Asymptotic analysis of Cohen's equation for retrial queues in the Halfin-Whitt regime

No readable abstrac

Convolution theory in a space of generalized functions

No abstrac

A decay result for certain windows generating orthogonal Gabor bases

We consider tight Gabor frames (h,a=1,b=1) at critical density with h of the form Z -1(Zg/|Zg|). Here Z is the standard Zak transform and g is an even, real, well-behaved window such that Zg has exactly one zero, at 1/2,1/2, in [0,1)2. We show that h and its Fourier transform have maximal decay as allowed by the Balian-Low theorem. Our result illustrates a theorem of Benedetto, Czaja, Gadzinski, and Powell, case p=q=2, on sharpness of the Balian-Low theorem

Adaptive interpolation of discrete-time signals that can be modeled as autoregressive processes

This paper presents an adaptive algorithm for the restoration of lost sample values in discrete-time signals that can locally be described by means of autoregressive processes. The only restrictions are that the positions of the unknown samples should be known and that they should be embedded in a sufficiently large neighborhood of known samples. The estimates of the unknown samples are obtained by minimizing the sum of squares of the residual errors that involve estimates of the autoregressive parameters. A statistical analysis shows that, for a burst of lost samples, the expected quadratic interpolation error per sample converges to the signal variance when the burst length tends to infinity. The method is in fact the first step of an iterative algorithm, in which in each iteration step the current estimates of the missing samples are used to compute the new estimates. Furthermore, the feasibility of implementation in hardware for real-time use is established. The method has been tested on artificially generated auto-regressive processes as well as on digitized music and speech signals

Relaxation time for the discrete D/G/1 queue

When queueing models are used for performance analysis of some stochastic system, it is usually assumed that the system is in steady-state. Whether or not this is a realistic assumption depends on the speed at which the system tends to its steady-state. A characterization of this speed is known in the queueing literature as relaxation time. The discrete D/G/1 queue has a wide range of applications. We derive relaxation time asymptotics for the discrete D/G/1 queue in a purely analytical way, mostly relying on the saddle point method. We present a simple and useful approximate upper bound which is sharp in case the load on the system is not very high. A sharpening of this upper bound, which involves the complementary error function, is then developed and this covers both the cases of low and high loads. For the discrete D/G/1 queue, the stationary waiting time distribution can be expressed in terms of infinite series that follow from Spitzer’s identity. These series involve convolutions of the probability distribution of a discrete random variable, which makes them suitable for computation. For practical purposes, though, the infinite series should be truncated. The relaxation time asymptotics can be applied to determine an appropriate truncation level based on a sharp estimate of the error caused by truncating

Equidistant sampling for the maximum of a Brownian motion with drift on a finite horizon

A Brownian motion observed at equidistant sampling points renders a random walk with normally distributed increments. For the difference between the expected maximum of the Brownian motion and its sampled version, an expansion is derived with coefficients in terms of the drift, the Riemann zeta function and the normal distribution function

Equidistant sampling for the maximum of a Brownian motion with drift on a finite horizon

A Brownian motion observed at equidistant sampling points renders a random walk with normally distributed increments. For the difference between the expected maximum of the Brownian motion and its sampled version, an expansion is derived with coefficients in terms of the drift, the Riemann zeta function and the normal distribution function