Behavior of Tandem Buffers with Geometric Input and Markovian Output

Hsu, Jung-Lun; Burke, Paul J.

doi:10.1109/tcom.1976.1093299

Cited by 73 publications

(59 citation statements)

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“…Hence, each of the depth-2 buckets can be modeled by Q( 1 4 , 1 2 ). Using a classic queuing theory result by Hsu and Burke [9] we can show that at further depths, a block leaves a bucket with some fixed probability at every time step, so that independent arrivals are satisfied at the child buckets.…”

Section: Examplementioning

confidence: 99%

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Oblivious RAM with O((logN)3) Worst-Case Cost

Shi

Chan

Stefanov

et al. 2011

Lecture Notes in Computer Science

287

426

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Abstract. Oblivious RAM is a useful primitive that allows a client to hide its data access patterns from an untrusted server in storage outsourcing applications. Until recently, most prior works on Oblivious RAM aim to optimize its amortized cost, while suffering from linear or even higher worst-case cost. Such poor worstcase behavior renders these schemes impractical in realistic settings, since a data access request can occasionally be blocked waiting for an unreasonably large number of operations to complete. This paper proposes novel Oblivious RAM constructions that achieves polylogarithmic worst-case cost, while consuming constant client-side storage. To achieve the desired worst-case asymptotic performance, we propose a novel technique in which we organize the O-RAM storage into a binary tree over data buckets, while moving data blocks obliviously along tree edges.

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Section: Examplementioning

confidence: 99%

“…The proof builds on top of a classic queuing theory result by Hsu and Burke [9]. Full proof is provide in our online technical report [14].…”

Section: Corollary 2 (Load Of An Internal Bucket)mentioning

confidence: 99%

Oblivious RAM with O((logN)3) Worst-Case Cost

Shi

Chan

Stefanov

et al. 2011

Lecture Notes in Computer Science

287

426

View full text Add to dashboard Cite

show abstract

“…In practice, new packets may be generated when the buffer is non-empty and thus experience a queueing delay. On the other hand, the study of queueing networks is concerned with the queueing delay rather than the access delay [5][6][7][8].…”

Section: Previous Workmentioning

confidence: 99%

“…Closed-form solutions for the delay of wireless regular line networks with a single source (like Fig. 1(b)) are available only if the arrival is Bernoulli [6] or the channels are error-free [8]. For other cases, approximations are needed.…”

Section: Previous Workmentioning

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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Jackson Networks (Open and Closed)

Daduna¹

2011

Wiley Encyclopedia of Operations Research and Management Science

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We describe the classical exponential networks of Jackson and Gordon and Newell and their successor networks and extensions in network theory. The characterizing feature of these networks is the product form steady‐state distribution for the joint queue length process, which we evaluate in detail. We characterize passage time behavior for customers traversing the networks or parts of it. This relies on finding the distributions, which characterizes the situation when such a passage commences. We sketch typical algorithmic methods to efficiently compute performance indices for the networks in steady state. Finally, we describe some networks with additional features that broaden the range of applicability of the networks.

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Behavior of Tandem Buffers with Geometric Input and Markovian Output

Cited by 73 publications

References 0 publications

Oblivious RAM with O((logN)3) Worst-Case Cost

Oblivious RAM with O((logN)3) Worst-Case Cost

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

Jackson Networks (Open and Closed)

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