101 research outputs found
Analysis of constrained theories without use of primary constraints
It is shown that the Dirac approach to Hamiltonization of singular theories
can be slightly modified in such a way that primary Dirac constraints do not
appear in the process. According to the modified scheme, Hamiltonian
formulation of singular theory is first order Lagrangian formulation, further
rewritten in special coordinates.Comment: LaTex file, 10 pages, published versio
Stochastic inequalities for single-server loss queueing systems
The present paper provides some new stochastic inequalities for the
characteristics of the and loss queueing systems. These
stochastic inequalities are based on substantially deepen up- and
down-crossings analysis, and they are stronger than the known stochastic
inequalities obtained earlier. Specifically, for a class of queueing
system, two-side stochastic inequalities are obtained.Comment: 17 pages, 11pt To appear in Stochastic Analysis and Application
The effective bandwidth problem revisited
The paper studies a single-server queueing system with autonomous service and
priority classes. Arrival and departure processes are governed by marked
point processes. There are buffers corresponding to priority classes,
and upon arrival a unit of the th priority class occupies a place in the
th buffer. Let , denote the quota for the total
th buffer content. The values are assumed to be large, and
queueing systems both with finite and infinite buffers are studied. In the case
of a system with finite buffers, the values characterize buffer
capacities.
The paper discusses a circle of problems related to optimization of
performance measures associated with overflowing the quota of buffer contents
in particular buffers models. Our approach to this problem is new, and the
presentation of our results is simple and clear for real applications.Comment: 29 pages, 11pt, Final version, that will be published as is in
Stochastic Model
Martin boundary of a reflected random walk on a half-space
The complete representation of the Martin compactification for reflected
random walks on a half-space is obtained. It is shown that the
full Martin compactification is in general not homeomorphic to the ``radial''
compactification obtained by Ney and Spitzer for the homogeneous random walks
in : convergence of a sequence of points to a
point of on the Martin boundary does not imply convergence of the sequence
on the unit sphere . Our approach relies on the large
deviation properties of the scaled processes and uses Pascal's method combined
with the ratio limit theorem. The existence of non-radial limits is related to
non-linear optimal large deviation trajectories.Comment: 42 pages, preprint, CNRS UMR 808
Transient phenomena for Markov chains and their applications
Projet MEVALIn this paper we consider a family of irreductible, ergodic and aperiodic Markov chains, depending on a parameter e > 0, so that the local drifts have a critical behaviour (in terms of Pakes lemma). The purpose is to analyze the steady state distributions of these chains (in the sense of weak convergence), when e ¯ 0. Under assumptions involving at most the existence of moments of order 2 + g for the jumps, we show that, whenever X (0) is not ergodic, it is possible to caracterize accurately these limit distributions. Connections with the gamma and uniform distributions are revealed
Large closed queueing networks in semi-Markov environment and its application
The paper studies closed queueing networks containing a server station and
client stations. The server station is an infinite server queueing system,
and client stations are single-server queueing systems with autonomous service,
i.e. every client station serves customers (units) only at random instants
generated by a strictly stationary and ergodic sequence of random variables.
The total number of units in the network is . The expected times between
departures in client stations are . After a service completion
in the server station, a unit is transmitted to the th client station with
probability , and being processed in the th client
station, the unit returns to the server station. The network is assumed to be
in a semi-Markov environment. A semi-Markov environment is defined by a finite
or countable infinite Markov chain and by sequences of independent and
identically distributed random variables. Then the routing probabilities
and transmission rates (which are expressed via
parameters of the network) depend on a Markov state of the environment. The
paper studies the queue-length processes in client stations of this network and
is aimed to the analysis of performance measures associated with this network.
The questions risen in this paper have immediate relation to quality control of
complex telecommunication networks, and the obtained results are expected to
lead to the solutions to many practical problems of this area of research.Comment: 35 pages, 1 figure, 12pt, accepted: Acta Appl. Mat
Spherical Model in a Random Field
We investigate the properties of the Gibbs states and thermodynamic
observables of the spherical model in a random field. We show that on the
low-temperature critical line the magnetization of the model is not a
self-averaging observable, but it self-averages conditionally. We also show
that an arbitrarily weak homogeneous boundary field dominates over fluctuations
of the random field once the model transits into a ferromagnetic phase. As a
result, a homogeneous boundary field restores the conventional self-averaging
of thermodynamic observables, like the magnetization and the susceptibility. We
also investigate the effective field created at the sites of the lattice by the
random field, and show that at the critical temperature of the spherical model
the effective field undergoes a transition into a phase with long-range
correlations .Comment: 29 page
Boundary non-crossings of Brownian pillow
Let B_0(s,t) be a Brownian pillow with continuous sample paths, and let
h,u:[0,1]^2\to R be two measurable functions. In this paper we derive upper and
lower bounds for the boundary non-crossing probability
\psi(u;h):=P{B_0(s,t)+h(s,t) \le u(s,t), \forall s,t\in [0,1]}. Further we
investigate the asymptotic behaviour of with
tending to infinity, and solve a related minimisation problem.Comment: 14 page
Boundary-crossing identities for diffusions having the time-inversion property
We review and study a one-parameter family of functional transformations, denoted by (S (β)) β∈ℝ, which, in the case β<0, provides a path realization of bridges associated to the family of diffusion processes enjoying the time-inversion property. This family includes Brownian motions, Bessel processes with a positive dimension and their conservative h-transforms. By means of these transformations, we derive an explicit and simple expression which relates the law of the boundary-crossing times for these diffusions over a given function f to those over the image of f by the mapping S (β), for some fixed β∈ℝ. We give some new examples of boundary-crossing problems for the Brownian motion and the family of Bessel processes. We also provide, in the Brownian case, an interpretation of the results obtained by the standard method of images and establish connections between the exact asymptotics for large time of the densities corresponding to various curves of each family
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