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A (min, ×) Network Calculus for MultiHop Fading Channels
, 2013
"... A fundamental problem for the delay and backlog analysis across multihop paths in wireless networks is how to account for the random properties of the wireless channel. Since the usual statistical models for radio signals in a propagation environment do not lend themselves easily to a description ..."
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Cited by 7 (1 self)
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A fundamental problem for the delay and backlog analysis across multihop paths in wireless networks is how to account for the random properties of the wireless channel. Since the usual statistical models for radio signals in a propagation environment do not lend themselves easily to a description of the available service rate, the performance analysis of wireless networks has resorted to higherlayer abstractions, e.g., using Markov chain models. In this work, we propose a network calculus that can incorporate common statistical models of fading channels and obtain statistical bounds on delay and backlog across multiple nodes. We conduct the analysis in a transfer domain, which we refer to as the SNR domain, where the service process at a link is characterized by the instantaneous signaltonoise ratio at the receiver. We discover that, in the transfer domain, the network model is governed by a dioid algebra, which we refer to as (min, ×) algebra. Using this algebra we derive the desired delay and backlog bounds. An application of the analysis is demonstrated for a simple multihop network with Rayleigh fading channels.
On the scaling of nonasymptotic capacity in multiaccess networks with bursty traffic
 IN PROC. IEEE ISIT
, 2011
"... The practicality of available (throughput) capacity results in multiaccess networks, which dispense with coding schemes, is often questioned for several reasons including 1) the underlying asymptotic regimes, and 2) the assumption of saturated traffic sources. This paper jointly addresses these li ..."
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Cited by 5 (3 self)
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The practicality of available (throughput) capacity results in multiaccess networks, which dispense with coding schemes, is often questioned for several reasons including 1) the underlying asymptotic regimes, and 2) the assumption of saturated traffic sources. This paper jointly addresses these limitations by providing capacity results in nonasymptotic regimes, i.e., holding at all time scales and network sizes, for the very broad class of exponentially bounded burstiness (EBB) traffic sources. Both upper and lower bounds on capacity are derived in terms of probability distributions, which immediately yield all the moments. The explicit and closedform nature of the results enable the investigation of the impact of burstiness on nonasymptotic network capacity. In particular, the results show that for the EBB class the nonasymptotic endtoend capacity rate decays linearly in the number of hops.
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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Cited by 3 (3 self)
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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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Cited by 2 (2 self)
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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.
A Network Calculus Approach for the Analysis of MultiHop Fading Channels
, 1207
"... A fundamental problem for the delay and backlog analysis across multihop paths in wireless networks is how to account for the random properties of the wireless channel. Since the usual statistical models for radio signals in a propagation environment do not lend themselves easily to a description o ..."
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Cited by 1 (1 self)
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A fundamental problem for the delay and backlog analysis across multihop paths in wireless networks is how to account for the random properties of the wireless channel. Since the usual statistical models for radio signals in a propagation environment do not lend themselves easily to a description of the available service rate, the performance analysis of wireless networks has resorted to higherlayer abstractions, e.g., using Markov chain models. In this work, we propose a network calculus that can incorporate common statistical models of fading channels and obtain statistical bounds on delay and backlog across multiple nodes. We conduct the analysis in a transfer domain, which we refer to as the SNR domain, where the service process at a link is characterized by the instantaneous signaltonoise ratio at the receiver. We discover that, in the transfer domain, the network model is governed by a dioid algebra, which we refer to as (min, ×) algebra. Using this algebra we derive the desired delay and backlog bounds. An application of the analysis is demonstrated for a simple multihop network with Rayleigh fading channels. I.
1 Towards a System Theoretic Approach to Wireless Network Capacity in Finite Time and Space
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