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Brandt M.,Konrad Zuse Zentrum fur Informationstechnik Berlin ZIB | Brandt A.,Humboldt University of Berlin
Queueing Systems | Year: 2010

We consider a system with Poisson arrivals and i.i.d. service times. The requests are served according to the state-dependent processor-sharing discipline, where each request receives a service capacity which depends on the actual number of requests in the system. The linear systems of PDEs describing the residual and attained sojourn times coincide for this system, which provides time reversibility including sojourn times for this system, and their minimal non-negative solution gives the LST of the sojourn time V(τ) of a request with required service time τ. For the case that the service time distribution is exponential in a neighborhood of zero, we derive a linear system of ODEs, whose minimal non-negative solution gives the LST of V(τ), and which yields linear systems of ODEs for the moments of V(τ) in the considered neighborhood of zero. Numerical results are presented for the variance of V(τ). In the case of an M/GI/2-PS system, the LST of V(τ) is given in terms of the solution of a convolution equation in the considered neighborhood of zero. For service times bounded from below, surprisingly simple expressions for the LST and variance of V(τ) in this neighborhood of zero are derived, which yield in particular the LST and variance of V(τ) in M/D/2-PS. © Springer Science+Business Media, LLC 2009. Source


D'Andreagiovanni F.,Konrad Zuse Zentrum fur Informationstechnik Berlin ZIB | Mannino C.,University of Rome La Sapienza | Sassano A.,University of Rome La Sapienza
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2011

The Wireless Network Design Problem (WND) consists in choosing values of radio-electrical parameters of transmitters of a wireless network, to maximize network coverage. We present a pure 0-1 Linear Programming formulation for the WND that may contain an exponential number of constraints. Violated inequalities of this formulation are hard to separate both theoretically and in practice. However, a relevant subset of such inequalities can be separated more efficiently in practice and can be used to strengthen classical MILP formulations for the WND. Preliminary computational experience confirms the effectiveness of our new technique both in terms of quality of solutions found and provided bounds. © 2011 Springer-Verlag. Source


Fugenschuh A.,Konrad Zuse Zentrum fur Informationstechnik Berlin ZIB
Journal of Scheduling | Year: 2011

We present an integer programming model for the integrated optimization of bus schedules and school starting times, which is a single-depot vehicle scheduling problem with additional coupling constraints among the time windows. For instances with wide time windows the linear relaxation is weak and feasible solutions found by an ILP solver are of poor quality. We apply a set partitioning relaxation to compute better lower bounds and, in combination with a primal construction heuristic, also better primal feasible solutions. Integer programs with at most two non-zero coefficient per constraint play a prominent role in our approach. Computational results for several random and a realworld instance are given and compared with results from a standard branch-and-cut approach. © 2011 Springer Science+Business Media, LLC. Source


D'Andreagiovanni F.,Konrad Zuse Zentrum fur Informationstechnik Berlin ZIB
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2011

Over the last decade, wireless networks have experienced an impressive growth and now play a main role in many telecommunications systems. As a consequence, scarce radio resources, such as frequencies, became congested and the need for effective and efficient assignment methods arose. In this work, we present a Genetic Algorithm for solving large instances of the Power, Frequency and Modulation Assignment Problem, arising in the design of wireless networks. To our best knowledge, this is the first Genetic Algorithm that is proposed for such problem. Compared to previous works, our approach allows a wider exploration of the set of power solutions, while eliminating sources of numerical problems. The performance of the algorithm is assessed by tests over a set of large realistic instances of a Fixed WiMAX Network. © 2011 Springer-Verlag. Source


Metzner P.,Free University of Berlin | Weber M.,Konrad Zuse Zentrum fur Informationstechnik Berlin ZIB | Schutte C.,Free University of Berlin
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

In many applications one is interested in finding a simplified model which captures the essential dynamical behavior of a real life process. If the essential dynamics can be assumed to be (approximately) memoryless then a reasonable choice for a model is a Markov model whose parameters are estimated by means of Bayesian inference from an observed time series. We propose an efficient Monte Carlo Markov chain framework to assess the uncertainty of the Markov model and related observables. The derived Gibbs sampler allows for sampling distributions of transition matrices subject to reversibility and/or sparsity constraints. The performance of the suggested sampling scheme is demonstrated and discussed for a variety of model examples. The uncertainty analysis of functions of the Markov model under investigation is discussed in application to the identification of conformations of the trialanine molecule via Robust Perron Cluster Analysis (PCCA+). © 2010 The American Physical Society. Source

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