The effective bandwidth problem revisited

The paper studies a single-server queueing system with autonomous service and $\ell$ priority classes. Arrival and departure processes are governed by marked point processes. There are $\ell$ buffers corresponding to priority classes, and upon arrival a unit of the $k$th priority class occupies a place in the $k$th buffer. Let $N^{(k)}$, $k=1,2,...,\ell$ denote the quota for the total $k$th buffer content. The values $N^{(k)}$ 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 $N^{(k)}$ 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

Variations of auroral hydrogen emission near substorm onset

The results of coordinated optical ground-based observations of the auroral substorm on 26 March 2004 in the Kola Peninsula are described. Imaging spectrograph data with high spectral and temporal resolution recorded the Doppler profile of the Hα hydrogen emission; this allows us to estimate the average energy of precipitating protons and the emission intensity of the hydrogen Balmer line. Two different populations of precipitating protons were observed during an auroral substorm. The first of these is associated with a diffuse hydrogen emission that is usually observed in the evening sector of the auroral oval and located equatorward of the discrete electron arcs associated with substorm onset. The average energy of the protons during this precipitation was ~20–35 keV, and the energy flux was ~3x10<sup>–4</sup>Joule/m<sup>2</sup>s. The second proton population was observed 1–2min after the breakup during 4–5min of the expansion phase of substorm into the zone of bright, discrete auroral structures (N-S arcs). The average energy of the protons in this population was ~60 keV, and the energy flux was ~2.2x10<sup>–3</sup>Joule/m<sup>2</sup>s. The observed spatial structure of hydrogen emission is additional evidence of the higher energy of precipitated protons in the second population, relative to the protons in the diffuse aurora. We believe that the most probable mechanism of precipitation of the second population protons was pitch-angle scattering of particles due to non-adiabatic motion in the region of local dipolarization near the equatorial plane.<p><b>Keywords.</b> Auroral ionosphere; Particle precipitation; Storms and substorm

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

The Hitting Times with Taboo for a Random Walk on an Integer Lattice

For a symmetric, homogeneous and irreducible random walk on d-dimensional integer lattice Z^d, having zero mean and a finite variance of jumps, we study the passage times (with possible infinite values) determined by the starting point x, the hitting state y and the taboo state z. We find the probability that these passages times are finite and analyze the tails of their cumulative distribution functions. In particular, it turns out that for the random walk on Z^d, except for a simple (nearest neighbor) random walk on Z, the order of the tail decrease is specified by dimension d only. In contrast, for a simple random walk on Z, the asymptotic properties of hitting times with taboo essentially depend on the mutual location of the points x, y and z. These problems originated in our recent study of branching random walk on Z^d with a single source of branching

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 $\psi(u;\gamma h)$ with $\gamma$ tending to infinity, and solve a related minimisation problem.Comment: 14 page