Loss probability approximation of a statistical multiplexer and its application to call admission control in high-speed networks

Ishizaki, Fumio; Takine, Tetsuya; Terada, Hiroaki; Hasegawa, Toshiharu

doi:10.1109/glocom.1995.501961

Cited by 6 publications

(12 citation statements)

References 12 publications

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“…As indicated in a.o. [5,23,25,26,38], this probability can be used to estimate the buffer overflow probability in a finite-capacity buffer system. In principle, the probability that the buffer occupancy exceeds a given threshold can be calculated based on the pgf U (z) by means of inverse z-transformation techniques [18].…”

Section: Tail Behaviour Of the Buffer Occupancymentioning

confidence: 99%

Discrete-time buffer systems with session-based arrival streams

Hoflack¹,

Vuyst²,

Wittevrongel³

et al. 2010

Performance Evaluation

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The paper considers a discrete-time buffer system with infinite storage capacity and one single output channel. Users can start and end sessions during which they are active and send packets to the buffer system. In this paper we study a simple model for the resulting session-based arrival process: we assume that each active user generates a random but strictly positive number of packets per time slot. Furthermore it is assumed that the time (expressed in slots) needed to transmit a packet is geometrically distributed. The distribution of the session lengths is also geometrical. This model can be applied to study the traffic of a file server, where one file download by a user is considered to be one session. The probability generating functions of the steady-state number of active sessions, the buffer occupancy and the packet delay are derived. We also derive an approximation for the tail probabilities of the buffer occupancy. Furthermore, an expression for the mean session delay is obtained. This allows us to study the influence of the different system parameters: some examples are presented. We end by applying the model to a web server, based on actual web traffic.

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Section: Tail Behaviour Of the Buffer Occupancymentioning

confidence: 99%

Discrete-time buffer systems with session-based arrival streams

Hoflack¹,

Vuyst²,

Wittevrongel³

et al. 2010

Performance Evaluation

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show abstract

“…Xiong and Bruneel [11] gave a simple approach to obtain tight upper bounds for the asymptotic queueing behavior of statistical multiplexers with heterogeneous 2-state Markov modulated Bernoulli processes (MMBP's). Ishizaki et al [9] studied the loss probability approximation of a statistical multiplexer and they proposed a new call admission control based on their results.…”

Section: Introductionmentioning

confidence: 99%

Closed-form expressions on the geometric tail behavior of statistical multiplexers with heterogeneous traffic

Hwang

Choi²

1998

IEEE Trans. Commun.

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In this paper, we consider a statistical multiplexer fed by heterogeneous ON and OFF sources. We provide closedform results on the tail behavior of the queue-length distribution for statistical multiplexers, where the tail behavior can be expressed in terms of traffic parameters such as the first and second moments of ON and OFF periods for individual sources. Since our results are of simple closed-form, they can be used to provide a simple and efficient way to predict the tail behavior and the impact of traffic parameters on performance.

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“…It has been shown that a = 1 -1/B and / 3 = 1 -p/ ((l -p)B). For this BMS, the Perron-Frobenius eigenvalue b* ( z ) is found to be [7, 8,91 where K = a + p -1. …”

Section: Modelmentioning

confidence: 99%

“…[7, 8,9,141. Before explaining GBMS, we describe a binary Markov source (BMS), where in any slot the BMS is in one of two different states.…”

Section: Modelmentioning

confidence: 99%

“…1 -p), wh;re 0 < a , p < 1. The matrix generating function A ( z ) for the BMS is then given by [7,8,91 Note that the BMS is characterized by two parameters, p and B (or equivalently a and p), which represents the traffic intensity and the mean burst length of a single BMS, respectively. It has been shown that a = 1 -1/B and / 3 = 1 -p/ ((l -p)B).…”

Section: Modelmentioning

confidence: 99%

See 1 more Smart Citation

Study on reduction of total bandwidth requirement by traffic dispersion

Ishizaki

Joint 4th IEEE International Conference on ATM(ICATM'01) and High Speed Intelligent Internet Symposium. ICATM 2001 (Cat. No.00E

Self Cite

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This paper studies the effect of traffic dispersion on the reduction of the total effective bandwidth requirement. In this paper, we consider a discrete-time queueing system and a particular source model which is called generalized binary Markov source (GBMS). We then focus on the effective bandwidth of GBMS. We provide some numerical results to investigate the effect of traffic dispersion on the total bandwidth requirement. The numerical results show that traffic dispersion is useful to reduce the total effective bandwidth required by GBMS.

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Loss probability approximation of a statistical multiplexer and its application to call admission control in high-speed networks

Cited by 6 publications

References 12 publications

Discrete-time buffer systems with session-based arrival streams

Discrete-time buffer systems with session-based arrival streams

Closed-form expressions on the geometric tail behavior of statistical multiplexers with heterogeneous traffic

Study on reduction of total bandwidth requirement by traffic dispersion

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