Queueing analysis and optimal control of and systems

We first consider a finite-buffer single server queue where arrivals occur according to batch Markovian arrival process (BMAP). The server serves customers in batches of maximum size ‘b’ with a minimum threshold size ‘a’. The service time of each batch follows general distribution independent of each other as well as the arrival process. We obtain queue length distributions at various epochs such as, pre-arrival, arbitrary, departure, etc. Some important performance measures, like mean queue length, mean waiting time, probability of blocking, etc. have been obtained. Total expected cost function per unit time is also derived to determine the optimal value N^* of N at a minimum cost for given values of a and b. Secondly, we consider a finite-buffer single server queue where arrivals occur according to BMAP and service process in this case follows a non-renewal one, namely, Markovian service process (MSP). Server serves customers according to general bulk service rule as described above. We derive queue length distributions and important performance measures as above. Such queueing systems find applications in the performance analysis of communication, manufacturing and transportation systems.     

Lyapunov and feedback characterizations of state constrained controllability and stabilization

A standard control system is considered, in conjunction with a state constraint S and a target set Σ. The properties of open loop S-constrained control to Σ and practical closed loop S-constrained control to Σ are shown to be equivalent, and to be characterizable in terms of the existence of certain types of control Lyapunov functions. Feedback S-constrained stabilizability to Σ can be added to the list of equivalences, when a small time controllability property is posited.     

复杂工程建模和模拟的验证与确认

综述国内外建模和模拟(Modeling and Simulation,MS)的验证与确认(Verification and Validation,VV)的相关概念、术语、规范、置信度评估方法和应用等方面的发展和研究进展,概括MS的VV中的几个关键问题,构建复杂工程MS的VV的知识指南,为MS的VV技术真正走向应用提供参考.     

Capability and limitation of max- and sum-type construction of Lyapunov functions for networks of iISS systems

This paper addresses the problem of verifying stability of networks whose subsystems admit dissipation inequalities of integral input-to-state stability (iISS). We focus on two ways of constructing a Lyapunov function satisfying a dissipation inequality of a given network. Their difference from one another is elucidated from the viewpoint of formulation, relation, fundamental limitation and capability. One is referred to as the max-type construction resulting in a Lipschitz continuous Lyapunov function. The other is the sum-type construction resulting in a continuously differentiable Lyapunov function. This paper presents geometrical conditions under which the Lyapunov construction is possible for a network comprising $n\ge 2$ subsystems. Although the sum-type construction for general $n>2$ has not yet been reduced to a readily computable condition, we obtain a simple condition of iISS small gain in the case of $n=2$. It is demonstrated that the max-type construction fails to offer a Lyapunov function if the network contains subsystems which are not input-to-state stable (ISS).     

Detection of rotational and involutional symmetries and congruity of polyhedra

We propose a simple and efficient general algorithm for determining both rotational and involutional symmetries of polyhedra. It requiresO(m ²) time and usesO(m) space, wherem is the number of edges of the polyhedron. As this is the lower bound of the symmetry detection problem for the considered output form, our algorithm is optimal. We show that a slight modification of our symmetry detection algorithm can be used to solve the related conguity problem of polyhedra.     

Approximation and derivatives of probabilities of survival in structural analysis and design

Yield stresses, allowable stresses, moment capacities (plastic moments), external loadings, manufacturing errors, etc., are not fixed quantities in practice, but must be modelled as random variables with a certain joint probability distribution. In reliability-oriented structural optimization the violation of the random behavioural constraints are evaluated by means of the corresponding probabilityp _s of survival. Hence, the approximative computation ofp _s and its sensitivities is of utmost importance. After the consideration of lower bounds ofp _s based on a selection of certain redundants in the vector of internal forces/bending moments, and the consideration of upper bounds ofp _s based on an optimizational representation of the yield or safety constraints by a pair of dual linear programs, a conical representation ofp _s is introduced based on a coneY _o of admissible pairs of external loads/strength increaments. Approximations ofp _s can be constructed then by replacing the (finitely generated) coneY _o by more simple ones, e.g. spherical or ellipsoidal cones. For the direct numerical computation of sensitivities ofp _s and its bounds or approximations by using e.g. sampling methods or asymptotic expansion techniques based on Laplace integral representation of multiple integrals, exact differentiation formulae — of arbitrary order — forp _s and its bounds or approximations with respect to deterministic input or design variables are obtained by applying the transformation method/stochastic completion techniques; the derivatives ofp _s are represented again by certain expectations or multiple integrals.     

A Calculus and logic of resources and processes

Recent advances in logics for reasoning about resources provide a new approach to compositional reasoning in interacting systems. We present a calculus of resources and processes, based on a development of Milner’s synchronous calculus of communication systems, SCCS, that uses an explicit model of resource. Our calculus models the co-evolution of resources and processes with synchronization constrained by the availability of resources. We provide a logical characterization, analogous to Hennessy–Milner logic’s characterization of bisimulation in CCS, of bisimulation between resource processes which is compositional in the concurrent and local structure of systems. An erratum to this article can be found at     

Systematic analyses and comparison of development performance and product quality of Incremental Process and Agile Process

ContextAlthough Agile software development models have been widely used as a base for the software project life-cycle since 1990s, the number of studies that follow a sound empirical method and quantitatively reveal the effect of using these models over Traditional models is scarce.ObjectiveThis article explains the empirical method of and the results from systematic analyses and comparison of development performance and product quality of Incremental Process and Agile Process adapted in two projects of a middle-size, telecommunication software development company. The Incremental Process is an adaption of the Waterfall Model whereas the newly introduced Agile Process is a combination of the Unified Software Development Process, Extreme Programming, and Scrum.MethodThe method followed to perform the analyses and comparison is benefited from the combined use of qualitative and quantitative methods. It utilizes; GQM Approach to set measurement objectives, CMMI as the reference model to map the activities of the software development processes, and a pre-defined assessment approach to verify consistency of process executions and evaluate measure characteristics prior to quantitative analysis.ResultsThe results of the comparison showed that the Agile Process had performed better than the Incremental Process in terms of productivity (79%), defect density (57%), defect resolution effort ratio (26%), Test Execution V&V Effectiveness (21%), and effort prediction capability (4%). These results indicate that development performance and product quality achieved by following the Agile Process was superior to those achieved by following the Incremental Process in the projects compared.ConclusionThe acts of measurement, analysis, and comparison enabled comprehensive review of the two development processes, and resulted in understanding their strengths and weaknesses. The comparison results constituted objective evidence for organization-wide deployment of the Agile Process in the company.     

Polynomial approximation of functions of matrices and applications

In solving a mathematical problem numerically, we frequently need to operate on a vector by an operator that can be expressed asf(A), whereA is anN ×N matrix [e.g., exp(A), sin(A), A^–-]. Except for very simple matrices, it is impractical to construct the matrixf (A) explicitly. Usually an approximation to it is used. This paper develops an algorithm based upon a polynomial approximation tof (A). First the problem is reduced to a problem of approximatingf (z) by a polynomial in z, where z belongs to a domainD in the complex plane that includes all the eigenvalues ofA. This approximation problem is treated by interpolatingf (z) in a certain set of points that is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problems is described. Since a solution to a linear systemAx=b isx=A ^–1 b, an iterative solution algorithm can be based upon a polynomial approximation tof (A)=A ^–1. We give special attention to this important problem.     

Correlations of the impedance parameters and conductivity and permittivity of liquid and gel phases in a series piezoelectric quartz crystal sensor

The impedance characteristics of a series piezoelectric quartz crystal (SPQC) sensor were investigated using a network/impedance analyzer. The correlations between the impedance parameters, including the magnitude and phase of the impedance and the resonant frequencies, and the conductivity and/or the permittivity of the test solutions were derived theoretically and in good agreement with the experimental results. It was shown that the value of the series frequency (f_s) decreases with increasing conductivity and permittivity of the liquid. The parallel frequency (f_p) is the constant. The values of the maximum impedance (|Z|_max) and corresponding frequency (f_max,), are not related to the conductivity and permittivity of the liquid. The value of the minimum impedance (|Z|_min) decreases with increasing permittivity and has a maximum in a solution of middle conductivity. The corresponding frequency (f_min) has the same value as the f_s. The maximum phase of the impedance (θ_max) increases slightly with increasing permittivity and has a minimum in electrolyte solution of middle conductivity. In the impedance–frequency curves, there is an iso-impedance point for the SPQC in electrolyte solutions. The SPQC method was applied to monitor the process of hydrogel formation.     

An experimental and numerical study of the structure and stability of laminar opposed-jet flows

Experiments, simulations, and numerical bifurcation analysis are used to study the incompressible flow between two opposed tubes with disks mounted at their exits. The experiments in this axisymmetric geometry show that for low and equal Reynolds numbers, Re, at both nozzles, the flow remains symmetric about the plane halfway through the nozzle exits and the stagnation plane is located halfway between the two jets. When Re is increased past a critical value, asymmetric flow fields are obtained even when the momentum fluxes of the two opposed streams are equal. For unequal Re at the jet exits, when the fixed velocity (and the corresponding Reynolds number, Re₁) of one stream is low, the stagnation plane location, SPL, changes smoothly with the Re₂. For high enough Re₁, a hysteretic jump of SPL is observed. Particle Image Velocimetry and flow visualization demonstrate that within the hysteretic range, the two stable flow fields are anti-symmetric. The experimental setup is also studied with transient incompressible flow simulations using a spectral element solver. It is found that to accurately model the flow, we either need to extend the domain into the nozzles, or impose experimental velocity profiles at the nozzle exits. As in the experiments asymmetric flows are obtained past a critical Re. Finally, bifurcation analysis using a Newton-Picard method shows that the transition from symmetric to asymmetric flows results from the loss of stability of the symmetric flows at a pitchfork bifurcation.     

Complexity of Weak Bisimilarity and Regularity for BPA and BPP

It is an open problem whether weak bisimilarity is decidable for Basic Process Algebra (BPA) and Basic Parallel Processes (BPP). A PSPACE lower bound for BPA and NP lower bound for BPP have been demonstrated by Stribrna. Mayr achieved recently a result, saying that weak bisimilarity for BPP is Π^p₂-hard. We improve this lower bound to PSPACE, moreover for the restricted class of normed BPP.Weak regularity (finiteness) of BPA and BPP is not known to be decidable either. In the case of BPP there is a Π^p₂-hardness result by Mayr, which we improve to PSPACE. No lower bound has previously been established for BPA. We demonstrate DP-hardness, which in particular implies both NP and co-NP-hardness.In each of the bisimulation/regularity problems we consider also the classes of normed processes.Note: full version of the paper appears as [18].     

Estimation of the mean of stationary and nonstationary Ornstein-Uhlenbeck processes and sheets

We consider the problem of estimating an unknown parameter m in case one observes in an interval (rectangle) stationary and nonstationary Ornstein-Uhlenbeck processes (sheets), which are shifted by m times a known deterministic function on the interval (rectangle). It turns out that the maximum likelihood estimator (MLE) has a normal distribution and, for instance, in case of the sheet this MLE is a weighted linear combination of the values at the vertices, integrals on the edges, and the integral on the whole rectangle of the weighted observed process. We do not use partial stochastic differential equations; we apply direct discrete time approach instead. To make the transition from the discrete time to the continuous time, a tool is developed, which might be of independent interest.     

Evaluating and improving the effectiveness and efficiency of design process communication

Project information management research enables the efficient exchange of information, but does not effectively communicate process. Design process management research effectively communicates processes, but with methods too inefficient to be adopted in practice. The lack of methods for effective and efficient design process communication manifests as a struggle for Architecture, Engineering, and Construction industry professionals to: (1) collaborate within projects, (2) share processes between projects, and (3) understand processes across projects to strategically invest in improvement. These struggles motivate the paper’s first contribution: a research method for evaluating a design management methodology’s ability to effectively and efficiently communicate design processes. As a second contribution, this paper validates the Design Process Communication Methodology (DPCM). DPCM specifies elements and methods for exchanging and organizing digital information to support knowledge-intensive design processes. Cloud computing enables the operationalization of DPCM as a tool that enables interaction with a project’s information. Results from this operationalization demonstrate that designers employing DPCM accurately capture processes with little effort. When collaborating, improved process clarity and information consistency result in less rework, and positive iteration enables increased consideration of multi-disciplinary design trends. Designers share processes between project teams with fewer process mistakes. DPCM enables the understanding of processes providing more insights into the relationships between design integration and project performance; and more opportunities for strategic investment in improved processes.     

Use and misuse of SPSS

This paper reports a survey of the use of SPSS at a major nationwide university computer centre. SPSS was modified to output a record each time it was used reporting:

• (a) who was using the program;
• (b) resource consumption;
• (c) size of data set;
• (d) SPSS commands used;
• (e) SPSS syntax errors which occurred;
• (f) job status at termination.

We found that SPSS was used 3,000-4,000 times monthly by a user community from over 30 departments. Resource consumption varied greatly but the majority of jobs are quite small in our terms. Data sets also varied greatly but most were up to 300 cases by up to 20 variables. The majority of users employ a subset of the SPSS command language and attempt only one ‘procedure’ in each run. About 30 per cent of jobs fail due to a user error in the syntax, and we found considerable consistency from month to month in the syntax errors made. Our detailed observations have many implications for the ongoing development of SPSS and its documentation, for the users, and for those who teach or advise in SPSS.     

Design and development of a MEMS butterfly resonator using synchronizing beam and out of plane actuation

This paper presents beam modeling techniques for maximizing mechanical sensitivity of a butterfly resonator for gyroscopic applications. We investigate the geometric aspects of synchronizing beam that connects the wings of a butterfly resonator. Our results show that geometric variation in the synchronizing beam can have a large effect on the frequency split and sensitivity of the device. The model simulation shows a sensitivity of \( 10^{ - 12} \)\( (m/^\circ /s) \) for a frequency split of 10 Hz resulting from the optimized synchronized beam. Out of plane actuation was developed to drive and sense the resonators displacement. Fabricated butterfly resonators were tested, and the experimental results show a frequency split of 305 Hz and 400 Hz while the model illustrated a split of 195 Hz and 330 Hz respectively. The design and analysis presented in this paper can further aid the development of MEMS butterfly resonators for inertial sensing applications.

     

Sorting and Counting Networks of Arbitrary Width and Small Depth

We present the first construction for sorting and counting networks of arbitrary width that requires both small depth and small constant factors in the depth expression. Let w be the product w = p ₀ ⋅ p ₁ ⋅s p _n-1 , whose factors are not necessarily prime. We present a novel network construction of width w and depth O(n ² ) = O(log ² w) , using comparators (or balancers) of width less than or equal to max(p _i ) . This construction is practical in the sense that the asymptotic notation does not hide any large constants. An interesting aspect of this construction is that it establishes a family of sorting and counting networks of width w , one for each distinct factorization of w . A factorization in which max(p _i ) is large and n is small yields a network that trades small depth for large comparators (or balancers), and a factorization where max(p _i ) is small and n is large makes the opposite tradeoff. Received June 18, 2001. Online publication October 30, 2001.     

Metabolic cost and subjective assessment of palletizing and subsequent recovery

Twenty-one male blue collar workers repeatedly lifted (palletized) a box weighing 22 kg six times min^-1 for 5 min to a shelf of fixed height. The experimental conditions included two planes of lifting (symmetries), two shelf clearances, and three headrooms. The metabolic (heart rate, caloric cost and ventilation volume) and psychophysical variables (rate of perceived exertion, RPE; visual analogue score, VAS; and body part discomfort ratings, BPDR) were measured during resting, palletization, and recovery phases. In palletization the heart rate and metabolic cost ranged between 25 to 35% of the maximal aerobic capacity. Of the three factors only headroom had a significant effect on metabolic cost (p < 0.02) and the BPDR for low back (p < 0.05). In the recovery phase only headroom had significantly effect (p < 0.001) on metabolic cost. The metabolic recovery took 10 min; however, recovery measured through psychophysical indices appeared to continue for 20 min.     

Shape and orientation of revolution surfaces from contours and reflections

The reconstruction of shape and pose of a solid of revolution from a single image is addressed. When there is no cross section, whose contour can be extracted from the image, this problem is underdeterminate; therefore, a reflection from a point light source is used in addition to the contour information. Under the orthoperspective hypothesis, when axial-symmetric reflection model is applicable, the reflection appears along a meridian of the revolution surface. This fact is exploited in order to determine both the orientation of the revolution axis and the shape of the profile. Promising experimental results have been obtained.