Systems Dynamics Applications to Industrial and Other Systems

This paper describes the results of ideas derived from the work of the System Dynamics Research Group at the University of Bradford. The basic underlying ideas of System Dynamics are outlined and examples of their application to a number of practical problems given. The major results obtained and the lines of research suggested by these studies are discussed.     

A Systems Approach to Management

A procedure is outlined for deciding the mix of price and variable non-price features, such as quality, delivery, service or financing, to be included in a bid. The level of each non-price feature is set independently by comparing incremental spending against the alternative price reduction and basing the choice on value to the faction in the customer organization expected to dominate in the choice of the successful bid. Divergence from competition on all non-price features, both fixed and variable, is then taken into account in setting price by calculating a net price equivalent of feature differences as against each competitor. For any given markup the probability of success against a competitor over whom there is a net advantage is the same as that for an equivalently lower markup were price to be the sole basis for allocating the order.     

The Systems Approach to Hospitals

By exploiting the relationship between scheduling and sorting, this paper describes a functional heuristic algorithm for seeking a quick and approximate solution to the n-job, M-machine flowshop scheduling problem under the assumption that all jobs are processed on all machines in the same order and no passing of jobs is permitted. The proposed functional heuristic algorithm can be executed by hand for reasonably large size problems and yields solutions which are closer to optimal solutions than those obtained by Palmer's slope index algorithm.     

Application of Homotopy Methods to Power Systems

In this paper, the application of homotopy methods to the load flow multi-solution problems of power systems is introduced. By the generalized Bernshtein theorem, the combinatorial number C2n^m is shown to be the BKK bound of the number of isolated solutions of the polynomial system transformed from load flow equations with generically chosen coefficients. As a result of the general Bezout number, the number of paths being followed is reduced significantly in the practical load flow computation. Finally, the complete P-V cures are obtained by tracking the load flow with homotopy methods.     

离散广义系统的平稳振荡

为了研究离散广义系统的平稳振荡，本文利用广义Ｌｙａｐｕｎｏｖ函数方法，给出了一个ｍ周期解存在的充要条件，得出了离散广义系统的周期解的存在性、唯一性、稳定性的有关定理，进而研究具有某种分解的复杂离散广义系统的平稳振荡问题，方法简单易行．     

组合系统的行为化方法

在行为框架下研究线性微分组合系统的建模问题 .建立了 n个子系统串、并联组合系统的行为化模型 ,给出了其能控性、能观性的判别条件 .分析过程表明用行为化方法对组合系统的研究有着比传统方法更便捷、适用的模型类更广等优点 .     

Energy-Preserving Integrators Applied to Nonholonomic Systems

We introduce energy-preserving integrators for nonholonomic mechanical systems. We will see that the nonholonomic dynamics is completely determined by a triple \(({{\mathcal {D}}}^*, \varPi , \mathcal {H})\), where \({{\mathcal {D}}}^*\) is the dual of the vector bundle determined by the nonholonomic constraints, \(\varPi \) is an almost-Poisson bracket (the nonholonomic bracket) and \( \mathcal {H}: {{\mathcal {D}}}^*\rightarrow \mathbb {R}\) is a Hamiltonian function. For this triple, we can apply energy-preserving integrators, in particular, we show that discrete gradients can be used in the numerical integration of nonholonomic dynamics. By construction, we achieve preservation of the constraints and of the energy of the nonholonomic system. Moreover, to facilitate their applicability to complex systems which cannot be easily transformed into the aforementioned almost-Poisson form, we rewrite our integrators using just the initial information of the nonholonomic system. The derived procedures are tested on several examples: a chaotic quartic nonholonomic mechanical system, the Chaplygin sleigh system, the Suslov problem and a continuous gearbox driven by an asymmetric pendulum. Their performance is compared with other standard methods in nonholonomic dynamics, and their merits verified in practice.

     

Applying Control Systems to Industrial Relations

A model of industrial relations is developed distinguishing between rule making—the central purpose of collective bargaining—and the subsequent steps of rule implementation, rule maintenance and rule adaptation. A further step is identified as rule breaking or rule avoidance, indicating the incompleteness of the rule-making-application-maintenance process. The reasons for rule breaking are examined focusing on pressures exerted in the production system and the underlying philosophy of negotiation as a satisficing rather than optimising activity. The role that formal control systems can play in making the industrial relations system more effective is examined. A distinction is drawn on the one hand between strategic planning, management control and operational control and on the other hand between three levels of feedback from the control system to the industrial relations system. The object of controls is seen firstly to encourage rule maintenance, secondly to aid rule adaptation and thirdly to assist in the strategic planning and design of the industrial relations system.     

Return to Equilibrium for Pauli-Fierz Systems

We study ergodic properties of Pauli-Fierz systems – W*-dynamical systems often used to describe the interaction of a small quantum system with a bosonic free field at temperature $ T \geq 0 $. We prove that, for a small coupling constant uniform as the positive temperature $ T \downarrow 0 $, a large class of Pauli-Fierz systems has the property of return to equilibrium. Most of our arguments are general and deal with mathematical theory of Pauli-Fierz systems for an arbitrary density of bosonic field. Communicated by Gian Michele Graf submitted 22/09/02, accepted: 06/05/03     

A Semigroup Approach to Queueing Systems

We prove asymptotic stability of the solutions of equations describing a simple queueing system consisting of two machines separated by a finite storage buffer. Following an approach by G. Gupur, we apply the theory of C₀-semigroups and spectral theory of positive operators.     

Algebraic Approaches to Stability Analysis of Biological Systems

In this paper, we improve and extend the approach of Wang and Xia for stability analysis of biological systems by making use of Gr?bner bases, (CAD-based) quantifier elimination, and discriminant varieties, as well as the stability criterion of Liénard and Chipart, and showing how to analyze the stability of Hopf bifurcation points. The stability and bifurcations for a class of self-assembling micelle systems with chemical sinks are analyzed in detail. We provide experimental results with comparisons for 15 biological models taken from the literature.      

Application of Computer Simulation to Freight Transport Systems

Selecting an appropriate simulation-model structure for complicated, large-scale transport systems is a non-trivial and challenging task. This paper reports practical research which evaluates a number of alternative model structures for the Arizona state-highway network system based on the immediate dependency on input data obtained from a multistage mail survey. The most appropriate topology structure selected is a data-driven, link-based, discrete-event simulation model using conditional probability branching logic. Separating model and data makes the simulation model a generic traffic-routeing logic processor that is easy to use and does not require simulation skills. Different transport systems can easily be accommodated by simply changing input data. The model is validated by comparative analysis of input data using statistical techniques. An upper bound on the size of the valid network is thus obtained.     

A New Approach to Analysis of Polling Systems

In this paper, we consider polling systems with J stations with Poisson arrivals and general service distributions attended by a cyclic server. The service discipline at each station is either exhaustive or gated. We propose a new approach to analysis of the mean waiting times in the polling systems. The outline of our method is as follows. We first define the stochastic process Q that represents an evolution of the system state, and define three types of the performance measures W _i ,H _i and F _i , which are the expected waiting times conditioned on the system state. Then from the analysis of customers at polling instants, we find their linear functional expressions. The steady state average waiting times can be derived from the performance measures by simple limiting procedures. Their actual values can be obtained by solving J(J+1) linear equations.