process with general release
- Harrison, Resnick
- 1976
(Show Context)
Citation Context ...e model, the input is acompound Poisson process, and the release rate (i.e. the rate at which the buffer is depleted) is constant, see [14]. Early extensions of this storage process are considered in =-=[5, 9]-=-, and references therein, in which the release rate is state-dependent; in fact it is a strictly positive piecewise continuous function of the current buffer content. Another paper worth mentioning in... |

11 |
Green's function method in probability theory
- Keilson
- 1965
(Show Context)
Citation Context ... Ø �, and finally equate these. The other method, which we describe in Section 3.2 is based on an interpretation of the forward equation in physical terms resulting in a continuity equation, see e.g. =-=[13]-=-. Here we fix a subset of the state space, rather than an event, and consider the in- and outflow of probability mass for this set. We believe that the discussion of the latter method is of interest b... |

11 | Simple analysis of a fluid queue driven by an M/M/1 queue, Queueing Syst - Adan, Resing - 1996 |

10 | Stochastic storage networks: Stationarity and the feedforward case - Kella - 1997 |

10 | A large family of semi-classical polynomials: the perturbed Chebyshev - Sansigre, Valent - 1995 |

9 | Markov’s Theorem revisited - Berg |

9 | A fluid reservoir regulated by a birth-death process. Stochastic Models - Doorn, Jagers, et al. - 1988 |

9 | Eigenvalues of a symmetric tridiagonal matrix: a divide-and-concquer approach - Krishnakumar, Morf - 1996 |

8 |
Ordinary Differential Equations
- Petrovski
- 1966
(Show Context)
Citation Context ... É Ý with initial condition � � � É , to compute � Ý �� Ý ÊsÝ and to normalize according to (20e). Remark 8.1. Formally, the matrix � � is invertible as it is a fundamental set of solutions, see e.g. =-=[20]-=- for a proof. However, numerically the state of affairs may be less agreeable as the problem (31) is principally ill-conditioned. When Æ is large, the two-point boundary value problem can be solved by... |

8 | A Fluid Model for Systems With Random Disruptions - Chen, Yao - 1992 |

8 | Controlled stochastic model of a communication system with multiple sources - Coffman, Igelnik, et al. - 1991 |

8 | The Effect of Interstage Buffer Storage on the Output of Two Unreliable - Wijngaard - 1979 |