Search results for: Perturbation Theory for Linear Operators

Authors: Watcharakorn Thongchuay, Puntip Toghaw, Montri Maleewong

Abstract:

The Wavelet-Galerkin finite element method for solving the one-dimensional heat equation is presented in this work. Two types of basis functions which are the Lagrange and multi-level wavelet bases are employed to derive the full form of matrix system. We consider both linear and quadratic bases in the Galerkin method. Time derivative is approximated by polynomial time basis that provides easily extend the order of approximation in time space. Our numerical results show that the rate of convergences for the linear Lagrange and the linear wavelet bases are the same and in order 2 while the rate of convergences for the quadratic Lagrange and the quadratic wavelet bases are approximately in order 4. It also reveals that the wavelet basis provides an easy treatment to improve numerical resolutions that can be done by increasing just its desired levels in the multilevel construction process.

Keywords: Galerkin finite element method, Heat equation , Lagrange basis function, Wavelet basis function.

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Authors: Nicholas Kyriazis, Emmanouil Marios L. Economou, Jr, Loukas Zachilas

Abstract:

In the present essay, a model of choice by actors is analysedby utilizing the theory of chaos to explain how change comes about. Then, by using ancient and modern sources of literature, the theory of the social contract is analysed as a historical phenomenon that first appeared during the period of Classical Greece. Then, based on the findings of this analysis, the practice of direct democracy and public choice in ancient Athens is analysed, through two historical cases: Eubulus and Lycurgus political program in the second half of the 4th century. The main finding of this research is that these policies can be interpreted as an implementation of a social contract, through which citizens were taking decisions based on rational choice according to economic considerations.

Keywords: Chaos theory, public choice, social contract, 4th century BC. Athens.

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Authors: Gesine Hellwig

Abstract:

Functional imaging procedures for the non-invasive assessment of tissue microcirculation are highly requested, but require a mathematical approach describing the trans- and intercapillary passage of tracer particles. Up to now, two theoretical, for the moment different concepts have been established for tracer kinetic modeling of contrast agent transport in tissues: pharmacokinetic compartment models, which are usually written as coupled differential equations, and the indicator dilution theory, which can be generalized in accordance with the theory of lineartime- invariant (LTI) systems by using a convolution approach. Based on mathematical considerations, it can be shown that also in the case of an open two-compartment model well-known from functional imaging, the concentration-time course in tissue is given by a convolution, which allows a separation of the arterial input function from a system function being the impulse response function, summarizing the available information on tissue microcirculation. Due to this reason, it is possible to integrate the open two-compartment model into the system-theoretic concept of indicator dilution theory (IDT) and thus results known from IDT remain valid for the compartment approach. According to the long number of applications of compartmental analysis, even for a more general context similar solutions of the so-called forward problem can already be found in the extensively available appropriate literature of the seventies and early eighties. Nevertheless, to this day, within the field of biomedical imaging – not from the mathematical point of view – there seems to be a trench between both approaches, which the author would like to get over by exemplary analysis of the well-known model.

Keywords: Functional imaging, Tracer kinetic modeling, LTIsystem, Indicator dilution theory / convolution approach, Two-Compartment model.

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Authors: Wei Bai, Ling-Wei Kong, Ai-Guo Guo

Abstract:

Base on extenics theory, the statistical physical and mechanical properties from laboratory experiments are used to evaluate the bearing capacity of lateritic soil foundation. The properties include water content, bulk density, liquid limit, cohesion, and so on. The matter-element and the dependent function are defined. Then the synthesis dependent degree and the final grade index are calculated. The results show that predicted outcomes can be matched with the in-situ test data, and a evaluate grade associate with bearing capacity can be deduced. The results provide guidance to assess and determine the bearing capacity grade of lateritic soil foundation.

Keywords: Lateritic soil, bearing capacity, extenics theory, plate loading test.

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Authors: Marina Velikova, Hennie Daniels, Ad Feelders

Abstract:

In many applications, it is a priori known that the target function should satisfy certain constraints imposed by, for example, economic theory or a human-decision maker. Here we consider partially monotone problems, where the target variable depends monotonically on some of the predictor variables but not all. We propose an approach to build partially monotone models based on the convolution of monotone neural networks and kernel functions. The results from simulations and a real case study on house pricing show that our approach has significantly better performance than partially monotone linear models. Furthermore, the incorporation of partial monotonicity constraints not only leads to models that are in accordance with the decision maker's expertise, but also reduces considerably the model variance in comparison to standard neural networks with weight decay.

Keywords: Mixture models, monotone neural networks, partially monotone models, partially monotone problems.

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Authors: S. A. Hashemi, A. Khoshraftar

Abstract:

This paper presents the influence of the vertical seismic component on the non-linear dynamics analysis of three different structures. The subject structures were analyzed and designed according to recent codes. This paper considers three types of buildings: 5-, 10-, and 15-story buildings. The non-linear dynamics analysis of the structures with assuming elastic-perfectlyplastic behavior was performed using RAM PERFORM-3D software; the horizontal component was taken into consideration with and without the incorporation of the corresponding vertical component. Dynamic responses obtained for the horizontal component acting alone were compared with those obtained from the simultaneous application of both seismic components. The results show that the effect of the vertical component of ground motion may increase the axial load significantly in the interior columns and, consequently, the stories. The plastic mechanisms would be changed. The P-Delta effect is expected to increase. The punching base plate shear of the columns should be considered. Moreover, the vertical component increases the input energy when the structures exhibit inelastic behavior and are taller.

Keywords: Inelastic behavior, non-linear dynamic analysis, steel structure, vertical component.

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Authors: Guangbin Wang, Fuping Tan, Deyu Sun

Abstract:

In this paper, we present new preconditioned generalized mixed-type splitting (GMTS) methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GMTS methods converge faster than the GMTS method whenever the GMTS method is convergent. Finally, we give a numerical example to confirm our theoretical results.

Keywords: Preconditioned, GMTS method, linear system, convergence, comparison.

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Authors: S. Swain, P. S. Khuntia

Abstract:

In this paper an optimal convex controller is designed to control the angle of attack of a FOXTROT aircraft. Then the order of the system model is reduced to a low-dimensional state space by using Balanced Truncation Model Reduction Technique and finally the robust stability of the reduced model of the system is tested graphically by using Kharitonov rectangle and Zero Exclusion Principle for a particular range of perturbation value. The same robust stability is tested theoretically by using Frequency Sweeping Function for robust stability.

Keywords: Convex Optimization, Kharitonov Stability Criterion, Model Reduction, Robust Stability.

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Authors: A. G. Sifalakis, E. P. Papadopoulou, Y. G. Saridakis

Abstract:

A generalized Dirichlet to Neumann map is one of the main aspects characterizing a recently introduced method for analyzing linear elliptic PDEs, through which it became possible to couple known and unknown components of the solution on the boundary of the domain without solving on its interior. For its numerical solution, a well conditioned quadratically convergent sine-Collocation method was developed, which yielded a linear system of equations with the diagonal blocks of its associated coefficient matrix being point diagonal. This structural property, among others, initiated interest for the employment of iterative methods for its solution. In this work we present a conclusive numerical study for the behavior of classical (Jacobi and Gauss-Seidel) and Krylov subspace (GMRES and Bi-CGSTAB) iterative methods when they are applied for the solution of the Dirichlet to Neumann map associated with the Laplace-s equation on regular polygons with the same boundary conditions on all edges.

Keywords: Elliptic PDEs, Dirichlet to Neumann Map, Global Relation, Collocation, Iterative Methods, Jacobi, Gauss-Seidel, GMRES, Bi-CGSTAB.

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Authors: Lakhdar Zaid, Albane Sangiovanni

Abstract:

A reconfigurable microstrip patch antenna with polyphase filter for polarization diversity and cross polarization filtering operation is presented in this paper. In our approach, a polyphase filter is used to obtain the four 90° phase shift outputs to feed a square microstrip patch antenna. The antenna can be switched between four states of polarization in transmission as well as in receiving mode. Switches are interconnected with the polyphase filter network to produce left-hand circular polarization, right-hand circular polarization, horizontal linear polarization, and vertical linear polarization. Additional advantage of using polyphase filter is its filtering capability for cross polarization filtering in right-hand circular polarization and left-hand circular polarization operation. The theoretical and simulated results demonstrated that polyphase filter is a good candidate to drive microstrip patch antenna to accomplish polarization diversity and cross polarization filtering operation.

Keywords: Microstrip patch antenna, polyphase filter, circular polarization, linear polarization, reconfigurable antenna.

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Authors: Aldalalah, M. Osamah, Soon Fook Fong

Abstract:

The purpose of this study was to investigate the effects of computer–based instructional designs, namely modality and redundancy principles on the attitude and learning of music theory among primary pupils of different Music Intelligence levels. The lesson of music theory was developed in three different modes, audio and image (AI), text with image (TI) and audio with image and text (AIT). The independent variables were the three modes of courseware. The moderator variable was music intelligence. The dependent variables were the post test score. ANOVA was used to determine the significant differences of the pretest scores among the three groups. Analyses of covariance (ANCOVA) and Post hoc were carried out to examine the main effects as well as the interaction effects of the independent variables on the dependent variables. High music intelligence pupils performed significantly better than low music intelligence pupils in all the three treatment modes. The AI mode was found to help pupils with low music intelligence significantly more than the TI and AIT modes.

Keywords: Modality, Redundancy, Music theory, Cognitivetheory of multimedia learning, Cognitive load theory, Musicintelligence.

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Authors: Minto Rattan, Tania Bose, Neeraj Chamoli

Abstract:

The present paper investigates the effect of linear thermal gradient on the steady-state creep behavior of rotating isotropic disc using threshold stress based Sherby’s creep law. The composite discs made of aluminum matrix reinforced with silicon carbide particulate has been taken for analysis. The stress and strain rate distributions have been calculated for discs rotating at linear thermal gradation using von Mises’ yield criterion. The material parameters have been estimated by regression fit of the available experimental data. The results are displayed and compared graphically in designer friendly format for the above said temperature profile with the disc operating under uniform temperature profile. It is observed that radial and tangential stresses show minor variation and the strain rates vary significantly in the presence of thermal gradation as compared to disc having uniform temperature.

Keywords: Creep, isotropic, steady-state, thermal gradient.

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Authors: Nino M. Pizarro

Abstract:

To the author’s knowledge, despite the written documents about Marist spirituality/charism, nothing has been done concerning a clear theoretical framework that highlights Marist spirituality/charism from the perspective or lived experience of the lay Marists of St. Marcellin Champagnat. The participants of the study are the lay Marist - educators who are from Marist Schools in the Philippines. Since the study would like to find out the respondents’ own concepts and meanings about Marist spirituality/charism, qualitative methodology is considered the approach to be used in the study. In particular, the study will use the qualitative methods of Barney Glaser. The theory will be generated systematically from data collection, coding and analyzing through memoing, theoretical sampling, sorting and writing and using the constant comparative method. The data collection method that will be employed in this grounded theory research is the in-depth interview that is semi-structured and participant driven. Data collection will be done through snowball sampling that is purposive. The study is considering to come up with a theoretical framework that will help the lay Marists to deepen their understanding of the Marist spirituality/charism and their vocation as lay partners of the Marist Brothers of the Schools.

Keywords: Grounded Theory, Lay Marists, Lived Experience, Marist Spirituality/Charism.

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Authors: Kwa-Sur Tam

Abstract:

This paper reviews various approaches that have been used for the modeling and simulation of large-scale engineering systems and determines their appropriateness in the development of a RICS modeling and simulation tool. Bond graphs, linear graphs, block diagrams, differential and difference equations, modeling languages, cellular automata and agents are reviewed. This tool should be based on linear graph representation and supports symbolic programming, functional programming, the development of noncausal models and the incorporation of decentralized approaches.

Keywords: Interdisciplinary, dynamic, functional programming, object-oriented.

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Authors: S. H. Lee, M. J. Park, O. M. Kwon

Abstract:

In this paper, reliable consensus of multi-agent systems with sampled-data is investigated. By using a suitable Lyapunov-Krasovskii functional and some techniques such as Wirtinger Inequality, Schur Complement and Kronecker Product, the results of such system are obtained by solving a set of Linear Matrix Inequalities (LMIs). One numerical example is included to show the effectiveness of the proposed criteria.

Keywords: Multi-agent, Linear Matrix Inequalities (LMIs), Kronecker Product, Sampled-Data, Lyapunov method.

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Authors: Zixin Liu, Huawei Yang, Fangwei Chen

Abstract:

This paper studies the mean square exponential synchronization problem of a class of stochastic neutral type chaotic neural networks with mixed delay. On the Basis of Lyapunov stability theory, some sufficient conditions ensuring the mean square exponential synchronization of two identical chaotic neural networks are obtained by using stochastic analysis and inequality technique. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. The feedback controller used in this paper is more general than those used in previous literatures. One simulation example is presented to demonstrate the effectiveness of the derived results.

Keywords: Exponential synchronization, stochastic analysis, chaotic neural networks, neutral type system.

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Authors: Kejun Zhuang

Abstract:

In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.

Keywords: Chaotic system, Hopf bifurcation, normal form theory.

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Authors: Soltani Amir, Hu Jiaxin

Abstract:

Determination of optimal parameters of a passive  control system device is the primary objective of this study.  Expanding upon the use of control devices in wind and earthquake  hazard reduction has led to development of various control systems.  The advantage of non-linearity characteristics in a passive control  device and the optimal control method using LQR algorithm are  explained in this study. Finally, this paper introduces a simple  approach to determine optimum parameters of a nonlinear viscous  damper for vibration control of structures. A MATLAB program is  used to produce the dynamic motion of the structure considering the  stiffness matrix of the SDOF frame and the non-linear damping  effect. This study concluded that the proposed system (variable  damping system) has better performance in system response control  than a linear damping system. Also, according to the energy  dissipation graph, the total energy loss is greater in non-linear  damping system than other systems.

 

Keywords: Passive Control System, Damping Devices, Viscous Dampers, Control Algorithm.

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Authors: A. Sina, A. Aeenmehr, H. Mohamadian

Abstract:

Optimization and control of reactive power distribution in the power systems leads to the better operation of the reactive power resources. Reactive power control reduces considerably the power losses and effective loads and improves the power factor of the power systems. Another important reason of the reactive power control is improving the voltage profile of the power system. In this paper, voltage and reactive power control using Neural Network techniques have been applied to the 33 shines- Tehran Electric Company. In this suggested ANN, the voltages of PQ shines have been considered as the input of the ANN. Also, the generators voltages, tap transformers and shunt compensators have been considered as the output of ANN. Results of this techniques have been compared with the Linear Programming. Minimization of the transmission line power losses has been considered as the objective function of the linear programming technique. The comparison of the results of the ANN technique with the LP shows that the ANN technique improves the precision and reduces the computation time. ANN technique also has a simple structure and this causes to use the operator experience.

Keywords: voltage control, linear programming, artificial neural network, power systems

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Authors: S. A. Hashemi, A. Khoshraftar

Abstract:

This paper presents the influence of the vertical seismic component on the non-linear dynamics analysis of three different structures. The subject structures were analyzed and designed according to recent codes. This paper considers three types of buildings: 5-, 10-, and 15-story buildings. The non-linear dynamics analysis of the structures with assuming elastic-perfectly-plastic behavior was performed using RAM PERFORM-3D software; the horizontal component was taken into consideration with and without the incorporation of the corresponding vertical component. Dynamic responses obtained for the horizontal component acting alone were compared with those obtained from the simultaneous application of both seismic components. The results show that the effect of the vertical component of ground motion may increase the axial load significantly in the interior columns and, consequently, the stories. The plastic mechanisms would be changed. The P-Delta effect is expected to increase. The punching base plate shear of the columns should be considered. Moreover, the vertical component increases the input energy when the structures exhibit inelastic behavior and are taller.

Keywords: Inelastic behavior, non-linear dynamic analysis, steel structure, vertical component.

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Authors: Khaled E. A. Negm

Abstract:

A neuron can emit spikes in an irregular time basis and by averaging over a certain time window one would ignore a lot of information. It is known that in the context of fast information processing there is no sufficient time to sample an average firing rate of the spiking neurons. The present work shows that the spiking neurons are capable of computing the radial basis functions by storing the relevant information in the neurons' delays. One of the fundamental findings of the this research also is that when using overlapping receptive fields to encode the data patterns it increases the network-s clustering capacity. The clustering algorithm that is discussed here is interesting from computer science and neuroscience point of view as well as from a perspective.

Keywords: Temporal Neurons, RBF Recognition, Perturbation, On Line Recognition.

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Authors: Ezequiel Garcia-Rodriguez, Luis A. Ochoa-Franco, Adrian I. Cervantes-Servin

Abstract:

In this work, the Ictalurus punctatus species estimated available physical habitat is compared with the estimated physical habitat for the same but modified river reach, with the aim of creating a linear park, along a length of 5 500 m. To determine the effect of ecological park construction, on physical habitat of the Lerma river stretch of study, first, the available habitat for the Ictalurus punctatus species was estimated through the simulation of the physical habitat, by using surveying, hydraulics, and habitat information gotten at the river reach in its actual situation. Second, it was estimated the available habitat for the above species, upon the simulation of the physical habitat through the proposed modification for the ecological park creation. Third, it is presented a comparison between both scenarios in terms of available habitat estimated for Ictalurus punctatus species, concluding that in cases of adult and spawning life stages, changes in the channel to create an ecological park would produce a considerable loss of potentially usable habitat (PUH), while in the case of the juvenile life stage PUH remains virtually unchanged, and in the case of life stage fry the PUH would increase due to the presence of velocities and depths of lesser magnitude, due to the presence of minor flow rates and lower volume of the wet channel. It is expected that habitat modification for linear park construction may produce the lack of Ictalurus punktatus species conservation at the river reach of the study.

Keywords: Habitat modification, Ictalurus punctatus, Lerma, river, linear park.

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Authors: Luis Arias, Jorge E. Pezoa, Daniel Sbárbaro

Abstract:

In this paper, an automated algorithm to estimate and remove the continuous baseline from measured spectra containing both continuous and discontinuous bands is proposed. The algorithm uses previous information contained in a Continuous Database Spectra (CDBS) to obtain a linear basis, with minimum number of sampled vectors, capable of representing a continuous baseline. The proposed algorithm was tested by using a CDBS of flame spectra where Principal Components Analysis and Non-negative Matrix Factorization were used to obtain linear bases. Thus, the radical emissions of natural gas, oil and bio-oil flames spectra at different combustion conditions were obtained. In order to validate the performance in the baseline estimation process, the Goodness-of-fit Coefficient and the Root Mean-squared Error quality metrics were evaluated between the estimated and the real spectra in absence of discontinuous emission. The achieved results make the proposed method a key element in the development of automatic monitoring processes strategies involving discontinuous spectral bands.

Keywords: Flame spectra, removing baseline, recovering spectrum.

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Authors: Hans H. Diel

Abstract:

In this paper a functional interpretation of quantum theory (QT) with emphasis on quantum field theory (QFT) is proposed. Besides the usual statements on relations between a functions initial state and final state, a functional interpretation also contains a description of the dynamic evolution of the function. That is, it describes how things function. The proposed functional interpretation of QT/QFT has been developed in the context of the author-s work towards a computer model of QT with the goal of supporting the largest possible scope of QT concepts. In the course of this work, the author encountered a number of problems inherent in the translation of quantum physics into a computer program. He came to the conclusion that the goal of supporting the major QT concepts can only be satisfied, if the present model of QT is supplemented by a "functional interpretation" of QT/QFT. The paper describes a proposal for that

Keywords: Computability, Foundation of Quantum Mechanics, Measurement Problem, Models of Physics.

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Authors: Sungin Jeong

Abstract:

This paper presents a linear oscillating generator of cylindrical type for hybrid electric vehicle application. The focus of the study is the suggestion of the optimal model and the design rule of the cylindrical linear oscillating generator with permanent magnet in the back-iron translator. The cylindrical topology is achieved using equivalent magnetic circuit considering leakage elements as initial modeling. This topology with permanent magnet in the back-iron translator is described by number of phases and displacement of stroke. For more accurate analysis of an oscillating machine, it will be compared by moving just one-pole pitch forward and backward the thrust of single-phase system and three-phase system. Through the analysis and comparison, a single-phase system of cylindrical topology as the optimal topology is selected. Finally, the detailed design of the optimal topology takes the magnetic saturation effects into account by finite element analysis. Besides, the losses are examined to obtain more accurate results; copper loss in the conductors of machine windings, eddy-current loss of permanent magnet, and iron-loss of specific material of electrical steel. The considerations of thermal performances and mechanical robustness are essential, because they have an effect on the entire efficiency and the insulations of the machine due to the losses of the high temperature generated in each region of the generator. Besides electric machine with linear oscillating movement requires a support system that can resist dynamic forces and mechanical masses. As a result, the fatigue analysis of shaft is achieved by the kinetic equations. Also, the thermal characteristics are analyzed by the operating frequency in each region. The results of this study will give a very important design rule in the design of linear oscillating machines. It enables us to more accurate machine design and more accurate prediction of machine performances.

Keywords: Equivalent magnetic circuit, finite element analysis, hybrid electric vehicle, free piston engine, cylindrical linear oscillating generator

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Authors: Sung Wook Yun, Yun Jong Choi, Kyong-min Lee, Poogyeon Park*

Abstract:

Repetitive systems stand for a kind of systems that perform a simple task on a fixed pattern repetitively, which are widely spread in industrial fields. Hence, many researchers have been interested in those systems, especially in the field of iterative learning control (ILC). In this paper, we propose a finite-horizon tracking control scheme for linear time-varying repetitive systems with uncertain initial conditions. The scheme is derived both analytically and numerically for state-feedback systems and only numerically for output-feedback systems. Then, it is extended to stable systems with input constraints. All numerical schemes are developed in the forms of linear matrix inequalities (LMIs). A distinguished feature of the proposed scheme from the existing iterative learning control is that the scheme guarantees the tracking performance exactly even under uncertain initial conditions. The simulation results demonstrate the good performance of the proposed scheme.

Keywords: Finite time horizon, linear matrix inequality (LMI), repetitive system, uncertain initial condition.

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Authors: Li Jiang, Baoguang Tian

Abstract:

In this paper, we present the preconditioned mixed-type splitting iterative method for solving the linear systems, Ax = b, where A is a Z-matrix. And we give some comparison theorems to show that the convergence rate of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give a numerical example to illustrate our results.

Keywords: Z-matrix, mixed-type splitting iterative method, precondition, comparison theorem, linear system.

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Authors: M. Sasajima, T. Yamaguchi, Y. Koike, A. Hara

Abstract:

This paper describes vibration analysis using the finite element method for a small earphone, especially for the diaphragm shape with a low-rigidity. The viscoelastic diaphragm is supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the nonlinear springs have cubic nonlinearity. The finite elements for the nonlinear springs with hysteresis are expressed and are connected to the diaphragm that is modeled by linear solid finite elements in consideration of a complex modulus of elasticity. Further, the discretized equations in physical coordinates are transformed into the nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. We computed the nonlinear stationary and non-stationary responses due to the internal resonance between modes with large amplitude in the nonlinear springs and elastic modes in the diaphragm. The non-stationary motions are confirmed as the chaos due to the maximum Lyapunov exponents with a positive number. From the time histories of the deformation distribution in the chaotic vibration, we identified nonlinear modal couplings.

Keywords: Nonlinear Vibration, Finite Element Method, Chaos , Small Earphone.

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Authors: Myung-Gon Yoon, Jung-Ho Moon, Tae Kwon Ha

Abstract:

This paper studies a robust stabilization problem of a single agent in a multi-agent consensus system composed of identical agents, when the network topology of the system is completely unknown. It is shown that the transfer function of an agent in a consensus system can be described as a multiplicative perturbation of the isolated agent transfer function in frequency domain. From an existing robust stabilization result, we present sufficient conditions for a robust stabilization of an agent against unknown network topology.

Keywords: Multi-agent System, Robust Stabilization, Transfer Function.

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Authors: Om Parkash, C.P.Gandhi

Abstract:

Probabilistic measures of uncertainty have been obtained as functions of time and birth and death rates in a queuing process. The variation of different entropy measures has been studied in steady and non-steady processes of queuing theory.

Keywords: Uncertainty, steady state, non-steady state, trafficintensity, monotonocity

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