354 research outputs found
Bounding the Bias of Tree-Like Sampling in IP Topologies
It is widely believed that the Internet's AS-graph degree distribution obeys
a power-law form. Most of the evidence showing the power-law distribution is
based on BGP data. However, it was recently argued that since BGP collects data
in a tree-like fashion, it only produces a sample of the degree distribution,
and this sample may be biased. This argument was backed by simulation data and
mathematical analysis, which demonstrated that under certain conditions a tree
sampling procedure can produce an artificail power-law in the degree
distribution. Thus, although the observed degree distribution of the AS-graph
follows a power-law, this phenomenon may be an artifact of the sampling
process. In this work we provide some evidence to the contrary. We show, by
analysis and simulation, that when the underlying graph degree distribution
obeys a power-law with an exponent larger than 2, a tree-like sampling process
produces a negligible bias in the sampled degree distribution. Furthermore,
recent data collected from the DIMES project, which is not based on BGP
sampling, indicates that the underlying AS-graph indeed obeys a power-law
degree distribution with an exponent larger than 2. By combining this empirical
data with our analysis, we conclude that the bias in the degree distribution
calculated from BGP data is negligible.Comment: 12 pages, 1 figur
Throughput Optimal On-Line Algorithms for Advanced Resource Reservation in Ultra High-Speed Networks
Advanced channel reservation is emerging as an important feature of ultra
high-speed networks requiring the transfer of large files. Applications include
scientific data transfers and database backup. In this paper, we present two
new, on-line algorithms for advanced reservation, called BatchAll and BatchLim,
that are guaranteed to achieve optimal throughput performance, based on
multi-commodity flow arguments. Both algorithms are shown to have
polynomial-time complexity and provable bounds on the maximum delay for
1+epsilon bandwidth augmented networks. The BatchLim algorithm returns the
completion time of a connection immediately as a request is placed, but at the
expense of a slightly looser competitive ratio than that of BatchAll. We also
present a simple approach that limits the number of parallel paths used by the
algorithms while provably bounding the maximum reduction factor in the
transmission throughput. We show that, although the number of different paths
can be exponentially large, the actual number of paths needed to approximate
the flow is quite small and proportional to the number of edges in the network.
Simulations for a number of topologies show that, in practice, 3 to 5 parallel
paths are sufficient to achieve close to optimal performance. The performance
of the competitive algorithms are also compared to a greedy benchmark, both
through analysis and simulation.Comment: 9 pages, 8 figure
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