Waiting time, busy periods and output models of a server analyzed via Wiener–Hopf factorization

Hasslinger, Gerhard

doi:10.1016/s0166-5316(99)00067-x

Cited by 25 publications

(20 citation statements)

References 32 publications

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“…In the literature, only a few papers address the departure process when the arrival process has correlation in time, e.g., [10]. Moreover, for non-Bernoulli and non-Poisson arrivals, it is known that the departure process is correlated with the queue length and arrival process [11], which results in cumbersome expressions [10,12] that prohibit a scalable e2e analysis. Closed-form solutions for the delay of wireless regular line networks with a single source (like Fig.…”

Section: Previous Workmentioning

confidence: 99%

“…So, an ALOHA node can also be modeled as GI/Geo/1 although the arrival process characterization is different from TDMA. We use a decomposition approach to analyze the tandem queueing network that decomposes the network into single nodes in isolation [19,20]. The e2e analysis is based on the single node analysis and thus requires not only the node delay performance but also node departure process characterization.…”

Section: Our Contributionsmentioning

confidence: 99%

“…Unsurprisingly, the departure processes would exhibit a state explosion problem if it were fed into a tandem network [12]. A natural approximation is to model the departure process as an on-off process, which captures both the correlation and burstiness property of a traffic flow.…”

Section: Delay Modelsmentioning

confidence: 99%

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Towards an end-to-end delay analysis of wireless multihop networks

Xie

Haenggi

2009

Ad Hoc Networks

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We employ discrete-time queueing theory to analyze the end-to-end (e2e) delay of wireless multihop networks for two MAC schemes, m-phase TDMA and slotted ALOHA. Unlike general two-dimensional networks where there exists sufficient traffic multiplexing that would permit the arrival processes to be approximated as independent, in linear networks with multihop communication, the arrival processes are correlated due to the lack of traffic multiplexing. This paper studies an extreme scenario, a linear network fed with a single flow. A decomposition approach is used to decouple the whole network into isolated nodes. Each node is modeled as a GI/Geo/1 queueing system. We derive the complete per-node delay distribution, Preprint submitted to Elsevier 5 June 2007accounting for both the queueing delay and access delay. Additionally, we characterize the departure processes by a correlated and bursty on-off traffic model. The per-node analysis provides the e2e delay mean while for the e2e delay variance, the strong correlations between the arrival processes need to be considered. Our study shows that the sign of the correlation coefficients depends on both the MAC scheme and the traffic burstiness, both of which determine the relative burst size of the source flow compared to a Bernoulli process, which constitutes an "eigentraffic"process. There is a wide gap in the e2e delay variances for the source flows with different burst sizes even if they have identical average rates. The relative burst size also determines from which direction and at which rate the departure processes converge to the eigentraffic process after traversing multiple relay nodes.

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Section: Previous Workmentioning

confidence: 99%

Section: Our Contributionsmentioning

confidence: 99%

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Towards an end-to-end delay analysis of wireless multihop networks

Xie

Haenggi

2009

Ad Hoc Networks

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“…Sengupta [13] provides a matrix-exponential solution to an SMP/PH/1 queue. Haβlinger [5] analyzes a discrete time SMP/G/1 queue using Wiener-Hopf factorization approach. To the best of our knowledge, there are few studies on multiple-server queues with SMP arrival.…”

Section: Introductionmentioning

confidence: 99%

<title>Multiserver queue with semi-Markovian batch arrivals with application to the MPEG frame sequence</title>

Takagi

2002

SPIE Proceedings

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We consider a queueing system consisting of multiple identical servers and a common queue. The service time follows an exponential distribution and the arrival process is governed by a semi-Markov process (SMP). The motivation to study the queueing system with SMP arrivals lies in that it can model the auto-correlated traffic on the high speed network generated by a real time communication, for example, the MPEG-encoded VBR video. Our analysis is based on the theory of piecewise Markov process. We first derive the distributions of the queue size and the waiting time. The stability condition of the system is also discussed. When the sojourn time of SMP follows an exponential distribution all the unknown constants contained in the generating function of queue size can be determined through the zeros of the denominator for this generating function. Based on the result of the analysis, we propose a model to evaluate the waiting time of MPEG video traffic on an ATM network with multiple channels. Here, the SMP corresponds to the exact MPEG sequence of frames. Finally, a numerical example using a real video data is shown.

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“…We use semi-Markov processes (SMPs) to model data arrival [12] as they are able to represent this correlation. An analysis of such models is possible via matrix-analytical [21] and factorization techniques [6,9,15,22]. The former are considered numerically more stable, whereas the latter are more efficient in terms of computation time and memory requirements.…”

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confidence: 99%

Parameter estimation and optimization techniques for discrete-time semi-Markov models of H.264/AVC video traffic

2008

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We investigate a variety of known and new approaches for the estimation of the parameters of discretetime semi-Markovian traffic models. We focus on modeling video traffic, since the accurate representation of its longterm autocorrelation is a challenge to the parameter estimation methods. The modeling techniques are applied to sample H.264/AVC-encoded video traces. We study their ability to reflect the autocorrelation and variability of the original traffic and also the delay probabilities of a resulting SMP/GI/1 queueing system. The delay probabilities are determined both by simulation and verified analysis of the queue.

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Waiting time, busy periods and output models of a server analyzed via Wiener–Hopf factorization

Cited by 25 publications

References 32 publications

Towards an end-to-end delay analysis of wireless multihop networks

Towards an end-to-end delay analysis of wireless multihop networks

<title>Multiserver queue with semi-Markovian batch arrivals with application to the MPEG frame sequence</title>

Parameter estimation and optimization techniques for discrete-time semi-Markov models of H.264/AVC video traffic

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