4,470 research outputs found
Integration of streaming services and TCP data transmission in the Internet
We study in this paper the integration of elastic and streaming traffic on a
same link in an IP network. We are specifically interested in the computation
of the mean bit rate obtained by a data transfer. For this purpose, we consider
that the bit rate offered by streaming traffic is low, of the order of
magnitude of a small parameter \eps \ll 1 and related to an auxiliary
stationary Markovian process (X(t)). Under the assumption that data transfers
are exponentially distributed, arrive according to a Poisson process, and share
the available bandwidth according to the ideal processor sharing discipline, we
derive the mean bit rate of a data transfer as a power series expansion in
\eps. Since the system can be described by means of an M/M/1 queue with a
time-varying server rate, which depends upon the parameter \eps and process
(X(t)), the key issue is to compute an expansion of the area swept under the
occupation process of this queue in a busy period. We obtain closed formulas
for the power series expansion in \eps of the mean bit rate, which allow us to
verify the validity of the so-called reduced service rate at the first order.
The second order term yields more insight into the negative impact of the
variability of streaming flows
Generating sequences and Poincar\'e series for a finite set of plane divisorial valuations
Let be a finite set of divisorial valuations centered at a 2-dimensional
regular local ring . In this paper we study its structure by means of the
semigroup of values, , and the multi-index graded algebra defined by ,
\gr_V R. We prove that is finitely generated and we compute its minimal
set of generators following the study of reduced curve singularities. Moreover,
we prove a unique decomposition theorem for the elements of the semigroup.
The comparison between valuations in , the approximation of a reduced
plane curve singularity by families of sets of divisorial
valuations, and the relationship between the value semigroup of and the
semigroups of the sets , allow us to obtain the (finite) minimal
generating sequences for as well as for .
We also analyze the structure of the homogeneous components of \gr_V R. The
study of their dimensions allows us to relate the Poincar\'e series for and
for a general curve of . Since the last series coincides with the
Alexander polynomial of the singularity, we can deduce a formula of A'Campo
type for the Poincar\'e series of . Moreover, the Poincar\'e series of
could be seen as the limit of the series of ,
Duality between Topologically Massive and Self-Dual models
We show that, with the help of a general BRST symmetry, different theories in
3 dimensions can be connected through a fundamental topological field theory
related to the classical limit of the Chern-Simons model.Comment: 13 pages, LaTe
Hybrid model predictive control for freeway traffic using discrete speed limit signals
HYCON2 Show day - Traffic modeling, Estimation and Control 13/05/2014 GrenobleIn this paper, two hybrid Model Predictive Control (MPC) approaches for freeway traffic control are proposed considering variable speed limits (VSL) as discrete variables as in current real world implementations. These discrete characteristics of the speed limits values and some necessary constraints for the actual operation of VSL are usually underestimated in the literature, so we propose a way to include them using a macroscopic traffic model within an MPC framework. For obtaining discrete signals, the MPC controller has to solve a highly non-linear optimization problem, including mixed-integer variables. Since solving such a problem is complex and difficult to execute in real-time, we propose some methods to obtain reasonable control actions in a limited computation time. The first two methods (-exhaustive and -genetic discretization) consist of first relaxing the discrete constraints for the VSL inputs; and then, based on this continuous solution and using a genetic or an exhaustive algorithm, to find discrete solutions within a distance of the continuous solution that provide a good performance. The second class of methods split the problem in a continuous optimization for the ramp metering signals and in a discrete optimization for speed limits. The speed limits optimization, which is much more time-consuming than the ramp metering one, is solved by a genetic or an exhaustive algorithm in communication with a non-linear solver for the ramp metering. The proposed methods are tested by simulation, showing not only a good performance, but also keeping the computation time reduced.UniĂłn Europea FP7/2007â201
A short note on the nested-sweep polarized traces method for the 2D Helmholtz equation
We present a variant of the solver in Zepeda-N\'u\~nez and Demanet (2014),
for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media.
By changing the domain decomposition from a layered to a grid-like partition,
this variant yields improved asymptotic online and offline runtimes and a lower
memory footprint. The solver has online parallel complexity that scales
\emph{sub linearly} as , where is
the number of volume unknowns, and is the number of processors, provided
that . The variant in Zepeda-N\'u\~nez and Demanet
(2014) only afforded . Algorithmic scalability is a
prime requirement for wave simulation in regimes of interest for geophysical
imaging.Comment: 5 pages, 5 figure
Some results on the eigenfunctions of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra E6
The quantum trigonometric Calogero-Sutherland models related to Lie algebras
admit a parametrization in which the dynamical variables are the characters of
the fundamental representations of the algebra. We develop here this approach
for the case of the exceptional Lie algebra E6.Comment: 17 pages, no figure
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