An Approximate Formula for Waiting Time in Single Server Queues

This note reports the development of a new approximation formula for the mean wait in queue of a single-server queue. Use of the formula requires knowledge of only the first two (2) moments of the interarrival and service time distributions. Comparison of the proposed approximation to existing techniques is included.     

Analysis and approximation for the performance of a workstation with various types of setups

Setups commonly exist in flexible manufacturing systems. Modelling the queue time correctly is of fundamental importance in evaluating the performance of manufacturing systems. An insightful classification is the first step towards correct modelling. Through the observation of practical production lines, two types of setups are classified: state-induced setups and product-induced setups. The product-induced setups can be a changeover setup or a replacement setup. Changeover setups are induced by switching manufacturing processes between products, whereas replacement setups are caused by changing components or consumables. Approximate models for the mean queue time of different setup types are proposed based on their distinct properties. The proposed models are validated with simulations and perform well in the examined cases.     

A constraint‐based approach to the modelling and analysis of packaging machinery

To enable packaging machinery manufacturers to compete at an international level, it is necessary to introduce them to more advanced design methods and technologies. For years, the evolution of packaging machinery has relied heavily on trial‐and‐error methods. The demands for continual increases in the performance capabilities of the machines, escalating legislation, environmental directives and changes in the characteristics of the product require rapid development of existing machine designs and the creation of new machines. This paper discusses the needs of SME packaging machinery manufacturers and identifies their requirements for methods in support of the design and redesign of packaging machinery. The need to identify, capture and manipulate design knowledge is critical for SMEs, where all too often design records are incomplete. Furthermore, a systems modelling approach that provides for support over the conceptual, embodiment and detailed design phases is essential for the rapid and effective development of designs. In order to meet these requirements, a methodology is proposed which incorporates ‘constraint modelling’ techniques. The methodology provides for experimental investigation and computer‐based modelling, which together aid the designer in gaining a fundamental understanding of the design problem. This enables the identification and representation of design knowledge, the determination of the limitations of an existing design, the evaluation of alternative designs and redesign strategies, as well as the embodiment, refinement and optimization of design solutions. The theory of ‘constraint modelling’ is discussed and the various phases of the methodology described. The applications of the methodology to a new machine design and a redesign program are also detailed. Copyright © 2001 John Wiley & Sons, Ltd.     

Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times

This paper is motivated by the performance evaluation of circulating vertical conveyor systems (CVCSs). CVCSs are bulk queues of transportation type. These material handling systems feature generally distributed inter-arrival times, which can be longer than the bulk service time. This leads to interdependencies between the number of arrivals in consecutive service intervals and the number of loads in the queue. We propose a new discrete-time approach for the steady-state analysis of such bulk service queues of transportation type with general arrival and service processes and finite server and limited queue capacities. The approach is based on a finite Markov chain that generates complete probability distributions for the key performance measures, including the queue length, waiting time and departing batch size. The proposed approach is exact in the cases of discrete-time slots, e.g. as in communication systems. We investigate the discretisation error that arises if the approach is used as an approximation for the continuous time using a numerical comparison to a discrete-event simulation. Moreover, we examine the impact of arrival stream variability on the system performance and compare the positive effects of a higher frequency of server visits with the effects arising from larger pickup capacities.     

Survival Science: Crisis Disciplines and the Shock of the Environment in the 1970s1

The 1970s mark a critical departure point in the history of science. The rise of the environmental crisis prompted not just new avenues of scientific inquiry but also the integration of scientific expertise into complex interactions with politics and society. This paper investigates the history of the new ‘crisis disciplines’ that emerged in response to explicit fears that the world was on the verge of ecological collapse. Crisis disciplines – a term coined by the conservation biologist Michael Soulé – engage in the urgent and reactionary pursuit of solutions to pressing environmental problems and the evidence scientists bring to bear on their work. Crisis disciplines involve acting ‘before knowing all the facts’, and therefore constitute ‘a mixture of science and art, and their pursuit requires intuition as well as information’. Combined, diverse crisis disciplines constitute a new kind of ‘survival science’, which emerged in the 1970s.     

Graph-based models to classify effective collaboration in SME networks

During the last decades, globalisation of goods’ markets and large disequilibrium amongst labour markets in different countries had a remarkable impact on small and medium enterprises – SMEs, which have been for many years the actual engine of industrial development in Europe. An ‘antidote’ to this crisis is the development of more profitable SME networks in the forms of either ‘clusters’, ‘competitiveness poles’, ‘industrial districts’ or ‘scientific parks’. A more strategic approach is needed, that builds upon existing SME aggregations and explores their main strong and weak points, such as to establish a framework for new innovative networks. The goal of this study is to offer a method to analyse the main features of existing SME networks, in order to offer to the network coordination/management committees some key parameters (KP) to evaluate the network composition and potentially to select networks modifications. The study analyses an archive of industrial networks provided by the European project CODESNET and defines different types of networks and their main KP. A further result of the analysis will be the modelling of each network type in terms of a specific graph. Graphs give a more intuitive representation of the network and an easier comprehension of its organisation. In a second stage, by a probabilistic approach, the authors propose an identification procedure to classify existing and new networks.     

A stochastic approach to quantifying the blur with uncertainty estimation for high-energy X-ray imaging systems

One of the primary causes of blur in a high-energy X-ray imaging system is the shape and extent of the radiation source, or ‘spot’. It is important to be able to quantify the size of the spot as it provides a lower bound on the recoverable resolution for a radiograph, and penumbral imaging methods – which involve the analysis of blur caused by a structured aperture – can be used to obtain the spot’s spatial profile. We present a Bayesian approach for estimating the spot shape that, unlike variational methods, is robust to the initial choice of parameters. The posterior is obtained from a normal likelihood, which was constructed from a weighted least squares approximation to a Poisson noise model, and prior assumptions that enforce both smoothness and non-negativity constraints. A Markov chain Monte Carlo algorithm is used to obtain samples from the target posterior, and the reconstruction and uncertainty estimates are the computed mean and variance of the samples, respectively. Synthetic data-sets are used to demonstrate accurate reconstruction, while real data taken with high-energy X-ray imaging systems are used to demonstrate applicability and feasibility.     

Enhancement of continuous estimation of distribution algorithms by density ensembles

In this article, two novel density ensembles methods – the resampling method and the subspaces method – are proposed for enhancing existing continuous Estimation of Distribution Algorithms (EDAs). In ‘resampling continuous EDAs’, a population of densities of the selected promising solutions is obtained by iteratively using the resampling operator and the density estimation operator, and new candidate solutions at the next generation are reproduced through sampling from all obtained densities of promising solutions. In ‘subspaces continuous EDAs’, a population of densities is obtained by randomly choosing a subset of all variables and estimating the density of all selected high-quality solutions in this subspace. The above steps iterate and many densities of high-quality solutions in different subspaces can be obtained. New candidate solutions at the next generation are reproduced through perturbing the old promising solutions by sampling from the densities in different subspaces. The results upon convergence with different numbers of variables and the effects of parameters on the performance of the density ensembles methods for continuous EDAs are studied based on the experimental results.     

Random matrix eigenvalue problems in structural dynamics

Natural frequencies and mode shapes play a fundamental role in the dynamic characteristics of linear structural systems. Considering that the system parameters are known only probabilistically, we obtain the moments and the probability density functions of the eigenvalues of discrete linear stochastic dynamic systems. Current methods to deal with such problems are dominated by mean‐centred perturbation‐based methods. Here two new approaches are proposed. The first approach is based on a perturbation expansion of the eigenvalues about an optimal point which is ‘best’ in some sense. The second approach is based on an asymptotic approximation of multidimensional integrals. A closed‐form expression is derived for a general rth‐order moment of the eigenvalues. Two approaches are presented to obtain the probability density functions of the eigenvalues. The first is based on the maximum entropy method and the second is based on a chi‐square distribution. Both approaches result in simple closed‐form expressions which can be easily calculated. The proposed methods are applied to two problems and the analytical results are compared with Monte Carlo simulations. It is expected that the ‘small randomness’ assumption usually employed in mean‐centred‐perturbation‐based methods can be relaxed considerably using these methods. Copyright © 2006 John Wiley & Sons, Ltd.     

The operating characteristics of‘ single’ and ‘ double’ non-mechanical flow line systems

Two types of ‘ series queue ’ type flow-lines are simulated. Both are balanced, mechanically unpaced systems with provision for interstage buffer stocks. The effects of buffer capacity, service-time variability and number of stations on the output efficiency of both types of line are examined and comparisons are made.     

Crushing behaviour of the energy absorbing 'tensor skin' panels

ABSTRACT Research results concerning the simulation of the crushing behaviour of composite systems with energy absorption characteristics are presented in the present work. The study is focused on the ‘tensor skin’ concept, an energy absorbing composite system that was originally developed to improve the crashworthiness of helicopters under water impact and which is promising for utilization in the construction of the lower part of composite fuselage aircraft. The ‘tensor skin’ concept comprises a folded or corrugated composite construction, which upon loading unfolds by forming ‘plastic hinges’, leading to an increase in the load bearing capability of the structure. The numerical modelling issues and the critical aspects of the simulation are discussed. Verification of the numerical simulation procedure is performed by experimental work. The experimental results utilized to assess and validate the numerical procedure were derived within the European Research Project ‘Design for Crash Survivability – CRASURV’ (BRITE – Aeronautics Area). The results of the simulations are generally in good agreement with experimental data.     

Multi-class queueing models for performance analysis of computer systems

Queueing models, networks of queues in particular, have been found especially useful for estimating the performance of computer systems. Networks of queues with multiple customer classes provide a flexible framework for modelling computer systems, where a rich set of analytical results and techniques are available. When because of the complexity of the system being modelled the analytical results cannot be applied directly, they often point to fairly accurate approximation schemes. In this paper, we present a brief survey of some of the important results and techniques from the theory of multi-class queueing networks. We also present a case study to illustrate how these results and techniques are used in a real-life situation where many of the modelling constraints are violated.     

Modelling of material handling systems for facility design in manufacturing environments with job-specific routing

Traditionally, flow times distance is used as a surrogate for cost in facility design. However, this performance measure does not fully capture the impact of facility design decisions on operational performance measures such as cycle time and work-in-progress in the system, which are often more meaningful for managers, especially in a manufacturing environment. To better measure operational performance, modelling of material handling systems using a queueing network must be integrated in the facility design process. A number of approaches are discussed in the facility design literature for modelling material flow using queueing networks. In these approaches, Poisson arrival or Markovian job routing assumptions have been used. However, for many manufacturing environments, these assumptions lead to an inaccurate estimation of the material handling system's performance and thus lead to poor facility designs. Incorporating more general queueing results for non-Markovian systems is difficult, however, because the facility design process must investigate a large number of potential solutions and thus the results from the queueing models for the material handling system must be quickly obtained. In this paper, the need for more general queueing models of material handling systems in facility design is confirmed. Then, an approach based on multi-class queueing models is adapted to capture the change in variability of the system performance caused by both different arrangements of workstations in the facility and different arrival processes to the workstations due to the job routing in a computationally efficient manner. The proposed modelling approach is shown to provide more accurate results than previous methods used in facility design based on numerical comparisons with results from discrete-event simulation.     

Underestimating the bullwhip effect: a simulation study of the decomposability assumption

We investigate the assumption of decomposability as it pertains to modelling the bullwhip effect in multi-stage supply chains. Decomposing a multi-stage supply chain into a set of node pairs, each of which can be efficiently represented with a two-stage model, is a common modelling technique when analysing the bullwhip effect in supply chains. This approach depends on the validity of the decomposability assumption since most supply chains are coupled systems that are a logical fit for singular, or ‘monolithic’, multi-stage models. We utilise a simulation study to compare decomposition-based supply-chain models with monolithic models and determine if decomposition modelling significantly alters the predicted severity of the bullwhip effect. We find decomposition-based models exhibit a significantly lower level of bullwhip effect than monolithic models of the same supply chain. The systematic underestimation of the bullwhip effect by decomposition-based models indicates that the assumption of decomposability is flawed. Our study also confirms previous work showing the significant benefit of using actual, instead of approximate, lead-time demand information. We discuss implications for supply-chain modelling, supply-chain design, and data collection.     

Human–machine interaction theories and lane departure warnings

A technological race toward always ever-increasing automation is engaged, a race in which automation users are hardly considered. This explains why more automation is not necessarily for the best. A variety of human–machine interaction (HMI) theories co-exist. First, those HMI theories and predictions for lane departure warnings systems (LDWS, assisted driving automation) are described. Second, a synthesis of the key questions currently addressed by empirical data on LDWS is offered. Lastly, a new model of human–machine cooperation modelling is proposed. The model has been inspired by previous theories and empirical data collected with LDWS-assisted driving. Interestingly, automation such as LDWS seems to avoid the ‘ironies of automation’ with no negative effects on human performance. However, a major issue to be addressed is poor automation acceptance. While the focus was set on LDWS to offer a complete overview for this type of device, the model may be extended to other warning assistance devices.     

Modelling of the interphase in polymer-matrix composite material systems

The interphase, or transition region between fibre and matrix in composite material systems, is known to play an essential role in the performance of composite components. In fact, it has recently been discovered that the interaction and cooperative action of the constituents in the system control the durability of such systems, in stark contrast to other behaviour characteristics such as stiffness and quasi-static (or ‘instantaneous’) properties wherein the constituents contribute to the properties, essentially, in proportion to their presence. Hence, this ‘systems effect’ has become the focus of much attention, and the object of modelling efforts. However, modelling the interphase with properly set boundary value problems is a considerable challenge, especially because the properties in these transition regions are often a function of spatial position, i.e., they are non-uniform as a function of position. The author has constructed models of the interphase region which admit this non-uniformity, and has achieved solutions to several classes of these problems. The present paper will describe the general problem of the ‘systems effect’, discuss the practical issues of how the interface enters micromechanical models of strength and durability, and present models for the interphase region that include the variability of material properties in those transition regions. Special attention will be given to the contrasts between these considerations and the rule-of-mixtures concepts that currently pervade the field, and to the importance of these differences to the practical opportunities offered by the ability to properly model and “design’ interphase regions in polymer-matrix composites.     

Testing a theoretical model underlying the ‘Toyota Way’ – an empirical study involving a large global sample of Toyota facilities

In this paper, we empirically test the theoretical model underlying the Toyota Way (TW), based on data obtained from Toyota’s logistics, sales and marketing functions across 27 countries. TW is the result of Toyota attempting to codify its culture to the global community. Using structural equation modelling techniques we show that the TW-associated measures challenge, kaizen, genchi genbutsu, respect and teamwork do adequately operationally define the TW; the first three measures corresponding to the construct ‘process improvement’ and the final two measures corresponding to the construct ‘people development’. Empirically, people development is found to have no direct effect on how the TW is deployed across a business unit. However, people development is found to be indirectly related to TW deployment through the mediating effect of process improvement. Our study provides quantitative evidence that while the intangible aspects of the TW (modelled as people development) may not directly relate to the results, they are an integral component of a complete implementation of the TW and related ‘Lean’ systems. By logical extension, this provides support for adoption of a holistic and long-term strategy, integrating soft and hard elements, by those organisations attempting to implement and sustain Toyota-style systems.     

Fatigue of asphaltic dike revetments under wave loading: validation and improved modelling

In the Netherlands, 600 km of the sea dikes are protected by an asphaltic revetment that has to resist considerable wave loads with a significant wave height of up to 4.5 m. The subsoil is normally sandy, and the asphalt layer acts as a protection against erosion. The asphalt layer can fail as a result of fatigue due to repeated loading under storm conditions. In case of very high wave loads, the asphalt can fail after a few large waves. Ageing of the asphalt has a large effect on the resistance against fatigue. Therefore, periodic monitoring is prescribed by law. This monitoring consists of: falling weight deflection measurements, lab testing, radar measurements, visual inspection and calculations with the software program ‘Wave impact’ (‘Golfklap’) in order to determine the strength under storm conditions. The subsoil bearing capacity determines how the asphaltic revetment deforms under wave loading. It is still unsure how the soil will behave and failure mechanisms may occur that are different from fatigue due to elastic bending, the latter being part of the current approach. A first step to validation consisted of finite element modelling that was compared with experiments on medium scale (scale 1:4). In these experiments, the wave attack was simulated by a mechanical system that was placed on a 5 cm thick asphalt plate on a sand layer. The deflection of the asphalt was measured. Crack development was detected by means of strain gauges. It was found that – as a first approximation and excluding extreme wave loads – the fatigue behaviour of aged asphalt on a typical sandy base under wave attack can be described with a combination of a relatively simple elastic–plastic response to wave loads and a special fatigue line that takes into account the flexural strength of the aged asphalt.     

Variability modelling and balancing of stochastic assembly lines

In a production flow line with stochastic environment, variability affects the system performance. These stochastic nature of real-world processes have been classified in three types: arrival, service and departure process variability. So far, only service process – or task time – variation has been considered in assembly line (AL) balancing studies. In this study, both service and flow process variations are modelled along with AL balancing problem. The best task assignment to stations is sought to achieve the maximal production. A novel approach which consists of queueing networks and constraint programming (CP) has been developed. Initially, the theoretical base for the usage of queueing models in the evaluation of AL performance has been established. In this context, a diffusion approximation is utilised to evaluate the performance of the line and to model the variability relations between the work stations. Subsequently, CP approach is employed to obtain the optimal task assignments to the stations. To assess the effectiveness of the proposed procedure, the results are compared to simulation. Results show that, the procedure is an effective solution method to measure the performance of stochastic ALs and achieve the optimal balance.     

Optimization of discrete event systems via simultaneous perturbation stochastic approximation

We investigate the use of simultaneous perturbation stochastic approximation for the optimization of discrete-event systems via simulation. Application of stochastic approximation to simulation optimization is basically a gradient-based method, so much recent research has focused on obtaining direct gradients. However, such procedures are still not as universally applicable as finite-difference methods. On the other hand, traditional finite-difference-based stochastic approximation schemes require a large number of simulation replications when the number of parameters of interest is large, whereas the simultaneous perturbation method is a finite-difference-like method that requires only two simulations per gradient estimate, regardless of the number of parameters of interest. This can result in substantial computational savings for large-dimensional systems. We report simulation experiments conducted on a variety of discrete-event systems: a single-server queue, a queueing network, and a bus transit network. For the single-server queue, we also compare our work with algorithms based on finite differences and perturbation analysis.