Generating function approach for discrete queueing analysis with decomposable arrival and service markov chains

Li, San-Qi

doi:10.1080/15326349308807272

Cited by 4 publications

(7 citation statements)

References 15 publications

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“…We here extend the technique developed in [3], which is to transform the queue generating function from z domain to x domain with x = z-l. Therefore, finding roots outside unit disk in z domain is equivalent to finding roots inside unit disk in x domain.…”

Section: C2 Non-vanishing Root Decompositionmentioning

confidence: 99%

“…It generalizes the traffic modeling and queueing analysis developed in [1]- [3], especially by taking the diverse traffic burstiness property into account. The prior studies have focused on exploring the effect of multiple time-varying scales on queueing, under the assumption that the peak access rate of each individual source has to be identical.…”

Section: Introductionmentioning

confidence: 99%

“…That is, both ON and OFF periods are assumed to be geometrically distributed and the access rate in ON period be constant. Here we use 2-state MC to characterize the first-order properties of each binary source, described by (1) average access rate, (2) peak access rate (3) rate time-varying scale. The average access rate is defined by the average input rate of each source in steady state.…”

Section: Introductionmentioning

confidence: 99%

“…Using the divide-and-conquer principle, we build input traffic by heterogeneous discrete-time 2-state MCs. Unlike the traffic model used in [1]- [3], here the original transition time interval of each chain can be substantially different to characterize the peak access rate of individual sources. We introduce a first-order approximation to renormalize all the transition intervals of arrival 2-state MCs, based on which the queue can be modeled by a multi-dimensional Markov process.…”

Section: Introductionmentioning

confidence: 99%

“…Due to the analytic difficulty, however, queueing results available today are mainly conducted by computer simulations [5]. The queueing technique developed here can also be extended to multi-state MCs if the number of states in each individual MC is kept less than five [3].…”

Section: Introductionmentioning

confidence: 99%

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Discrete queueing analysis of multimedia traffic with diversity of correlation and burstiness properties

Sheng

1994

IEEE Trans. Commun.

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Key properties of multimedia trafflc are characterized by the great diversity of correlation and burstiness. Construct the multimedia trafflc by heterogeneous 2-state Markov chains as in [l, 21. Here we allow each 2-state MC to be defined on different transition intervals, representing the diversity of peak access rate from individual sources. Upon time renormalization, the queue is modeled by a multi-dimensional discrete Markov process. Generalizing the technique developed in [2, 31, we are able to construct the entire solution of queue length distributions. It uses generating function approach. By matrix spectral decomposition, one can decompose the evaluation of each individual vanishing/non-vanishing root. Each vanishing root is used to obtain the queue boundary values; each nonvanishing root constructs a geometric term in the expression of the queue length distribution. It is found that all the vanishing roots must be real and all the complex non-vanishing roots can be ignored. In numerical studies, we examine the effect of diverse source access rates and time-varying scales on ATM queues. Professor. He published more than 70 techhical papers in computer communication network research fi. 14. His current research interests are multimedia traffic analysis w d control of high speed networks.Dr. Li has served as a meqber of the Technical Program Committee for the IEEE INFOCOM Conference since 1988.

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Section: C2 Non-vanishing Root Decompositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Discrete queueing analysis of multimedia traffic with diversity of correlation and burstiness properties

Sheng

1994

IEEE Trans. Commun.

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Queueing model of an adaptive type-I hybrid-ARQ with a generalized Markovian source and channel

Seo

Lee

Park

et al.

Canadian Conference on Electrical and Computer Engineering, 2005.

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In this paper, the queueing performance of an adaptive type-I hybrid automatic repeat request(ARQ) with a generalized Markovian source is studied for a TDMA/TDD system over a Markovian channel. In the adaptive type-I hybrid ARQ of our interest, the payload size for information in a packet(or ARQ block) and the coding rate of ARQ block vary, according to the channel state, e.g., high coding rate and small payload size for information in a bad state of channel. We assume that an arriving message over a medium access control(MAC) layer consists of a number of information units of fixed size. We analyze the delay of a message, which is composed of its queueing delay and its transmission time, and the message dropping probability. In the numerical examples, we have shown that the correlation of either traffic source or radio channel affects the queueing performance in a similar way, due to its Markovian structure. The analytical work presented here can be used to control physical parameters, such as coding rate, in order to meet QoS requirements in a higher layer which is over the MAC layer.

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Second order effect of binary sources on characteristics of queue and loss rate

Sheng

1994

IEEE Trans. Commun.

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A wideband source in high speed networks is typitally represented by a binary &andom process. In this paper we characterize the second-order properties of each binary source by a multi-state MMPP. A comprehensive numerical study is carried out to identify the individual effect of the source second-order dynamics on the queue length and loss rate. The results can be used to verify the validity of the two-state Markov chain binary assumption which is commonly made within the framework of input rate control and bandwidth allocation in high speed networks. The coflcept of input power spectrum is then developed as a unified source characterization for multimedia traffic queueing analyses. ~ 1 I Research Scientist and Principal Investigator of Center for Telecommunications Research at Columbia University where he was actively involved in conducting research, supervising doctoral students, and collaborating with faculty members. In September 1989, he joined the faculty of the Department of Electrical and Computer Engineering, University of Texas at Austin, where he is presently Assistimt Professor. He published more than 70 technical papers in computer communication network research field. His current research interests are multimedia traffic analysis and control of high speed networks.Dr. Li has served as a member of the Technical Program Committee for the IEEE INFOCOM Conference since 1988.

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Generating function approach for discrete queueing analysis with decomposable arrival and service markov chains

Cited by 4 publications

References 15 publications

Discrete queueing analysis of multimedia traffic with diversity of correlation and burstiness properties

Discrete queueing analysis of multimedia traffic with diversity of correlation and burstiness properties

Queueing model of an adaptive type-I hybrid-ARQ with a generalized Markovian source and channel

Second order effect of binary sources on characteristics of queue and loss rate

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