397,527 research outputs found
Specifying and Placing Chains of Virtual Network Functions
Network appliances perform different functions on network flows and
constitute an important part of an operator's network. Normally, a set of
chained network functions process network flows. Following the trend of
virtualization of networks, virtualization of the network functions has also
become a topic of interest. We define a model for formalizing the chaining of
network functions using a context-free language. We process deployment requests
and construct virtual network function graphs that can be mapped to the
network. We describe the mapping as a Mixed Integer Quadratically Constrained
Program (MIQCP) for finding the placement of the network functions and chaining
them together considering the limited network resources and requirements of the
functions. We have performed a Pareto set analysis to investigate the possible
trade-offs between different optimization objectives
Service Chain (SC) Mapping with Multiple SC Instances in a Wide Area Network
Network Function Virtualization (NFV) aims to simplify deployment of network
services by running Virtual Network Functions (VNFs) on commercial
off-the-shelf servers. Service deployment involves placement of VNFs and
in-sequence routing of traffic flows through VNFs comprising a Service Chain
(SC). The joint VNF placement and traffic routing is usually referred as SC
mapping. In a Wide Area Network (WAN), a situation may arise where several
traffic flows, generated by many distributed node pairs, require the same SC,
one single instance (or occurrence) of that SC might not be enough. SC mapping
with multiple SC instances for the same SC turns out to be a very complex
problem, since the sequential traversal of VNFs has to be maintained while
accounting for traffic flows in various directions. Our study is the first to
deal with SC mapping with multiple SC instances to minimize network resource
consumption. Exact mathematical modeling of this problem results in a quadratic
formulation. We propose a two-phase column-generation-based model and solution
in order to get results over large network topologies within reasonable
computational times. Using such an approach, we observe that an appropriate
choice of only a small set of SC instances can lead to solution very close to
the minimum bandwidth consumption
A Primal-Dual Algorithm for Link Dependent Origin Destination Matrix Estimation
Origin-Destination Matrix (ODM) estimation is a classical problem in
transport engineering aiming to recover flows from every Origin to every
Destination from measured traffic counts and a priori model information. In
addition to traffic counts, the present contribution takes advantage of probe
trajectories, whose capture is made possible by new measurement technologies.
It extends the concept of ODM to that of Link dependent ODM (LODM), keeping the
information about the flow distribution on links and containing inherently the
ODM assignment. Further, an original formulation of LODM estimation, from
traffic counts and probe trajectories is presented as an optimisation problem,
where the functional to be minimized consists of five convex functions, each
modelling a constraint or property of the transport problem: consistency with
traffic counts, consistency with sampled probe trajectories, consistency with
traffic conservation (Kirchhoff's law), similarity of flows having close
origins and destinations, positivity of traffic flows. A primal-dual algorithm
is devised to minimize the designed functional, as the corresponding objective
functions are not necessarily differentiable. A case study, on a simulated
network and traffic, validates the feasibility of the procedure and details its
benefits for the estimation of an LODM matching real-network constraints and
observations
Asymptotically Optimal Approximation Algorithms for Coflow Scheduling
Many modern datacenter applications involve large-scale computations composed
of multiple data flows that need to be completed over a shared set of
distributed resources. Such a computation completes when all of its flows
complete. A useful abstraction for modeling such scenarios is a {\em coflow},
which is a collection of flows (e.g., tasks, packets, data transmissions) that
all share the same performance goal.
In this paper, we present the first approximation algorithms for scheduling
coflows over general network topologies with the objective of minimizing total
weighted completion time. We consider two different models for coflows based on
the nature of individual flows: circuits, and packets. We design
constant-factor polynomial-time approximation algorithms for scheduling
packet-based coflows with or without given flow paths, and circuit-based
coflows with given flow paths. Furthermore, we give an -approximation polynomial time algorithm for scheduling circuit-based
coflows where flow paths are not given (here is the number of network
edges).
We obtain our results by developing a general framework for coflow schedules,
based on interval-indexed linear programs, which may extend to other coflow
models and objective functions and may also yield improved approximation bounds
for specific network scenarios. We also present an experimental evaluation of
our approach for circuit-based coflows that show a performance improvement of
at least 22% on average over competing heuristics.Comment: Fixed minor typo
Renormalization group for network models of Quantum Hall transitions
We analyze in detail the renormalization group flows which follow from the
recently proposed all orders beta functions for the Chalker-Coddington network
model. The flows in the physical regime reach a true singularity after a finite
scale transformation. Other flows are regular and we identify the asymptotic
directions. One direction is in the same universality class as the disordered
XY model.
The all orders beta function is computed for the network model of the spin
Quantum Hall transition and the flows are shown to have similar properties. It
is argued that fixed points of general current-current interactions in 2d
should correspond to solutions of the Virasoro master equation. Based on this
we identify two coset conformal field theories osp(2N|2N)_1 /u(1)_0 and
osp(4N|4N)_1/su(2)_0 as possible fixed points and study the resulting
multifractal properties. We also obtain a scaling relation between the typical
amplitude exponent alpha_0 and the typical point contact conductance exponent
X_t which is expected to hold when the density of states is constant.Comment: 35 pages, 5 color figures, v2: references adde
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