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Sharp PerFlow Delay Bounds for Bursty Arrivals: The Case of FIFO, SP, and EDF Scheduling
"... The practicality of the stochastic network calculus (SNC) is often questioned on grounds of potential looseness of its performance bounds. In this paper, it is uncovered that for bursty arrival processes (specifically MarkovModulated OnOff (MMOO)), whose amenability to perflow analysis is typica ..."
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The practicality of the stochastic network calculus (SNC) is often questioned on grounds of potential looseness of its performance bounds. In this paper, it is uncovered that for bursty arrival processes (specifically MarkovModulated OnOff (MMOO)), whose amenability to perflow analysis is typically proclaimed as a highlight of SNC, the bounds can unfortunately be very loose (e.g., by several orders of magnitude off). In response to this uncovered weakness of SNC, the (Standard) perflow bounds are herein improved by deriving a general samplepath bound, using martingale based techniques, which accommodates FIFO, SP, and EDF scheduling. The obtained (Martingale) bounds capture an extra exponential decay factor of O
Towards a System Theoretic Approach to Wireless Network Capacity in Finite Time and Space
"... Abstract—In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in nonJackson networks. This simplifying doublelimit model, however, lends itself to conservative numerical results in finite ..."
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Abstract—In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in nonJackson networks. This simplifying doublelimit model, however, lends itself to conservative numerical results in finite regimes. To properly account for queueing behavior beyond a simple calculus based on average rates, we advocate a system theoretic methodology for the capacity problem in finite time and space regimes. This methodology also accounts for spatial correlations arising in networks with CSMA/CA scheduling and it delivers rigorous closedform capacity results in terms of probability distributions. Unlike numerous existing asymptotic results, subject to anecdotal practical concerns, our transient one can be used in practical settings: for example, to compute the time scales at which multihop routing is more advantageous than singlehop routing. I.
On the catalyzing effect of randomness on the perflow throughput in wireless networks
, 2013
"... This paper investigates the throughput capacity of a flow crossing a multihop wireless network, whose geometry is characterized by general randomness laws including Uniform, Poisson, HeavyTailed distributions for both the nodes ’ densities and the number of hops. The key contribution is to demons ..."
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This paper investigates the throughput capacity of a flow crossing a multihop wireless network, whose geometry is characterized by general randomness laws including Uniform, Poisson, HeavyTailed distributions for both the nodes ’ densities and the number of hops. The key contribution is to demonstrate how the perflow throughput depends on the distribution of 1) the number of nodes Nj inside hops ’ interference sets, 2) the number of hops K, and 3) the degree of spatial correlations. The randomness in both Nj ’s and K is advantageous, i.e., it can yield larger scalings (as large as Θ(n)) than in nonrandom settings. An interesting consequence is that the perflow capacity can exhibit the opposite behavior to the network capacity, which was shown to suffer from a logarithmic decrease in the presence of randomness. In turn, spatial correlations along the endtoend path are detrimental by a logarithmic term.
Performance of innetwork processing for visual analysis in wireless sensor networks
"... AbstractNodes in a sensor network are traditionally used for sensing and data forwarding. However, with the increase of their computational capability, they can be used for innetwork data processing, leading to a potential increase of the quality of the networked applications as well as the netwo ..."
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AbstractNodes in a sensor network are traditionally used for sensing and data forwarding. However, with the increase of their computational capability, they can be used for innetwork data processing, leading to a potential increase of the quality of the networked applications as well as the network lifetime. Visual analysis in sensor networks is a prominent example where the processing power of the network nodes needs to be leveraged to meet the frame rate and the processing delay requirements of common visual analysis applications. The modeling of the endtoend performance for such networks is, however, challenging, because innetwork processing violates the flow conservation law, which is the basis for most queuing analysis. In this work we propose to solve this methodological challenge through appropriately scaling the arrival and the service processes, and we develop probabilistic performance bounds using stochastic network calculus. We use the developed model to determine the main performance bottlenecks of networked visual processing. Our numerical results show that an endtoend delay of 23 frame length is obtained with violation probability in the order of 10 −6 . Simulation shows that the obtained bounds overestimates the endtoend delay by no more than 10%.
Analyzing Multimode Wireless Sensor Networks Using the Network Calculus
"... The network calculus is a powerful tool to analyze the performance of wireless sensor networks. But the original network calculus can only model the singlemode wireless sensor network. In this paper, we combine the original network calculus with the multimode model to analyze the maximum delay bou ..."
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The network calculus is a powerful tool to analyze the performance of wireless sensor networks. But the original network calculus can only model the singlemode wireless sensor network. In this paper, we combine the original network calculus with the multimode model to analyze the maximum delay bound of the flow of interest in the multimode wireless sensor network. There are two combined methods AMM and NMM. The method AMM models the whole network as a multimode component, and the method NMM models each node as a multimode component. We prove that the maximum delay bound computed by the method AMM is tighter than or equal to that computed by the method NMM. Experiments show that our proposed methods can significantly decrease the analytical delay bound comparing with the separate flow analysis method. For the largescale wireless sensor network with 32 thousands of sensor nodes, our proposed methods can decrease about 70% of the analytical delay bound.
Capacity–Delay–Error Boundaries: A Composable Model of Sources and Systems
"... Abstract—This paper develops a notion of capacity–delay–error (CDE) boundaries as a performance model of networked sources and systems. The goal is to provision effective capacities that sustain certain statistical delay guarantees with a small probability of error. We use a stochastic nonequilibr ..."
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Abstract—This paper develops a notion of capacity–delay–error (CDE) boundaries as a performance model of networked sources and systems. The goal is to provision effective capacities that sustain certain statistical delay guarantees with a small probability of error. We use a stochastic nonequilibrium approach that models the variability of traffic and service to formalize the influence of delay constraints on the effective capacity. Permitting unbounded delays, known ergodic capacity results from information theory are recovered in the limit. We prove that the model has the property of additivity, which enables composing CDE boundaries obtained for sources and systems as if in isolation. A method for construction of CDE boundaries is devised based on momentgenerating functions, which includes the large body of results from the theory of effective bandwidths. Solutions for essential sources, channels, and respective coders are derived, including Huffman coding, MPEG video, Rayleigh fading, and hybrid automatic repeat request. Results for tandem channels and for the composition of sources and channels are shown. Index Terms—Queueing analysis, information theory, channel models, time varying channels, quality of service. I.