Infinite networks and quadratic optimal control

A discrete-time quadratic optimal control problem is shown to be equivalent to an infinite cascade ofn-port electrical networks. Both problems can be expressed as a generalized Schur complement (or shorted operator) of a block tridiagonal operator. Using Maxwell's principle for resistive networks, a variational formulation of the cascade limit ofn-port networks is given. For one special case a formula for the solution of the quadratic control problem is given in terms of the geometric mean of operators.     

A new electron-trapping model for the gate insulator of insulated gate field-effect transistors

In the present paper, a new model for electron trapping kinetics in the gate insulator of an insulated gate field-effect transistor (IGFET) is proposed. This model includes a continuous variation of the trapping cross section, σ_o, as a function of the number of filled traps,N _D . The dependency of σ_o is believed to be related physically to the annihilation, or buildup of coulombic charge, which effect has heretofore been neglected in first-order trapping kinetics that describe the entire defect concentration range. The result is that in order to model the experimental data fewer classes of trap cross sections are needed. AsN _D traps fill, the trapping cross section, σ_o, is assumed to be reduced by a factor (1 -N _D /N _T ) whereN _T is the total number of available traps per unit area. This decrease in δ_o is consistent, physically, with a concept of increasing repulsion of carriers as traps fill. This new model also indicates that the number of injected electrons needed to populate 99% of the total traps is about 20 times greater than that predicted by the existing first-order trapping kinetics model. Comparisons between the results of the new model and the first-order trapping kinetics model applied to experimental defect data are also given.     

Wide-Band Network Modeling of Interacting Inductive Irises and Steps

Methods of field and network theory are jointly applied to the problem of deriving wide-band models for interacting inductive irises and steps in standard and oversize lossless rectangular guides. The resulting equivalent network is a cascade of lumped multiports, described by means of their reactance matrix, given in the canonical Foster's form, and of several parallel transmission lines, connecting the interacting discontinuities. The required frequency band and the accuracy of the model can be prescribed at will. The features of the approach are: the solution of the field problem yields a reactance matrix with monotonic convergence properties; small matrices only need be manipulated; the frequency dependence is explicit, so that the field analysis need not be repeated at each frequency point; a true network model (and not a "spot frequency" equivalent circuit) is produced, which is prerequisite for exact synthesis.     

Bounded-distance multi-clusterhead formation in wireless ad hoc networks

We present a clustering technique addressing redundancy for bounded-distance clusters, which means being able to determine the minimum number of cluster-heads per node, and the maximum distance from nodes to their cluster-heads. This problem is similar to computing a (k, r)-dominating set, (k, r)-DS, of the network. (k, r)-DS is defined as the problem of selecting a minimum cardinality vertex set D of the network such that every vertex u not in D is at a distance smaller than or equal to r from at least k vertices in D. In mobile ad hoc networks (MANETs), clusters should be computed distributively, because the topology may change frequently. We present the first centralized and distributed solutions to the (k, r)-DS problem for arbitrary topologies. The centralized algorithm computes a (k · ln Δ)-approximation, where Δ is the largest cardinality among all r-hop neighborhoods in the network. The distributed approach is extended for clustering applications, while the centralized is used as a lower bound for comparison purposes. Extensive simulations are used to compare the distributed solution with the centralized one. As a case study, we propose a novel multi-core multicast protocol that applies the distributed solution for the election of cores. The new protocol is compared against PUMA, one of the best performing multicast protocols for MANETS. Simulation results show that the new protocol outperforms PUMA on the context of static networks.     

The synthesis of two-dimensional passive n-ports containing lumped elements

Two-dimensional (2-D) passive networks are of interest e.g. for use as reference filters for two-dimensional wave digital filters. Necessary properties of the impedance matrix and scattering matrix, respectively, of such n-ports have been established, but not yet been shown to be also sufficient for a given two-variable rational matrix to be the impedance matrix or scattering matrix, respectively, of a passive network containing lumped elements. In the design of 2-D passive n-ports it will be however of great interest whether this mentioned feature can be used as a basis for ageneral synthesis procedure.In this paper it is shown that this is the case. The method presented for the synthesis of 2-D multiports is based mainly on a paraunitary bordering of the given scattering matrix of the desired network in order to obtain the scattering matrix of alossless 2-D multiport, which can be realized by using known procedures. The socalled spectral factorization of a two-variable para-Hermitian polynomial matrix which is nonnegative definite forp =j w plays a crucial role in the design approach presented. No restrictions are made concerning the coefficients of the given rational scattering matrix; they may be either real or complex, so as to include even complex networks which are of special interest for multidimensional systems.     

Transfer Function Approximations for a New Class of Bandpass Distributed Network Structures

Characteristic functions for a new class of prototype bandpass transmission-line structures have been derived for both the maximally flat and equiripple or Chebyshev characteristics. The class of bandpass distributed structures considered in this paper consists of commensurate transmission lines with constraints in the form of a shunt open-circuited stub and/or a series short-circuited stub. The gain-bandwidth restrictions imposed by the reactance constraints have been derived and some explicit results are presented for the synthesis of this class of bandpass transmission-line networks. Results presented in this paper are directly applicable to the design of broad-band microwave passive and active networks. In particular, the results are applied to the design of broad-band matching networks for octave-band GaAs FET amplifiers.     

Randomized 3-<Emphasis Type="BoldItalic">D</Emphasis> Routing in Fully- and Partially-Covered Sensor Networks

In recent years, sensor network technology has been proposed to improve the detection level of natural disasters (e.g. volcanoes, tornadoes, tsunamis). However, this technology has several design issues that need to be improved. We, therefore in this paper, focus on two main design issues: coverage and routing. For coverage issue, we introduce a new approach for obtaining a fully covered network in 3-D\boldsymbol{3}\textbf{-}{\boldsymbol D} environment such that every single point in a region is fully covered by at least one sensor node. This approach is referred to as the Chipset Coverage Model and Algorithm. This would be accomplished by using a small number of sensor nodes in order to save up some energy. Based on our coverage approach, we address the routing issue by proposing a new position-based routing protocol referred to as the 3-D\boldsymbol{3}\textbf{-}{\boldsymbol D} Randomized Sensing Spheres routing protocol (3-D\boldsymbol{3}\textbf{-}{\boldsymbol D} RSS\boldsymbol{RSS}). We show that the 3-D\boldsymbol{3}\textbf{-}{\boldsymbol D} RSS\boldsymbol{RSS} protocol guarantees packet delivery. Moreover, from our simulation, we demonstrate that the 3-D\boldsymbol{3}\textbf{-}{\boldsymbol D} RSS\boldsymbol{RSS} has a behaviour close to the behaviour of an existing 3-D\boldsymbol{3\textbf{-}D} progress-based protocol in terms of hop dilation and routing delay, where the delay is defined as Quality of Service (QoS) metric. Furthermore, we demonstrate that the 3-D\boldsymbol{3}\textbf{-}{\boldsymbol D} RSS\boldsymbol{RSS} protocol outperforms the existing progress-based protocol in terms of Euclidean and power dilations. Thus, the new protocol reduces the energy consumption of the nodes and, therefore, prolongs the lifetime of the sensing nodes. For partially covered networks, we propose a dynamic position-based routing protocol referred to as the 3-D\boldsymbol{3}\textbf{-}{\boldsymbol D} Randomized Sensing Spheres version 1 routing protocol (3-D\boldsymbol{3}\textbf{-}{\boldsymbol D} RSSv1\boldsymbol{RSSv1}). This protocol increases the chances of delivering packets by moving linearly towards the destinations. We demonstrate that the 3-D\boldsymbol{3}\textbf{-}{\boldsymbol D} RSSv1\boldsymbol{RSSv1} has a remarkable delivery rate compared to an existing progress-based routing protocol.     

Modelling of 2-D Real Rational Reactance Functions. A Parameter-Based Approach

Lossless (reactive) one-ports are of great importance in the field of linear network theory. This statement also applies for the two-dimensional (2-D) case, where the design of corresponding impedance or admittance functions is a much more challenging task. In this paper a model for 2-D real rational reactance functions is introduced which is a rational function in p₁ and p₂ where the coefficients are functions of parameters. The following features make it best suited for the computer based design of lossless one-ports, namely no dependencies between the real valued parameters, coverage of the whole class of 2-D real rational reactance functions, and the coefficients are polynomials in the parameters. The synthesis of 2-D lossless networks and skew symmetric matrices form the basis of our considerations.     

A new formula and an algorithm for reliability analysis of networks

In 1978, Satyanarayana and Prabhakar (SP) proposed a new topological formula for the source-to-terminal (ST) reliability of complex networks. The formula generates only non-cancelling terms of the reliability expression which correspond one-to-one with the p-acyclic subgraphs of the given network. Based on the concept of neutral sequences in acyclic graphs, a powerful SP algorithm was presented for generating all p-acyclic subgraphs and computing the ST reliability of the network. Combining an inclusion-exclusion algorithm with a sum of disjoint products algorithm, we introduce a new topological formula which includes the SP formulas as a special case. A new efficient algorithm which has all features of the SP algorithm is proposed. In general, the reliability expressions obtained by this algorithm are more compact than the ones obtained by the SP algorithm.     

Common-cause failure analysis of a k-out-of-n:G system with repairable units

A newly developed generalized expression for the mean time to failure of a k-out-of-n: G system composed of repairable units and subject to common-cause failures is presented. Also, reported are some special case system reliability and variance of time to failure formulas.     

General Synthesis of Quarter-Wave Impedance Transformers

This paper presents the general synthesis of a radio frequency impedance transformer of n quarter-wave steps, given an "insertion loss function" of permissible form. This procedure parallels that of Darlington for lumped constant filters by providing the connection between Collin's canonical form for the insertion loss function and Richards' demonstration that a reactance function may always be realized as a cascade of equal length impedance transformers terminated in either a short or open circuit. In particular, it is shown that insertion loss functions of the form selected by Collin are always realizable with positive characteristic impedances, and that the synthesis procedure, for maximally flat and Tchebycheff performance, involves the solution, at most, of quadratic equations. In addition, this procedure permits the proof of Collin's conjecture that, for his insertion loss function, the resulting reflection coefficients are symmetrical. Finally, closed expressions are given for the coefficients of the input impedance of a given n section transformer in terms of the n characteristic impedances and vice versa.     

A Formal Analysis of Fault Diagnosis with <Emphasis Type="Italic">D</Emphasis>-matrices

As new approaches and algorithms are developed for system diagnosis, it is important to reflect on existing approaches to determine their strengths and weaknesses. Of concern is identifying potential reasons for false pulls during maintenance. Within the aerospace community, one approach to system diagnosis—based on the D-matrix derived from test dependency modeling—is used widely, yet little has been done to perform any theoretical assessment of the merits of the approach. Past assessments have been limited, largely, to empirical analysis and case studies. In this paper, we provide a theoretical assessment of the representation power of the D-matrix and suggest algorithms and model types for which the D-matrix is appropriate. We also prove a surprising result relative to the difficulty of generating optimal diagnostic strategies from D-matrices. Finally, we relate the processing of the D-matrix with several diagnostic approaches and suggest how to extend the power of the D-matrix to take advantage of the power of those approaches.     

Burstiness and resource management in ATM networks

Networks based upon the asynchronous transfer mode (ATM) provide for high flexibility to cope with a wide range of applications, some of them producing highly sporadic traffic. Therefore, the problem of burstiness has become in the last few years a key issue for such networks. A basic question is how to dimension network buffers in the presence of bursty traffic? In this paper we investigate the concept of burstiness and its impact on resource management. In burstiness characterization encountered in the literature, special attention has been given to the squared coefficient of variation of inter-arrival time Cv² in a cell arrival process. In order to observe the impact of bursty traffic on a queue, we develop in the present paper a ‘bursty’ traffic model, namely the two-stage hyper-Bernoulli cell arrival process, HBP₂, for short. We numerically solve the HBP₂/D/1/K queue. We especially derive the rejection probability P_loss. Numerical results are then thoroughly studied and we discuss the relevance for burstiness characterization of Cv² and peak to mean rate ratio B. We draw attention to the concept of local overload, i.e. when the arrival rate is greater than the server rate. This seems to be the most relevant phenomenon in the impact of a bursty traffic on a queue. These results are finally applied to the problem of resource management in ATM networks.     

Synthèse de filtres numériques simulant Des filtres a inductances et capacités

Recursive digital filters structures much less sensitive than ordinary cascade or parallel structures are obtained when imitating analogue non dissipative filters. General principles for the transposition of (L, C) ladders filters are established and the synthesis of the socalled Fettweis wave filtersis described. Numerical results for a lowpass Cauer filter and final conclusions are also given.     

Repairable consecutive-2-out-of-n:F system

In this paper, a linear consecutive-2-out-of-n:F repairable system is studied. Assume that the working time and the repair time of each component are both exponentially distributed, and each component after repair is as good as new. By using the definition of generalized transition probability, we derive the state transition probability of the system. When n is given, we obtain the exact formulas of the system reliability (or its Laplace transform) and the system mean time to first failure.     

Computer Optimization of a Stabilizing Network for a Tunnel-Diode Amplifier

Computer-aided direct search is a useful and flexible method of optimizing noncommensurate networks or networks for which exact synthesis theories culminating in some particular response are not available. It can accommodate network parameter constraints and unconventional performance specifications and is not accompanied by problems of component realizability. A simple form of direct search is applied in this paper to the design of a microwave network whose performance is optimized within certain specifications. The network is a stabilizing and biasing arrangement for a tunnel-diode amplifier operating in a reduced height S-band rectangular waveguide, and takes the form of a coaxial-line band-stop filter. Parameter constraints are inherent to the problem so they are taken into account. The requirements of stability and low noise broadband amplification in conjunction with the external circuitry impose nonsymmetrical response restrictions on the input resistance and reactance of the network. At the same time it is required to minimize the square of the input reactance at selected frequencies. No available exact synthesis of band-stop filters can solve this problem as presented here.     

Mean time to failure formulas for standard reliability networks with erlangian distributed component failure times

This paper presents newly developed mean time to failure formulas for reliability networks such as series, parallel, k-out-of-n, series-parallel, parallel-series and a bridge with special case Erlangian distributed component failure times.     

A modified offered load approximation for nonstationary circuit switched networks

In this paper, we develop approximation methods to analyze blocking in circuit switched networks with nonstationary call arrival traffic. We formulate generalizations of the pointwise stationary and modified offered load approximations used for the nonstationary Erlang loss model or M(t)/M/c/c queue. These approximations reduce the analysis of nonstationary circuit switched networks to solving a small set of simple differential equations and using the methods for computing the steady state distributions for the stationary versions of such loss networks. We also discuss how the use of time varying arrival rates literally adds a new dimension to the class of telecommunication networks we can model. For example, we can model the behavior of alternate routing due to link‐failure, which is a feature that the classical stationary version of the model cannot capture. Our nonstationary model can also describe aspects of the dynamic calling traffic behavior arising in cellular mobile traffic. For the special case of a two‐link, three node network, we present numerical results to compare the various approximation methods to calculations of the exact blocking probabilities. We also adapt these calculations to approximate the behavior of rerouting calling traffic due to link‐failure. The results are achieved by formulating some new recursions for evaluating the steady state blocking probabilities of such networks. We also generalize these techniques to develop analogous formulas for a linear N‐node circuit switched network. This revised version was published online in June 2006 with corrections to the Cover Date.     

低压电缆在谐波环境下的阻抗特性研究

电缆广泛用于低压配电网中,研究低压配电系统中电力电缆的谐波特性十分重要。基于电路理论对电缆在谐波环境下的电阻和电抗计算方法进行分析,提出了在谐波频率下求解电缆全矩阵阻抗的实验测算方法,并探究不同参数对电缆电阻和电抗的影响。对电缆谐波阻抗进行实验测算并与公式计算结果进行对比,结果表明:电缆电阻会随谐波次数的增加而增大,而电缆电感则随谐波次数的增加而减小,电缆谐波阻抗近似计算公式对于单芯电缆和多芯电缆分别具有不同的准确精度,论文研究成果对电缆特性研究具有指导意义。