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Papers by A.j.e.m. Janssen

$Research paper thumbnail of Advanced analytic treatment and efficient computation of the diffraction integrals in the extended Nijboer-Zernike theory$

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

International Journal of Wavelets, Multiresolution and Information Processing, 2005

We consider a discrete-time multi-server queue for which the moments of the stationary queue leng... more We consider a discrete-time multi-server queue for which the moments of the stationary queue length can be expressed in terms of series over the zeros in the closed unit disk of a queue-specific characteristic function. In many important cases these zeros can be considered to be located on a queue-specific curve, called generalized Szegö curve. By adopting a special parametrization of these Szegö curves, the relevant zeros occur as equidistant samples of a 2π-periodic function whose Fourier coefficients can be determined analytically. Thus the series occurring in the expressions for the moments can be written as Fourier aliasing series with terms given in analytic form. This gives rise to formulas for e.g. the mean and variance of the queue length that are reminiscent of Spitzer's identity for the moment generating function of the steady-state waiting time for a G/G/1 queue. Indeed, by considering the queue under investigation as a G/G/1 queue, the new formulas for the mean and ...

Macromolecules, 2008

Queueing Systems, 2005

In commonly used approaches for the discrete-time bulk service queue, the stationary queue length... more In commonly used approaches for the discrete-time bulk service queue, the stationary queue length distribution follows from the roots inside or outside the unit circle of a characteristic equation. We present analytic representations of these roots in the form of sample values of periodic functions with analytically given Fourier series coefficients, making these approaches more transparent and explicit. The resulting computational scheme is easy to implement and numerically stable. We also discuss a method to determine the roots by applying successive substitutions to a fixed point equation. We outline under which conditions this method works, and compare these conditions with those needed for the Fourier series representation. Finally, we present a solution for the stationary queue length distribution that does not depend on roots. This solution is explicit and well-suited for determining tail probabilities up to a high accuracy, as demonstrated by some numerical examples.

Random-access networks may exhibit severe unfairness in throughput, in the sense that some nodes ... more Random-access networks may exhibit severe unfairness in throughput, in the sense that some nodes receive consistently higher throughput than others. Recent studies show that this unfairness is due to local differences in the neighborhood structure: nodes with fewer neighbors receive better access. We study the unfairness in saturated linear networks, and adapt the random-access CSMA protocol to remove the unfairness completely, by choosing the activation rates of nodes as a specific function of the number of neighbors. We then investigate the consequences of this choice of activation rates on the network-average saturated throughput, and we show that these rates perform well in non-saturated settings.

Stochastic Processes and their Applications, 2007

Let X1, X2, . . . be independent variables, each having a normal distribution with negative mean ... more Let X1, X2, . . . be independent variables, each having a normal distribution with negative mean −β < 0 and variance 1. We consider the partial sums Sn = X1 + . . . + Xn, with S0 = 0, and refer to the process {Sn : n ≥ 0} as the Gaussian random walk. This paper is concerned with the cumulants of the maximum M β = max{Sn : n ≥ 0}.

Performance Evaluation, 2011

Random-access algorithms such as CSMA provide a popular mechanism for distributed medium access c... more Random-access algorithms such as CSMA provide a popular mechanism for distributed medium access control in large-scale wireless networks. In recent years, tractable stochastic models have been shown to yield accurate throughput estimates for CSMA networks. We consider a saturated random-access network on a general conflict graph, and prove that for every feasible combination of throughputs, there exists a unique vector

Journal of Fourier Analysis and Applications, 2007

In this paper we investigate the computational aspects of some recently proposed iterative method... more In this paper we investigate the computational aspects of some recently proposed iterative methods for approximating the canonical tight and canonical dual window of a Gabor frame (g, a, b). The iterations start with the window g while the iteration steps comprise the window g, the k th iterand γ k , the frame operators S and S k corresponding to (g, a, b) and (γ k , a, b), respectively, and a number of scalars. The structure of the iteration step of the method is determined by the envisaged convergence order m of the method. We consider two strategies for scaling the terms in the iteration step: norm scaling, where in each step the windows are normalized, and initial scaling where we only scale in the very beginning. Norm scaling leads to fast, but conditionally convergent methods, while initial scaling leads to unconditionally convergent methods, but with possibly suboptimal convergence constants. The iterations, initially formulated for time-continuous Gabor systems, are considered and tested in a discrete setting in which one passes to the appropriately sampled-and-periodized windows and frame operators. Furthermore, they are compared with respect to accuracy and efficiency with other methods to approximate canonical windows associated with Gabor frames.

Indagationes Mathematicae, 2013

Consider the all-time maximum of a Brownian motion with negative drift. Assume that this process ... more Consider the all-time maximum of a Brownian motion with negative drift. Assume that this process is sampled at certain points in time, where the time between two consecutive points is rendered by an Erlang distribution with mean 1/ω. The family of Erlang distributions covers the range between deterministic and exponential distributions. We show that the average convergence rate as ω → ∞ for all such Erlangian sampled Brownian motions is O(ω −1/2 ), and that the constant involved in O ranges from −ζ (1/2)/ √ 2π for deterministic sampling to 1/ √ 2 for exponential sampling. The basic ingredients of our analysis are a finite-series expression for the expected maximum, an asymptotic expansion of  k−1 j=1 (1−exp(2πi j/k)) −s , s ∈ R, as k → ∞ using Euler-Maclaurin summation, and Fourier sampling of functions analytic in an open set containing the closed unit disk.

IEEE Transactions on Information Theory, 2003

Let g be a continuous, compactly supported function on R such that the integer translates of g co... more Let g be a continuous, compactly supported function on R such that the integer translates of g constitute a partition of unity. We show that the Gabor system (g, a, b), with window g and time-shift and frequency-shift parameters a, b > 0 has no lower frame bound larger than 0 if b = 2, 3, . . . and a > 0. In is not a Gabor frame if g is a continuous, compactly supported wavelet scaling function and if b = 2, 3, . . . and a > 0. We exemplify our result for the case that g = B 1 , the triangle function supported by [−1, 1], by showing pictures of the canonical dual corresponding to (g, a, b) when ab = 1/4 and b crosses the lines N = 2, 3, . . . .

Journal of Functional Analysis, 2001