372 research outputs found
Directionally Convex Ordering of Random Measures, Shot Noise Fields and Some Applications to Wireless Communications
Directionally convex () ordering is a tool for comparison of dependence
structure of random vectors that also takes into account the variability of the
marginal distributions. When extended to random fields it concerns comparison
of all finite dimensional distributions. Viewing locally finite measures as
non-negative fields of measure-values indexed by the bounded Borel subsets of
the space, in this paper we formulate and study the ordering of random
measures on locally compact spaces. We show that the order is preserved
under some of the natural operations considered on random measures and point
processes, such as deterministic displacement of points, independent
superposition and thinning as well as independent, identically distributed
marking. Further operations such as position dependent marking and displacement
of points though do not preserve the order on all point processes, are
shown to preserve the order on Cox point processes. We also examine the impact
of order on the second moment properties, in particular on clustering and
on Palm distributions. Comparisons of Ripley's functions, pair correlation
functions as well as examples seem to indicate that point processes higher in
order cluster more. As the main result, we show that non-negative
integral shot-noise fields with respect to ordered random measures
inherit this ordering from the measures. Numerous applications of this result
are shown, in particular to comparison of various Cox processes and some
performance measures of wireless networks, in both of which shot-noise fields
appear as key ingredients. We also mention a few pertinent open questions.Comment: Accepted in Advances in Applied Probability. Propn. 3.2 strengthened
and as a consequence Cor 6.1,6.2,6.
On Monotonicity and Propagation of Order Properties
In this paper, a link between monotonicity of deterministic dynamical systems
and propagation of order by Markov processes is established. The order
propagation has received considerable attention in the literature, however,
this notion is still not fully understood. The main contribution of this paper
is a study of the order propagation in the deterministic setting, which
potentially can provide new techniques for analysis in the stochastic one. We
take a close look at the propagation of the so-called increasing and increasing
convex orders. Infinitesimal characterisations of these orders are derived,
which resemble the well-known Kamke conditions for monotonicity. It is shown
that increasing order is equivalent to the standard monotonicity, while the
class of systems propagating the increasing convex order is equivalent to the
class of monotone systems with convex vector fields. The paper is concluded by
deriving a novel result on order propagating diffusion processes and an
application of this result to biological processes.Comment: Part of the paper is to appear in American Control Conference 201
Routing in multi-class queueing networks
PhD ThesisWe consider the problem of routing (incorporating local scheduling) in a distributed
network. Dedicated jobs arrive directly at their specified station for processing. The
choice of station for generic jobs is open. Each job class has an associated holding cost
rate. We aim to develop routing policies to minimise the long-run average holding cost
rate.
We first consider the class of static policies. Dacre, Glazebrook and Nifio-Mora (1999)
developed an approach to the formulation of static routing policies, in which the work at
each station is scheduled optimally, using the achievable region approach. The achievable
region approach attempts to solve stochastic optimisation problems by characterising
the space of all possible performances and optimising the performance objective over
this space. Optimal local scheduling takes the form of a priority policy. Such static
routing policies distribute the generic traffic to the stations via a simple Bernoulli routing
mechanism. We provide an overview of the achievements made in following this approach
to static routing. In the course of this discussion we expand upon the study of Becker et al.
(2000) in which they considered routing to a collection of stations specialised in processing
certain job classes and we consider how the composition of the available stations affects
the system performance for this particular problem. We conclude our examination of
static routing policies with an investigation into a network design problem in which the
number of stations available for processing remains to be determined.
The second class of policies of interest is the class of dynamic policies. General DP
theory asserts the existence of a deterministic, stationary and Markov optimal dynamic
policy. However, a full DP solution may be unobtainable and theoretical difficulties posed
by simple routing problems suggest that a closed form optimal policy may not be available.
This motivates a requirement for good heuristic policies. We consider two approaches to
the development of dynamic routing heuristics. We develop an idea proposed, in the
context of simple single class systems, by Krishnan (1987) by applying a single policy
improvement step to some given static policy. The resulting dynamic policy is shown
to be of simple structure and easily computable. We include an investigation into the
comparative performance of the dynamic policy with a number of competitor policies and
of the performance of the heuristic as the number of stations in the network changes. In
our second approach the generic traffic may only access processing when the station has
been cleared of all (higher priority) jobs and can be considered as background work. We
deploy a prescription of Whittle (1988) developed for RBPs to develop a suitable approach
to station indexation. Taking an approximative approach to Whittle's proposal results
in a very simple form of index policy for routing the generic traffic. We investigate the
closeness to optimality of the index policy and compare the performance of both of the
dynamic routing policies developed here
Self-Evaluation Applied Mathematics 2003-2008 University of Twente
This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008
Smart antennas: state of the art
Aim of this contribution is to illustrate the state of the art of smart antenna research from several perspectives. The bow is drawn from transmitter issues via channel measurements and modeling, receiver signal processing, network aspects, technological challenges towards first smart antenna applications and current status of standardization. Moreover, some future prospects of different disciplines in smart antenna research are given.Peer Reviewe
Towards Fast-Convergence, Low-Delay and Low-Complexity Network Optimization
Distributed network optimization has been studied for well over a decade.
However, we still do not have a good idea of how to design schemes that can
simultaneously provide good performance across the dimensions of utility
optimality, convergence speed, and delay. To address these challenges, in this
paper, we propose a new algorithmic framework with all these metrics
approaching optimality. The salient features of our new algorithm are
three-fold: (i) fast convergence: it converges with only
iterations that is the fastest speed among all the existing algorithms; (ii)
low delay: it guarantees optimal utility with finite queue length; (iii) simple
implementation: the control variables of this algorithm are based on virtual
queues that do not require maintaining per-flow information. The new technique
builds on a kind of inexact Uzawa method in the Alternating Directional Method
of Multiplier, and provides a new theoretical path to prove global and linear
convergence rate of such a method without requiring the full rank assumption of
the constraint matrix
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