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  • 1
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    Springer
    Computing 24 (1980), S. 341-347 
    ISSN: 1436-5057
    Keywords: Numerical analysis ; Volterra integral equations of the second kind ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Ziel dieser Arbeit ist es, die Stabilitätseigenschaften einer Klasse Volterrascher Integralgleichungen zweiter Art zu untersuchen. Unsere Behandlung ist der üblichen Stabilitätsanalyse ähnlich, in der die Kernfunktionen zu einer im voraus beschränkten Klasse von Testfunktionen gehören. Wir haben die Klasse der “endlich zerlegbaren” Kerne betrachtet. Stabilitätsbedingungen werden abgeleitet und verglichen mit den Bedingungen für die einfache Testgleichung. Es zeigt sich, daß die neuen Kriteria einschränkender sind als die konventionellen Bedingungen. Der praktische Wert wird getestet durch numerische Experimente mit der Trapezregel.
    Notes: Abstract The purpose of this paper is to analyse the stability properties of a class of multistep methods for second kind Volterra integral equations. Our approach follows the usual analysis in which the kernel function is a priori restricted to a special class of test functions. We consider the class of finitely decomposable kernels. Stability conditions will be derived and compared with those obtained with the simple test equation. It turns out that the new criteria are more severe than the conventional conditions. The practical value is tested by numerical experiments with the trapezoidal rule.
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  • 2
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    Computing 51 (1993), S. 271-292 
    ISSN: 1436-5057
    Keywords: 65N15 ; 65N99 ; 35A40 ; Box method ; boundary value problem ; finite volume method ; variational formulation ; stability ; error bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Box-Methoden (Finite-Volumen-Methoden) sind verbreitete Verfahren zur Lösung physikalischer Erhaltungsgleichungen, insbesondere in der Strömungsmechanik. In dieser Arbeit werden zwei Methoden für elliptische Differentialgleichungen untersucht, die Diagonal-Boxen und die Schwerpunkt-Boxen. Da die Box-Methoden im Sinne von Petrov-Galerkin-Verfahren interpretiert werden können, erhält man vergleichbar zur Finiten-Element-Methode eine variationsrechnerische Stabilitäts- und Fehleranalyse. Damit werdenO(h)- undO(h 2)-Fehlerabschätzungen hergeleitet. Lokale Eigenwertprobleme führen zu Stabilitätsaussagen. Allerdings ergibt sich eine Abhängigkeit von der Anzahl und Art gestörter Vierecke. Insbesondere die Diagonal-Boxen sind anfällig für lokale Störungen.
    Notes: Abstract Box schemes (finite volume methods) are widely used in fluiddynamics, especially for the solution of conservation laws. In this paper two box-schemes for elliptic equations are analysed with respect to quadrilateral meshes. Using a variational formulation, we gain stability theorems for two different box methods, namely the so-called diagonal boxes and the centre boxes. The analysis is based on an elementwise eigenvalue problem. Stability can only be guaranteed under additional assumptions on the geometry of the quadrilaterals. For the diagonal boxes unsuitable elements can lead to global instabilities. The centre boxes are more robust and differ not so much from the finite element approach. In the stable case, convergence results up to second order are proved with well-known techniques.
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  • 3
    ISSN: 1436-5057
    Keywords: 65 L 05 ; Rosenbrock-type methods ; quasilinear-implicit differential equations ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Bei der Lösung quasilinear-impliziter ODEs mittels Rosenbrock-Typ-Methoden können trotz guter Stabilitätseigenschaften (A- bzw. L-Stabilität) des Grundverfahrens Stabilitätsprobleme auftreten. Diese Schwierigkeiten sind auf Ungenauigkeiten bei der Berechnung künstlich eingeführter Komponenten (Überführung in DAEs) zurückzuführen. Die Arbeit untersucht die Ursachen für diese Effekte und zeigt Möglichkeiten, diese zu überwinden.
    Notes: Abstract The solution of quasilinear-implicit ODEs using Rosenbrock type methods may suffer from stability problems despite stability properties such as A-stability or L-stability, respectively. These problems are caused by inexact computation of artificial introduced components (transformation to DAE system). The paper investigates the source of the numerical difficulties and shows modifications to overcome them.
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  • 4
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    Mathematical programming 47 (1990), S. 117-141 
    ISSN: 1436-4646
    Keywords: Bifurcation ; singularity ; parametric programming ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The structure of solutions to the nonlinear parametric programming problem with a one dimensional parameter is analyzed in terms of the bifurcation behavior of the curves of critical points and the persistence of minima along these curves. Changes in the structure of the solution occur at singularities of a nonlinear system of equations motivated by the Fritz John first-order necessary conditions. It has been shown that these singularities may be completely partitioned into seven distinct classes based upon the violation of one or more of the following: a complementarity condition, a constraint qualification, and the nonsingularity of the Hessian of the Lagrangian on a tangent space. To apply classical bifurcation techniques to these singularities, a further subdivision of each case is necessary. The structure of curves of critical points near singularities of lowest (zero) codimension within each case is analyzed, as well as the persistence of minima along curves emanating from these singularities. Bifurcation behavior is also investigated or discussed for many of the subcases giving rise to a codimension one singularity.
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  • 5
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    Mathematical programming 54 (1992), S. 57-67 
    ISSN: 1436-4646
    Keywords: Matchings ; stability ; extreme points ; polytope
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this paper is to extend a modified version of a recent result of Vande Vate (1989) which characterizes stable matchings as the extreme points of a certain polytope. Our proofs are simpler and more transparent than those of Vande Vate.
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  • 6
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    Mathematical programming 61 (1993), S. 197-214 
    ISSN: 1436-4646
    Keywords: Epi-convergence ; epi-distance ; stability ; convex optimization ; approximate solutions ; subgradients ; level sets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We prove that theε-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that theε-subgradient mapping is Lipschitz continuous.
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  • 7
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    Computing 44 (1990), S. 187-196 
    ISSN: 1436-5057
    Keywords: 65M10 ; Spectral method ; stability ; stability threshold
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Zur numerischen Lösung einer nichtlinearen Differentialgleichung dritter Ordnung, herrührend aus einem Strömungsproblem bei Gasteilchen, wird ein zeitdiskreter Pseudo-spektral-Algorithmus vorgeschlagen. Stabilität und Konvergenz des neuen Differenzenverfahrens werden analysiert. Numerische Vergleiche mit bestehenden Differenzenschemata sprechen klar zugunsten des neuen Verfahrens.
    Notes: Abstract A time-discrete pseudospectral algorithm is suggested for the numerical solution of a nonlinear third order equation arising in fluidization. The nonlinear stability and convergence of the new scheme are analyzed. Numerical comparisons with available finite-difference methods are also reported which clearly indicate the superiority of the new scheme.
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  • 8
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    Queueing systems 12 (1992), S. 369-389 
    ISSN: 1572-9443
    Keywords: Perturbation analysis ; stability ; stochastic difference equations ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We investigate the stability of waiting-time derivatives when inputs to a queueing system-service times and interarrival times-depend on a parameter. We give conditions under which the sequence of waiting-time derivatives admits a stationary distribution, and under which the derivatives converge to the stationary regime from all initial conditions. Further hypotheses ensure that the expectation of a stationary waiting-time derivative is, in fact, the derivative of the expected stationary waiting time. This validates the use of simulation-based infinitesimal perturbation analysis estimates with a variety of queueing processes. We examine waiting-time sequences satisfying recursive equations. Our basic assumption is that the input and its derivatives are stationary and ergodic. Under monotonicity conditions, the method of Loynes establishes the convergence of the derivatives. Even without such conditions, the derivatives obey a linear difference equation with random coefficients, and we exploit this fact to find stability conditions.
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  • 9
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    Queueing systems 13 (1993), S. 87-110 
    ISSN: 1572-9443
    Keywords: Manufacturing systems ; semiconductor manufacturing ; thin film lines ; re-entrant lines ; scheduling policies ; queueing networks ; buffer priority policies ; due date policies ; stability ; stochastic control ; mean delay ; variance of delay ; machine failures ; set-up times
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Traditionally, manufacturing systems have mainly been treated as either job shops or flow shops. In job shops, parts may arrive with random routes, with each route having a low volume. In flow shops, the routes are fixed and acyclic, as in assembly lines. With the advent of semiconductor manufacturing plants, and more recently, thin film lines, this dichotomy needs to be expanded to consider another class of systems, which we call “re-entrant lines”. The distinguishing feature of these manufacturing systems is that parts visit some machines more than once at different stages of processing. Scheduling problems arise because several parts at different stages of processing may be in contention with each other for service at the same machine. There may be uncertainties in the form of random service or set-up times, as well as random machine failures and repairs. The goal of scheduling is to improve performance measures such as mean sojourn time in the system, which is also known as the mean “cycle-time”, or the variance of the cycle-time. In this paper we provide a tutorial account of some recent results in this field. We describe several scheduling policies of interest, and provide some results concerning their stability and performance. Several open problems are suggested.
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  • 10
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    Queueing systems 15 (1994), S. 279-288 
    ISSN: 1572-9443
    Keywords: Sample-path ; point processes ; workload ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper, by exploiting recent results on the pathwise behavior of the workload process in single server, work conserving queues of theG/G/1/∞ type, we show that the workload of multiserver, work conserving queues ofG/G/m/∞ (m〈∞) (andG/G/∞) queues satisfies an o(t) growth condition, provided that the time average of the work brought into the system is less thanm form 〈 ∞ (and finite form=∞).
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  • 11
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    Queueing systems 21 (1995), S. 67-95 
    ISSN: 1572-9443
    Keywords: Polling systems ; stability ; stationary regime
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A stationary regime for polling systems with general ergodic (G/G) arrival processes at each station is constructed. Mutual independence of the arrival processes is not required. It is shown that the stationary workload so constructed is minimal in the stochastic ordering sense. In the model considered the server switches from station to station in a Markovian fashion, and a specific service policy is applied to each queue. Our hypotheses cover the purely gated, thea-limited, the binomial-gated and other policies. As a by-product we obtain sufficient conditions for the stationary regime of aG/G/1/∞ queue with multiple server vacations (see Doshi [11]) to be ergodic.
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  • 12
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    Queueing systems 22 (1996), S. 47-63 
    ISSN: 1572-9443
    Keywords: Sample-path analysis ; stability ; rate stability ; ω-rate stability ; input-output process ; queueing ; infinite-server queues
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract An input-output processZ = {Z(t), t ⩾ 0} is said to beω-rate stable ifZ(t) = o(ω(t)) for some non-negative functionω(t). We prove that the processZ is ω-rate stable under weak conditions that include the assumption that input satisfies a linear burstiness condition and Z is asymptotically average stable. In many cases of interest, the conditions forω-rate-stability can be verified from input data. For example, using input information, we establishω-rate stability of the workload for multiserver queues, an ATM multiplexer, andω-rate stability of queue-length processes for infinite server queues.
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  • 13
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    Queueing systems 22 (1996), S. 345-366 
    ISSN: 1572-9443
    Keywords: State-dependent service and interarrival times ; Lindley equation ; recursive stochastic equations ; stability ; normal approximations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider a modification of the standardG/G/1 queueing system with infinite waiting space and the first-in-first-out discipline in which the service times and interarrival times depend linearly and randomly on the waiting times. In this model the waiting times satisfy a modified version of the classical Lindley recursion. When the waiting-time distributions converge to a proper limit, Whitt [10] proposed a normal approximation for this steady-state limit. In this paper we prove a limit theorem for the steady-state limit of the system. Thus, our result provides a solid foundation for Whitt's normal approximation of the steady-state distribution of the system.
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  • 14
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    Queueing systems 29 (1998), S. 55-73 
    ISSN: 1572-9443
    Keywords: multi‐server queue ; customer class ; state‐dependent routing ; stability ; Markov chain ; fluid limit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider a multi‐station queue with a multi‐class input process when any station is available for the service of only some (not all) customer classes. Upon arrival, any customer may choose one of its accessible stations according to some state‐dependent policy. We obtain simple stability criteria for this model in two particular cases when service rates are either station‐ or class‐independent. Then, we study a two‐station queue under general assumptions on service rates. Our proofs are based on the fluid approximation approach.
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  • 15
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    Queueing systems 32 (1999), S. 131-168 
    ISSN: 1572-9443
    Keywords: stability ; positive recurrence ; fluid limit ; polling system ; exhaustive service policy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We introduce a generalized criterion for the stability of Markovian queueing systems in terms of stochastic fluid limits. We consider an example in which this criterion may be applied: a polling system with two stations and two heterogeneous servers.
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  • 16
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    Queueing systems 16 (1994), S. 115-137 
    ISSN: 1572-9443
    Keywords: Polling systems ; stability ; stochastic continuity ; general arrival process ; functional limit theorems.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The stability of a polling system with exhaustive service and a finite number of users, each with infinite buffers is considered. The arrival process is more general than a Poisson process and the system is not slotted. Stochastic continuity of the stationary distributions, rates of convergence and functional limit theorems for the queue length and waiting time processes have also been proved. The results extend to the gated service discipline.
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  • 17
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    Queueing systems 14 (1993), S. 159-175 
    ISSN: 1572-9443
    Keywords: Queueing networks ; nonproduct form networks ; stability ; stochastic continuity ; functional limit theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A finite number of nodes, each with a single server and infinite buffers, is considered in discrete time. The service may be FIFO and the service times are constant. The external arrivals and the routing decision variables form a general stationary sequence. Stability of the system is proved under these assumptions. Extension to multiple servers at a node and general stationary distributions holds. If the external input is i.i.d. and the routing is Markovian then stochastic ordering, continuity of stationary distributions, rates of convergence, a functional CLT and a functional LIL and various other limit theorems for the queue length process are also proved. Generalizations to multiple servers at nodes, customers with priority, multiple customer classes, general service length and Markov modulated external arrival cases are discussed.
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  • 18
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    Queueing systems 15 (1994), S. 211-238 
    ISSN: 1572-9443
    Keywords: polling system ; stability ; Markov chain ; stochastic monotonicity ; heavy traffic ; nonpreemptive local priority
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper deals with the stability of periodic polling models with a mixture of service policies. Customers arrive according to independent Poisson processes. The service times and the switchover times are independent with general distributions. The necessary and sufficient condition for the stability of such polling systems is established. The proof is based on the stochastic monotonicity of the state process at the polling instants. The stability of only a subset of the queues is also analyzed and, in case of heavy traffic, the order of explosion of the queues is given. The results are valid for a model with set-up times, and also when there is a local priority rule at the queues.
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  • 19
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    Queueing systems 17 (1994), S. 317-345 
    ISSN: 1572-9443
    Keywords: Single-server queue ; spatially distributed arrival points ; travelling server ; Brownian motion ; embedded Markov chain ; stability ; Tweedie's lemma ; regenerative processes ; stochastic decomposition ; equilibrium equations ; mean queue length
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server's movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The service times are independent, but arbitrarily distributed. The model generalizes the continuous cyclic polling system (the diffusion coefficient of the Brownian motion is zero in this case) and can be interpreted as a continuous version of a Markov polling system. Using Tweedie's lemma for positive recurrence of Markov chains with general state space, we show that the system is stable if and only if the traffic intensity is less than one. Moreover, we derive a stochastic decomposition result which leads to equilibrium equations for the stationary configuration of customers on the circle. Steady-state performance characteristics are determined, in particular the expected number of customers in the system as seen by a travelling server and at an arbitrary point in time.
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  • 20
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    Queueing systems 27 (1997), S. 205-226 
    ISSN: 1572-9443
    Keywords: multiclass queueing networks ; ergodicity ; stability ; performance analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We develop the use of piecewise linear test functions for the analysis of stability of multiclass queueing networks and their associated fluid limit models. It is found that if an associated LP admits a positive solution, then a Lyapunov function exists. This implies that the fluid limit model is stable and hence that the network model is positive Harris recurrent with a finite polynomial moment. Also, it is found that if a particular LP admits a solution, then the network model is transient.
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  • 21
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    Queueing systems 28 (1998), S. 33-54 
    ISSN: 1572-9443
    Keywords: queueing networks ; throughput ; closed networks ; efficiency ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A closed network is said to be “guaranteed efficient” if the throughput converges under all non-idling policies to the capacity of the bottlenecks in the network, as the number of trapped customers increases to infinity. We obtain a necessary condition for guaranteed efficiency of closed re-entrant lines. For balanced two-station systems, this necessary condition is almost sufficient, differing from it only by the strictness of an inequality. This near characterization is obtained by studying a special type of virtual station called “alternating visit virtual station”. These special virtual stations allow us to relate the necessary condition to certain indices arising in heavy traffic studies using a Brownian network approximation, as well as to certain policies proposed as being extremal with respect to the asymptotic loss in the throughput. Using the near characterization of guaranteed efficiency we also answer the often pondered question of whether an open network or its closed counterpart has greater throughput - the answer is that neither can assure a greater guaranteed throughput.
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  • 22
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    Queueing systems 11 (1992), S. 7-33 
    ISSN: 1572-9443
    Keywords: Token passing rings ; stability ; substability ; ergodicity ; Markov chains ; Loynes' scheme ; stochastically dominant ; Little's formula ; regenerative processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A sufficient stability condition for the standard token passing ring has been “known” since the seminal paper by Kuehn in 1979. However, this condition was derived without formal proof, and the proof seems to be of considerable interest to the research community. In fact, Watson observed that in the performance evaluation of token passing rings, “it is convenient to derive stability conditions ... (without proof)”. Our intention is to fill this gap, and to provide a formal proof of thesufficient and necessary stability condition for the token passing ring. In this paper, we present the case when the arrival process to each queue is Poisson but service times and switchover times are generally distributed. We consider in depth a gatedl-limited (l≤ ∞) service discipline for each station. We also indicate that the basic steps of our technique can be used to study the stability of some other multiqueue systems.
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  • 23
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    Queueing systems 33 (1999), S. 293-325 
    ISSN: 1572-9443
    Keywords: stability ; fluid models ; multiclass queueing networks ; piecewise linear Lyapunov functions ; linear Lyapunov functions ; monotone global stability ; static buffer priority disciplines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper studies the stability of a three‐station fluid network. We show that, unlike the two‐station networks in Dai and Vande Vate [18], the global stability region of our three‐station network is not the intersection of its stability regions under static buffer priority disciplines. Thus, the “worst” or extremal disciplines are not static buffer priority disciplines. We also prove that the global stability region of our three‐station network is not monotone in the service times and so, we may move a service time vector out of the global stability region by reducing the service time for a class. We introduce the monotone global stability region and show that a linear program (LP) related to a piecewise linear Lyapunov function characterizes this largest monotone subset of the global stability region for our three‐station network. We also show that the LP proposed by Bertsimas et al. [1] does not characterize either the global stability region or even the monotone global stability region of our three‐station network. Further, we demonstrate that the LP related to the linear Lyapunov function proposed by Chen and Zhang [11] does not characterize the stability region of our three‐station network under a static buffer priority discipline.
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  • 24
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    Queueing systems 29 (1998), S. 129-159 
    ISSN: 1572-9443
    Keywords: rate-based feedback control ; ATM networks ; stability ; optimal algorithms
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    Topics: Computer Science
    Notes: Abstract Motivated by ABR class of service in ATM networks, we study a continuous time queueing system with a feedback control of the arrival rate of some of the sources. The feedback about the queue length or the total workload is provided at regular intervals (variations on it, especially the traffic management specification TM 4.0, are also considered). The propagation delays can be nonnegligible. For a general class of feedback algorithms, we obtain the stability of the system in the presence of one or more bottleneck nodes in the virtual circuit. Our system is general enough that it can be useful to study feedback control in other network protocols. We also obtain rates of convergence to the stationary distributions and finiteness of moments. For the single botterneck case, we provide algorithms to compute the stationary distributions and the moments of the sojourn times in different sets of states. We also show analytically (by showing continuity of stationary distributions and moments) that for small propagation delays, we can provide feedback algorithms which have higher mean throughput, lower probability of overflow and lower delay jitter than any open loop policy. Finally these results are supplemented by some computational results.
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  • 25
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    Queueing systems 31 (1999), S. 171-206 
    ISSN: 1572-9443
    Keywords: scheduling ; open multiclass queueing networks ; discrete-review policies ; fluid models ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper describes a family of discrete-review policies for scheduling open multiclass queueing networks. Each of the policies in the family is derived from what we call a dynamic reward function: such a function associates with each queue length vector q and each job class k a positive value r k (q), which is treated as a reward rate for time devoted to processing class k jobs. Assuming that each station has a traffic intensity parameter less than one, all policies in the family considered are shown to be stable. In such a policy, system status is reviewed at discrete points in time, and at each such point the controller formulates a processing plan for the next review period, based on the queue length vector observed. Stability is proved by combining elementary large deviations theory with an analysis of an associated fluid control problem. These results are extended to systems with class dependent setup times as well as systems with alternate routing and admission control capabilities.
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  • 26
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    Queueing systems 6 (1990), S. 335-351 
    ISSN: 1572-9443
    Keywords: State-dependent service and interarrival times ; Lindley equation ; recursive stochastic equations ; stability ; stochastic comparisons ; normal approximations ; scheduling arrivals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider a modification of the standardG/G/1 queue with unlimited waiting space and the first-in first-out discipline in which the service times and interarrival times depend linearly and randomly on the waiting times. In this model the waiting times satisfy a modified version of the classical Lindley recursion. We determine when the waiting-time distributions converge to a proper limit and we develop approximations for this steady-state limit, primarily by applying previous results of Vervaat [21] and Brandt [4] for the unrestricted recursionY n+1=C n Y n +X n . Particularly appealing for applications is a normal approximation for the stationary waiting time distribution in the case when the queue only rarely becomes empty. We also consider the problem of scheduling successive interarrival times at arrival epochs, with the objective of achieving nearly maximal throughput with nearly bounded waiting times, while making the interarrival time sequence relatively smooth. We identify policies depending linearly and deterministically upon the work in the system which meet these objectives reasonably well; with these policies the waiting times are approximately contained in a specified interval a specified fraction of time.
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  • 27
    ISSN: 1572-9443
    Keywords: dam ; storage process ; saturation rule ; intermittent production ; state dependent rates ; state dependent jumps ; stability ; positive Harris recurrence
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    Notes: Abstract We consider a dam process with a general (state dependent) release rule and a pure jump input process, where the jump sizes are state dependent. We give sufficient conditions under which the process has a stationary version in the case where the jump times and sizes are governed by a marked point process which is point (Palm) stationary and ergodic. We give special attention to the Markov and Markov regenerative cases for which the main stability condition is weakened. We then study an intermittent production process with state dependent rates. We provide sufficient conditions for stability for this process and show that if these conditions are satisfied, then an interesting new relationship exists between the stationary distribution of this process and a dam process of the type we explore here.
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    Queueing systems 26 (1997), S. 343-363 
    ISSN: 1572-9443
    Keywords: retrial queues ; stability ; ergodicity ; renovation
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    Topics: Computer Science
    Notes: Abstract We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ 〉 λ is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers.
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    Queueing systems 32 (1999), S. 99-130 
    ISSN: 1572-9443
    Keywords: neural network ; inhibition ; stability ; Markov process ; fluid limit ; Harris-recurrence ; transience
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    Topics: Computer Science
    Notes: Abstract The subject of the paper is the stability analysis of some neural networks consisting of a finite number of interacting neurons. Following the approach of Dai [5] we use the fluid limit model of the network to derive a sufficient condition for positive Harris-recurrence of the associated Markov process. This improves the main result in Karpelevich et al. [11] and, at the same time, sheds some new light on it. We further derive two different conditions that are sufficient for transience of the state process and illustrate our results by classifying some examples according to positive recurrence or transience.
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    Queueing systems 32 (1999), S. 195-231 
    ISSN: 1572-9443
    Keywords: window flow control ; TCP ; stability ; multiclass networks ; stationary ergodic point processes ; (max,+)-linear system
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    Notes: Abstract We focus on window flow control as used in packet-switched communication networks. The approach consists in studying the stability of a system where each node on the path followed by the packets of the controlled connection is modeled by a FIFO (First-In-First-Out) queue of infinite capacity which receives in addition some cross traffic represented by an exogenous flow. Under general stochastic assumptions, namely for stationary and ergodic input processes, we show the existence of a maximum throughput allowed by the flow control. Then we establish bounds on the value of this maximum throughput. These bounds, which do not coincide in general, are reached by time-space scalings of the exogenous flows. Therefore, the performance of the window flow control depends not only on the traffic intensity of the cross flows, but also on fine statistical characteristics such as the burstiness of these flows. These results are illustrated by several examples, including the case of a nonmonotone, nonconvex and fractal stability region.
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    Computing 57 (1996), S. 281-299 
    ISSN: 1436-5057
    Keywords: 65N15 ; 65N99 ; 35A40 ; Finite volume method ; box scheme ; stability ; error estimates
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine Box-Methode mit quadratischen Ansatzfunktionen zur Diskretisierung elliptischer Randwertaufgaben vorgestellt. Die entstehende Diskretisierungsmatrix ist nichsymmetrisch. Die Stabilitätsanalyse basiert auf einer elementweisen Abschätzung des Skalarproduktes 〈A h u h ,u h 〉. Hinreichende Bedingungen an die Geometrie der Dreiecke der Triangulierung führen zur diskreten Elliptizität. Unter diesen Voraussetzungen wird eineO(h 2)-Fehlerabschätzung bewiesen.
    Notes: Abstract The paper presents a box scheme with quadratic basis functions for the discretisation of elliptic boundary value problems. The resulting discretisation matrix is non-symmetrical (and also not an M-matrix). The stability analysis is based on an elementwise estimation of the scalar product 〈A h u h ,u h 〉. Sufficient conditions placed on the triangles of the triangulation lead to discrete ellipticity. Proof of anO(h 2) error estimate is given for these conditions.
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    Computing 31 (1983), S. 261-267 
    ISSN: 1436-5057
    Keywords: 65M10 ; Dispersive equation ; finite difference ; stability
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Dieser Artikel beinhaltet eine Zusammenstellung von Differenzenverfahren für die Dispersionsgleichungu 1=au xxx. Es werden Kriterien zur Herleitung von Stabilitätsbedingungen für Differenzenverfahren angegeben und auf die angegebenen Differenzenverfahren angewendet.
    Notes: Abstract In this paper a table of difference schemes for the dispersive equationu i=au xxx is presented. A collection of criterions for deriving stability conditions of difference schemes is given and applied to these difference schemes.
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    Computing 32 (1984), S. 229-237 
    ISSN: 1436-5057
    Keywords: 65L05 ; 65L07 ; Stiff system ; Rosenbroek method ; stability
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird die Stabilität des Kaps-Rentrop-Verfahrens in die Anwesenheit nichtlinearer Steifheit (Stiffness) analysiert. Dazu werden mittels eines einfachen Modells zwei Größen introduziert. Die Werte dieser Größen reflektieren gewissermaßen das Verhalten eines Kaps-Rentrop-Verfahrens in die Anwesenheit einer bestimmten Kopplung zwischen die beiden Komponenten in das steife System gewöhnlicher Differentialgleichungen. Einige numerische Beispiele veranschaulichen die Analyse.
    Notes: Abstract In this paper we give an analysis of the effect of stiff nonlinearities on the behavior of a Kaps-Rentrop method. To that end we introduce two quantities related to a simple model. The values of these quantities determine to some extent the behavior of a Kaps-Rentrop method in case of a strong coupling between the smooth component and the transient one. Numerical examples illustrate the theoretical results.
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    Journal of intelligent and robotic systems 3 (1990), S. 259-289 
    ISSN: 1573-0409
    Keywords: Nonlinear decoupling ; feedback linearization ; functional analysis ; elastic robots ; robustness ; stability ; pole assignment ; nonlinear systems ; robot control
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A robustness analysis and synthesis for incomplete nonlinear decoupling for a class of nonlinear systems is discussed. Rigid and elastic-joint robot models belong to this class. For the elastic case, a transformation facilitates the robustness analysis under a weak assumption. Charts with H 1- and H ∞- norms of closed-loop disturbance transfer functions of the nonlinear-decoupled system are presented for a robust pole assignment.
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    Journal of intelligent and robotic systems 6 (1992), S. 51-63 
    ISSN: 1573-0409
    Keywords: Scheduling ; flexible manufacturing systems ; stability ; feedback
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A genetic manufacturing environment is considered. The emphasis is on small-lot, discrete, and asynchronous type of manufacturing systems rather than high volume and continuous type. Two classes of scheduling policies are proposed to render the machine stable. The policies are of feedback type. The decision is made in real-time and on-line.
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    Journal of intelligent and robotic systems 6 (1992), S. 219-240 
    ISSN: 1573-0409
    Keywords: Force control ; slip-stick friction ; stability
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper explores two practical issues related to the force control of manipulators. The first issue examined is how system stability is effected by commonly occurring manipulator nonlinearities, such as sampled-data, control signal saturation and slip-stick friction. It is shown that discretely implemented force control algorithms can drive the feedback force controlled manipulator into a limit cycle, even for a very small sampling period that by far satisfies Shannon's sampling theorem. The bounds of stability are enhanced by the presence of control signal saturation and slip stick friction. The second issue investigated is the inclusion of a high gain inner position loop as a means to minimize the unpredictability in the steady state error due to slip-stick friction. In order to support the theoretical conclusions, experiments were performed with the PUMP 560 industrial robot testbed facility developed at Colorado State University.
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    Journal of intelligent and robotic systems 23 (1998), S. 27-43 
    ISSN: 1573-0409
    Keywords: autonomous control ; actuator delays ; stability
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper, we consider the control design problem of vehicle following systems with actuator delays. An upper bound for the time delays is first constructed to guarantee the vehicle stability. Second, sufficient conditions are presented to avoid slinky-effects in the vehicle following. Next, zero steady state achieved by the proposed controller is proven. Finally, simulations are given to examine our claims.
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    Journal of intelligent and robotic systems 20 (1997), S. 131-155 
    ISSN: 1573-0409
    Keywords: robot adaptive control ; basis function-like networks ; stability ; discrete variable structure
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Stable neural network-based sampled-data indirect and direct adaptivecontrol approaches, which are the integration of a neural network (NN)approach and the adaptive implementation of the discrete variable structurecontrol, are developed in this paper for the trajectory tracking control ofa robot arm with unknown nonlinear dynamics. The robot arm is assumed tohave an upper and lower bound of its inertia matrix norm and its states areavailable for measurement. The discrete variable structure control servestwo purposes, i.e., one is to force the system states to be within the stateregion in which neural networks are used when the system goes out of neuralcontrol; and the other is to improve the tracking performance within the NNapproximation region. Main theory results for designing stable neuralnetwork-based sampled data indirect and direct adaptive controllers aregiven, and the extension of the proposed control approaches to the compositeadaptive control of a flexible-link robot is discussed. Finally, theeffectiveness of the proposed control approaches is illustrated throughsimulation studies.
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    Journal of intelligent and robotic systems 22 (1998), S. 23-38 
    ISSN: 1573-0409
    Keywords: robot dynamic model ; stiffness matrix ; constant disturbance ; integrator backstepping ; Liapunov functions ; Barbalat lemma ; stability
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A robust regulator for flexible-joint robots is proposed, which yields constant torque disturbance rejection acting on the links. The design uses the integrator backstepping technique [4,5] to cancel nonlinearities and disturbance not in the range space of the control. Stability of the closed loop system is shown using iterative Liapunov functions.
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    Journal of intelligent and robotic systems 19 (1997), S. 411-436 
    ISSN: 1573-0409
    Keywords: assembly planning ; stability ; robot ; forward ; operations
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The paper presents an approach to sequence planning consisting in determining assembly sequences defined in terms of mating and non-mating operations and based on a dynamic expansion of the assembly tree obtained using a knowledge base management system. The planner considers the case of a single-robot assembly workcell. The use of stability and the detailed definition of sequences also by means of several non-mating operations are shown to be powerful instruments in the control of the tree expansion. Forward assembly planning has been chosen, in order to minimize the number of stability checks. Backtracking is avoided by combining precedence relations and stability analysis. Hard and soft constrains are introduced to drive the tree expansion. Hard constraints are precedence relations and stability analysis. All operations are associated to costs, which are used as soft constraints. The operation based approach enables one to manage even non-mating operations and to easily overcome the linearity constraint. Costs enable the planner to manage the association among tools and components. The first section of the paper concerns Stability Analysis that is subdivided into Static and Dynamic Stability Analysis. The former is mainly involved in analyzing gravity effects; the latter is mainly involved in evaluate inertia effects due to manipulation. Stability Analysis is implemented in a simplified form. Fundamental assumptions are: no rotational equilibrium condition is considered; for each reaction force only direction and versus, but not magnitude, are considered; friction is neglected. The second section discusses the structure of the planner and its implementation. The planner is a rule based system. Forward chaining and hypothetical reasoning are the inference strategies used. The knowledge base and the data base of the system are presented and the advantages obtained using a rule based system are discussed. The third section shows two planning examples, showing the performance of the system in a simple case and in an industrial test case, the assembly of a microwave branching filter composed of 26 components.
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    Journal of intelligent and robotic systems 26 (1999), S. 91-100 
    ISSN: 1573-0409
    Keywords: robots ; neural networks ; adaptiveness ; stability ; approximation
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract An indirect adaptive control approach is developed in this paper for robots with unknown nonlinear dynamics using neural networks (NNs). A key property of the proposed approach is that the actual joint angle values in the control law are replaced by the desired joint angles, angle velocities and accelerators, and the bound on the NN reconstruction errors is assumed to be unknown. Main theoretical results for designing such a neuro-controller are given, and the control performance of the proposed controller is verified with simulation studies.
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    Machine learning 20 (1995), S. 23-33 
    ISSN: 0885-6125
    Keywords: stability ; bias ; accuracy ; repeatability ; agreement ; similarity
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    Topics: Computer Science
    Notes: Abstract Research on bias in machine learning algorithms has generally been concerned with the impact of bias on predictive accuracy. We believe that there are other factors that should also play a role in the evaluation of bias. One such factor is the stability of the algorithm; in other words, the repeatability of the results. If we obtain two sets of data from the same phenomenon, with the same underlying probability distribution, then we would like our learning algorithm to induce approximately the same concepts from both sets of data. This paper introduces a method for quantifying stability, based on a measure of the agreement between concepts. We also discuss the relationships among stability, predictive accuracy, and bias.
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    Machine learning 8 (1992), S. 363-395 
    ISSN: 0885-6125
    Keywords: Connectionism ; reinforcement learning ; robot path finding ; stability ; reactive systems
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    Notes: Abstract This paper presents a reinforcement connectionist system which finds and learns the suitable situation-action rules so as to generate feasible paths for a point robot in a 2D environment with circular obstacles. The basic reinforcement algorithm is extended with a strategy for discovering stable solution paths. Equipped with this strategy and a powerful codification scheme, the path-finder (i) learns quickly, (ii) deals with continuous-valued inputs and outputs, (iii) exhibits good noise-tolerance and generalization capabilities, (iv) copes with dynamic environments, and (v) solves an instance of the path finding problem with strong performance demands.
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    Machine learning 8 (1992), S. 363-395 
    ISSN: 0885-6125
    Keywords: Connectionism ; reinforcement learning ; robot path finding ; stability ; reactive systems
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    Notes: Abstract This paper presents a reinforcement connectionist system which finds and learns the suitable situation-action rules so as to generate feasible paths for a point robot in a 2D environment with circular obstacles. The basic reinforcement algorithm is extended with a strategy for discovering stable solution paths. Equipped with this strategy and a powerful codification scheme, the path-finder (i) learns quickly, (ii) deals with continuous-valued inputs and outputs, (iii) exhibits good noise-tolerance and generalization capabilities, (iv) copes with dynamic environments, and (v) solves an instance of the path finding problem with strong performance demands.
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    Machine learning 20 (1995), S. 23-33 
    ISSN: 0885-6125
    Keywords: stability ; bias ; accuracy ; repeatability ; agreement ; similarity
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    Topics: Computer Science
    Notes: Abstract Research on bias in machine learning algorithms has generally been concerned with the impact of bias on predictive accuracy. We believe that there are other factors that should also play a role in the evaluation of bias. One such factor is the stability of the algorithm; in other words, the repeatability of the results. If we obtain two sets of data from the same phenomenon, with the same underlying probability distribution, then we would like our learning algorithm to induce approximately the same concepts from both sets of data. This paper introduces a method for quantifying stability, based on a measure of the agreement between concepts. We also discuss the relationships among stability, predictive accuracy, and bias.
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    ISSN: 1432-0770
    Keywords: Key words: Hebbian learning rule ; attractor dynamics ; symmetric connections ; multiplicative normalization ; self-organization ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract. While learning and development are well characterized in feedforward networks, these features are more difficult to analyze in recurrent networks due to the increased complexity of dual dynamics – the rapid dynamics arising from activation states and the slow dynamics arising from learning or developmental plasticity. We present analytical and numerical results that consider dual dynamics in a recurrent network undergoing Hebbian learning with either constant weight decay or weight normalization. Starting from initially random connections, the recurrent network develops symmetric or near-symmetric connections through Hebbian learning. Reciprocity and modularity arise naturally through correlations in the activation states. Additionally, weight normalization may be better than constant weight decay for the development of multiple attractor states that allow a diverse representation of the inputs. These results suggest a natural mechanism by which synaptic plasticity in recurrent networks such as cortical and brainstem premotor circuits could enhance neural computation and the generation of motor programs.
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    Numerical algorithms 8 (1994), S. 201-220 
    ISSN: 1572-9265
    Keywords: Automatic ; adaptive ; cubature ; singularity ; extrapolation ; stability ; 65D30 ; 65-04 ; 65B05
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    Topics: Computer Science , Mathematics
    Notes: Abstract We describe an automatic cubature algorithm for functions that have a singularity on the surface of the integration region. The algorithm combines an adaptive subdivision strategy with extrapolation. The extrapolation uses a non-uniform subdivision that can be directly incorporated into the subdivision strategy used for the adaptive algorithm. The algorithm is designed to integrate a vector function over ann-dimensional rectangular region and a FORTRAN implementation is included.
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    Numerical algorithms 10 (1995), S. 225-244 
    ISSN: 1572-9265
    Keywords: Cholesky factorization error analysis ; Hankel matrix ; least squares ; normal equations ; orthogonal factorization ; QR factorization ; semi-normal equations ; stability ; Toeplitz matrix ; weak stability ; Primary 65F25 ; Secondary 47B35 ; 65F05 ; 65F30 ; 65Y05 ; 65Y10
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    Notes: Abstract We show that a fast algorithm for theQR factorization of a Toeplitz or Hankel matrixA is weakly stable in the sense thatR T R is close toA T A. Thus, when the algorithm is used to solve the semi-normal equationsR TRx=AT b, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear systemAx=b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem min ||Ax-b||2.
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    Numerical algorithms 14 (1997), S. 343-359 
    ISSN: 1572-9265
    Keywords: progressive interpolation ; stability ; spline ; shape parameters ; geometric continuity ; 41A05 ; 41A15 ; 65D05 ; 65D07
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    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we study several interpolating and smoothing methods for data which are known “progressively”. The algorithms proposed are governed by recurrence relations and our principal goal is to study their stability. A recurrence relation will be said stable if the spectral radius of the associated matrix is less than one. The iteration matrices depend on shape parameters which come either from the connection at the knots, or from the nature of the interpolant between two knots. We obtain various stability domains. Moving the parameters inside these domains leads to interesting shape effects.
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    Numerical algorithms 10 (1995), S. 245-260 
    ISSN: 1572-9265
    Keywords: Multistep methods ; differential-algebraic equations ; stability ; existence and uniqueness ; convergence of iterative method ; 65L06 ; 65L20 ; 65N22
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    Topics: Computer Science , Mathematics
    Notes: Abstract Multistep methods for the differential/algebraic equations (DAEs) in the form of $$F_1 (x) = 0, F_2 (x,x',z) = 0$$ are presented, whereF 1 maps from ℝ n to ℝ ′ ,F 2 from ℝ n x ℝ n x ℝ m to ℝ s andr〈n≤r+s=n+m. By employing the deviations of the available existence theories, a new form of the multistep method for solutions of (1) is developed. Furthermore, it is shown that this method has no typical instabilities such as those that may occur in the application of multistep method to DAEs in the traditional manner. A proof of the solvability of the multistep system is provided, and an iterative method is developed for solving these nonlinear algebraic equations. Moreover, a proof of the convergence of this iterative method is presented.
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    Journal of scientific computing 13 (1998), S. 173-183 
    ISSN: 1573-7691
    Keywords: Modified conjugate gradient method ; conjugate gradient method ; Krylov space ; convergence rate ; stability
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    Topics: Computer Science
    Notes: Abstract In this note, we examine a modified conjugate gradient procedure for solving $$A\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x} = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{b}$$ in which the approximation space is based upon the Krylov space ( $$A\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x} = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{b}$$ ) associated with $$\sqrt A$$ and $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{b}$$ . We show that, given initial vectors $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{b}$$ and $$\sqrt A \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{b}$$ (possibly computed at some expense), the best fit solution in $$K^k \sqrt A ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{b}$$ can be computed using a finite-term recurrence requiring only one multiplication by A per iteration. The initial convergence rate appears, as expected, to be twice as fast as that of the standard conjugate gradient method, but stability problems cause the convergence to be degraded.
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    Journal of scientific computing 12 (1997), S. 361-369 
    ISSN: 1573-7691
    Keywords: Alternating-direction implicit ; difference scheme ; stability ; convergence
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    Topics: Computer Science
    Notes: Abstract A new alternating-direction implicit (ADI) scheme for solving three-dimensional parabolic differential equations has been developed based on the idea of regularized difference scheme. It is unconditionally stable and second-order accurate. Further, it overcomes the drawback of the Douglas scheme and is to be very well to simulate fast transient phenomena and to efficiently capture steady state solutions of parabolic differential equations. Numerical example is illustrated.
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    Journal of network and systems management 3 (1995), S. 371-380 
    ISSN: 1573-7705
    Keywords: Telephone traffic ; network management ; control theory ; dynamic flows ; stability ; routing algorithms ; broadband networks ; simulation
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    Topics: Computer Science
    Notes: Abstract The control of telephony traffic is the task of network management and routing algorithms. In this paper, a study of two trunk groups carrying telephony traffic is used to show that instabilities can arise if there is a delay in getting feedback information for a network controller. The network controller seeks to balance the traffic in the two trunk groups, which may represent two paths from a source to a destination. An analysis shows how factors such as holding time, controller gain and feedback delay influence stability. Simulation of a two service case is also carried out to show that the same instabilities can arise.
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    Neural processing letters 10 (1999), S. 267-271 
    ISSN: 1573-773X
    Keywords: recurrent neural networks ; stability
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    Notes: Abstract In this paper, we point out that the conditions given in [1] are sufficient but unnecessary for the global asymptotically stable equilibrium of a class of delay differential equations. Instead, we prove that under weaker conditions, it is still global asymptotically stable.
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    International journal of parallel programming 12 (1983), S. 193-209 
    ISSN: 1573-7640
    Keywords: Database ; characteristic frequency ; aggregated model ; decomposition ; stability ; dynamic distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A time decomposition technique is suggested for large-database (DB) models. The problem of network aggregation is studied and the results used to create a meaningful decomposed model. Decomposition conditions and assumptions are discussed and illustrated by examples. A practical operating schedule is presented for the time-separated DB model. The schedule uses a sequence of decomposed models, which are to be constructed recursively. The application of the time separation technique for large-DB models is presented in the form of a closed-loop algorithm. The problem of decomposition stability with respect to variations in time constants is considered as well. Two alternative approaches to the problem are suggested. For a probabilistic approach, practical approximate formulas are obtained for subsystem time constants and recommendations are made with respect to the decomposition structure. An approximate performance analysis is done for both standard and time-decomposed models. A comparison of the results is given.
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  • 56
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    Journal of scientific computing 12 (1997), S. 215-231 
    ISSN: 1573-7691
    Keywords: Transport models ; shallow water ; splitting methods ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We investigate the use of splitting methods for the numerical integration of three-dimensional transport-chemistry models. In particular, we investigate various possibilities for the time discretization that can take advantage of the parallelization and vectorization facilities offered by multi-processor vector computers. To suppress wiggles in the numerical solution, we use third-order, upwind-biased discretization of the advection terms, resulting in a five-point coupling in each direction. As an alternative to the usual splitting functions, such as co-ordinate splitting or operator splitting, we consider a splitting function that is based on a three-coloured hopscotch-type splitting in the horizontal direction, whereas full coupling is retained in the vertical direction. Advantages of this splitting function are the easy application of domain decomposition techniques and unconditional stability in the vertical, which is an important property for transport in shallow water. The splitting method is obtained by combining the hopscotch-type splitting function with various second-order splitting formulae from the literature. Although some of the resulting methods are highly accurate, their stability behaviour (due to horizontal advection) is quite poor. Therefore we also discuss several new splitting formulae with the aim to improve the stability characteristics. It turns out that this is possible indeed, but the price to pay is a reduction of the accuracy. Therefore, such methods are to be preferred if accuracy is less crucial than stability; such a situation is frequently encountered in solving transport problems. As part of the project TRUST (Transport and Reactions Unified by Splitting Techniques), preliminary versions of the schemes are implemented on the Cray C98 4256 computer and are available for benchmarking.
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  • 57
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    Journal of scientific computing 12 (1997), S. 353-360 
    ISSN: 1573-7691
    Keywords: Alternating-direction implicit ; difference scheme ; stability ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A generalized Peaceman–Rachford alternating-direction implicit (ADI) scheme for solving two-dimensional parabolic differential equations has been developed based on the idea of regularized difference scheme. It is to be very well to simulate fast transient phenomena and to efficiently capture steady state solutions of parabolic differential equations. Numerical example is illustrated.
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  • 58
    ISSN: 1573-773X
    Keywords: constrained learning ; factorization ; feedforward networks ; IIR filters ; polynomials ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Adaptive artificial neural network techniques are introduced and applied to the factorization of 2-D second order polynomials. The proposed neural network is trained using a constrained learning algorithm that achieves minimization of the usual mean square error criterion along with simultaneous satisfaction of multiple equality and inequality constraints between the polynomial coefficients. Using this method, we are able to obtain good approximate solutions for non-factorable polynomials. By incorporating stability constraints into the formalism, our method can be successfully used for the realization of stable 2-D second order IIR filters in cascade form.
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  • 59
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    Journal of logic, language and information 7 (1998), S. 143-163 
    ISSN: 1572-9583
    Keywords: Belief revision ; consolidation ; coherence ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Linguistics and Literary Studies , Computer Science
    Notes: Abstract The notion of epistemic coherence is interpreted as involving not only consistency but also stability. The problem how to consolidate a belief system, i.e., revise it so that it becomes coherent, is studied axiomatically as well as in terms of set-theoretical constructions. Representation theorems are given for subtractive consolidation (where coherence is obtained by deleting beliefs) and additive consolidation (where coherence is obtained by adding beliefs).
    Type of Medium: Electronic Resource
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