2,197 research outputs found
Separation of timescales in a two-layered network
We investigate a computer network consisting of two layers occurring in, for
example, application servers. The first layer incorporates the arrival of jobs
at a network of multi-server nodes, which we model as a many-server Jackson
network. At the second layer, active servers at these nodes act now as
customers who are served by a common CPU. Our main result shows a separation of
time scales in heavy traffic: the main source of randomness occurs at the
(aggregate) CPU layer; the interactions between different types of nodes at the
other layer is shown to converge to a fixed point at a faster time scale; this
also yields a state-space collapse property. Apart from these fundamental
insights, we also obtain an explicit approximation for the joint law of the
number of jobs in the system, which is provably accurate for heavily loaded
systems and performs numerically well for moderately loaded systems. The
obtained results for the model under consideration can be applied to
thread-pool dimensioning in application servers, while the technique seems
applicable to other layered systems too.Comment: 8 pages, 2 figures, 1 table, ITC 24 (2012
Unveiling the Dynamics of the Universe
We explore the dynamics and evolution of the Universe at early and late
times, focusing on both dark energy and extended gravity models and their
astrophysical and cosmological consequences. Modified theories of gravity not
only provide an alternative explanation for the recent expansion history of the
universe, but they also offer a paradigm fundamentally distinct from the
simplest dark energy models of cosmic acceleration. In this review, we perform
a detailed theoretical and phenomenological analysis of different modified
gravity models and investigate their consistency. We also consider the
cosmological implications of well motivated physical models of the early
universe with a particular emphasis on inflation and topological defects.
Astrophysical and cosmological tests over a wide range of scales, from the
solar system to the observable horizon, severely restrict the allowed models of
the Universe. Here, we review several observational probes -- including
gravitational lensing, galaxy clusters, cosmic microwave background temperature
and polarization, supernova and baryon acoustic oscillations measurements --
and their relevance in constraining our cosmological description of the
Universe.Comment: 94 pages, 14 figures. Review paper accepted for publication in a
Special Issue of Symmetry. "Symmetry: Feature Papers 2016". V2: Matches
published version, now 79 pages (new format
On the Flow-level Dynamics of a Packet-switched Network
The packet is the fundamental unit of transportation in modern communication
networks such as the Internet. Physical layer scheduling decisions are made at
the level of packets, and packet-level models with exogenous arrival processes
have long been employed to study network performance, as well as design
scheduling policies that more efficiently utilize network resources. On the
other hand, a user of the network is more concerned with end-to-end bandwidth,
which is allocated through congestion control policies such as TCP.
Utility-based flow-level models have played an important role in understanding
congestion control protocols. In summary, these two classes of models have
provided separate insights for flow-level and packet-level dynamics of a
network
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