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Dive into the research topics where Michael Scheutzow is active.

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Featured researches published by Michael Scheutzow.


IEEE Transactions on Reliability | 2011

Survivability Analysis of Next-Generation Passive Optical Networks and Fiber-Wireless Access Networks

Navid Ghazisaidi; Michael Scheutzow; Martin Maier

Passive optical networks (PONs) are currently evolving into next-generation PONs (NG-PONs) which aim at achieving higher data rates, wavelength channel counts, number of optical network units (ONUs), and extended coverage compared to their conventional counterparts. Due to the increased number of stages and ONUs, NG-PONs face significant challenges to provide the same level of survivability like conventional PONs without exceeding the budget constraints of cost-sensitive access networks. Toward this end, partial optical protection, in combination with interconnecting a subset of ONUs through a wireless mesh network (WMN) front-end, are promising solutions to render NG-PONs survivable in a cost-effective manner. In this paper, we present a probabilistic analysis of the survivability of NG-PONs and hybrid fiber-wireless (FiWi) access networks, taking both optical and wireless protection into account. In addition, we propose different selection schemes to wirelessly upgrade a subset of ONUs, and investigate their performance for a wide range of fiber link failure scenarios and different NG-PON topologies.


Probability Theory and Related Fields | 1995

Perfect cocycles through stochastic differential equations

Ludwig Arnold; Michael Scheutzow

SummaryWe prove that if ϕ is a random dynamical system (cocycle) for whicht→ϕ(t, ω)x is a semimartingale, then it is generated by a stochastic differential equation driven by a vector field valued semimartingale with stationary increment (helix), and conversely. This relation is succinctly expressed as “semimartingale cocycle=exp(semimartingale helix)”. To implement it we lift stochastic calculus from the traditional one-sided time ℝ to two-sided timeT=ℝ and make this consistent with ergodic theory. We also prove a general theorem on the perfection of a crude cocycle, thus solving a problem which was open for more than ten years.


Journal of Lightwave Technology | 2008

Just-in-Time Scheduling for Multichannel EPONs

Michael P. McGarry; Martin Reisslein; Charles J. Colbourn; Martin Maier; Frank Aurzada; Michael Scheutzow

We investigate optical network unit (ONU) grant scheduling techniques for multichannel Ethernet passive optical networks (EPONs), such as wavelength division multiplexed (WDM) EPONs. We take a scheduling theoretic approach to solving the grant scheduling problem. We introduce a two-layer structure of the scheduling problem and investigate techniques to be used at both layers. We present an extensive ONU grant scheduling simulation study that provides: 1) insight into the nature of the ONU grant scheduling problem and 2) indication of which scheduling techniques are best for certain conditions. We find that the choice of scheduling framework has typically the largest impact on average queueing delay and achievable channel utilization. An offline scheduling framework is not work conserving and consequently wastes channel resources while waiting for all ONU REPORT messages before making access decisions. An online scheduling framework, although work conserving, does not provide the best performance since scheduling decisions are made with the information contained in a single ONU REPORT. We propose a novel online just-in-time (JIT) scheduling framework that is work conserving while increasing scheduling control by allowing the channel availability to drive the scheduling process. In online JIT, multiple ONU REPORTs can be considered together when making scheduling decisions, resulting in lower average queueing delay under certain conditions and a more effective service differentiation of ONUs.


IEEE Transactions on Communications | 2011

Capacity and Delay Analysis of Next-Generation Passive Optical Networks (NG-PONs)

Frank Aurzada; Michael Scheutzow; Martin Reisslein; Navid Ghazisaidi; Martin Maier

Building on the Ethernet Passive Optical Network (EPON) and Gigabit PON (GPON) standards, Next-Generation (NG) PONs (i) provide increased data rates, split ratios, wavelengths counts, and fiber lengths, as well as (ii) allow for all-optical integration of access and metro networks. In this paper we provide a comprehensive probabilistic analysis of the capacity (maximum mean packet throughput) and packet delay of subnetworks that can be used to form NG-PONs. Our analysis can cover a wide range of NG-PONs through taking the minimum capacity of the subnetworks forming the NG-PON and weighing the packet delays of the subnetworks. Our numerical and simulation results indicate that our analysis quite accurately characterizes the throughput-delay performance of EPON/GPON tree networks, including networks upgraded with higher data rates and wavelength counts. Our analysis also characterizes the trade-offs and bottlenecks when integrating EPON/GPON tree networks across a metro area with a ring, a Passive Star Coupler (PSC), or an Arrayed Waveguide Grating (AWG) for uniform and non-uniform traffic. To the best of our knowledge, the presented analysis is the first to consider multiple PONs interconnected via a metro network.


Journal of Optical Networking | 2008

Delay analysis of Ethernet passive optical networks with gated service

Frank Aurzada; Michael Scheutzow; Martin Herzog; Martin Maier; Martin Reisslein

We analyze the mean packet delay in an Ethernet passive optical network (EPON) with gated service. For an EPON with a single optical network unit (ONU), we derive (i) a closed form delay expression for reporting at the end of an upstream transmission, and (ii) a Markov chain-based approach requiring the numerical solution of a system of equations for reporting at the beginning of an upstream transmission. Reporting at the beginning, which has not been previously examined in detail, achieves significantly smaller delays than reporting at the end of an upstream transmission for a small number of ONUs. Both of these analyses are fundamentally different from existing polling system analyses in that they consider the dependent switchover times of the EPON. We extend the analysis for reporting at the beginning of an upstream transmission to approximate the mean packet delay in an EPON with multiple ONUs and verify the accuracy of the analysis with simulations. Overall, our numerical results indicate that for utilizations up to ~75%, the mean packet delay is close to its minimum of four times the one-way propagation delay.


Stochastic Analysis and Applications | 1993

Stabilization and Destabilization by Noise in the Plane

Michael Scheutzow

We provide two dynamical systems in R 2given by an ODE:One which explodes in finite time for every initial condition but becomes stable by adding white noise of arbitrary positive intensity in the sense that the system becomes nonexplosive and even positive recurrent and another system which is globally asymptotically stable and which becomes explosive when it is perturbed by additive white noise


Journal of Theoretical Probability | 2003

On the Link Between Small Ball Probabilities and the Quantization Problem for Gaussian Measures on Banach Spaces

Steffen Dereich; F. Fehringer; A. Matoussi; Michael Scheutzow

Let μ be a centered Gaussian measure on a separable Banach space E and N a positive integer. We study the asymptotics as N→∞ of the quantization error, i.e., the infimum over all subsets ℰ of E of cardinality N of the average distance w.r.t. μ to the closest point in the set ℰ. We compare the quantization error with the average distance which is obtained when the set ℰ is chosen by taking N i.i.d. copies of random elements with law μ. Our approach is based on the study of the asymptotics of the measure of a small ball around 0. Under slight conditions on the regular variation of the small ball function, we get upper and lower bounds of the deterministic and random quantization error and are able to show that both are of the same order. Our conditions are typically satisfied in case the Banach space is infinite dimensional.


Journal of Lightwave Technology | 2003

Wavelength reuse for efficient packet-switched transport in an AWG-based metro WDM network

Michael Scheutzow; Martin Maier; Martin Reisslein; Adam Wolisz

Metro wavelength-division multiplexed (WDM) networks play an important role in the emerging Internet hierarchy; they interconnect the backbone WDM networks and the local-access networks. The current circuit-switched SONET/synchronous digital hierarchy (SDH)-over-WDM-ring metro networks are expected to become a serious bottleneck-the so-called metro gap-as they are faced with an increasing amount of bursty packet data traffic and quickly increasing bandwidths in the backbone networks and access networks. Innovative metro WDM networks that are highly efficient and able to handle variable-size packets are needed to alleviate the metro gap. In this paper, we study an arrayed-waveguide grating (AWG)-based single-hop WDM metro network. We analyze the photonic switching of variable-size packets with spatial wavelength reuse. We derive computationally efficient and accurate expressions for the network throughput and delay. Our extensive numerical investigations-based on our analytical results and simulations-reveal that spatial wavelength reuse is crucial for efficient photonic packet switching. In typical scenarios, spatial wavelength reuse increases the throughput by 60% while reducing the delay by 40%. Also, the throughput of our AWG-based network with spatial wavelength reuse is roughly 70% larger than the throughput of a comparable single-hop WDM network based on a passive star coupler (PSC).


Dynamical Systems-an International Journal | 2004

On the structure of attractors and invariant measures for a class of monotone random systems

Igor Chueshov; Michael Scheutzow

Under rather general conditions we show that any monotone random dynamical system on an (admissible) subset of a partially ordered Banach space V has a unique invariant measure. This measure is Dirac, i.e. it is generated by some stationary process. If the cone V + of non-negative elements of V is normal, then this stationary process is a global random attractor with respect to convergence in probability. As examples we consider one-dimensional ordinary and retarded stochastic differential equations, a stochastic model of a biochemical control circuit, a class of parabolic stochastic partial differential equations (PDEs) with additive noise and interacting particle systems.


Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2013

Constructive quantization: Approximation by empirical measures

Steffen Dereich; Michael Scheutzow; Reik Schottstedt

In this article, we study the approximation of a probability measure

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Martin Maier

Institut national de la recherche scientifique

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Frank Aurzada

Technical University of Berlin

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Salah-Eldin A. Mohammed

Southern Illinois University Carbondale

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Jochen Blath

Technical University of Berlin

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M. Cranston

University of California

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Patrick Seeling

Central Michigan University

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Abdelhadi Es-Sarhir

Technical University of Berlin

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Steffen Dereich

Technical University of Berlin

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