Mathematical programming time-based decomposition algorithm for discrete event simulation

Mathematical programming has been proposed in the literature as an alternative technique to simulating a special class of Discrete Event Systems. There are several benefits to using mathematical programs for simulation, such as the possibility of performing sensitivity analysis and the ease of better integrating the simulation and optimisation. However, applications are limited by the usually long computational times. This paper proposes a time-based decomposition algorithm that splits the mathematical programming model into a number of submodels that can be solved sequentially to make the mathematical programming approach viable for long running simulations. The number of required submodels is the solution of an optimisation problem that minimises the expected time for solving all of the submodels. In this way, the solution time becomes a linear function of the number of simulated entities.     

The costs and benefits of bowel cancer service developments using discrete event simulation

Colorectal cancer includes cancerous growths in the colon, rectum and appendix and affects around 30?000 people in England each year. Maximizing health benefits for patients with colorectal cancer requires consideration of costs and outcomes across the whole service. In an era of scarce healthcare resources, there is a need to consider not only whether technologies and services may be considered clinically effective, but also whether they are cost-effective, that is, whether they represent value for money for the health service. Through the development of a whole disease model, it is possible to evaluate the cost-effectiveness of a range of options for service development consistently within a common framework. Discrete event simulation has been used to model the complete colorectal cancer patient pathway from patient presentation through to referral and diagnosis, treatment, follow-up, potential recurrence, treatment of metastases and end-of-life care. This simulation model has been used to examine the potential cost-effectiveness of different options for change across the entire colorectal cancer pathway. This paper provides an empirical demonstration of the potential application of modelling entire disease areas to inform clinical policy and resource allocation decision-making.     

Numerical simulation of dense fluid-particle flows using computational fluid dynamics (CFD) and discrete element method (DEM)

Discrete Element Method (DEM) has been successfully coupled with Computational Fluid Dynamics (CFD) in the framework of OpenFOAM an open source CFD simulation code. In the current study, at first the model is validated with the simple test case of spherical particle comparing the results with the analytical solution. Then the simulation of a gaseous fluidized bed is considered. The coupled mass and momentum balance equations are used to calculate the flow behavior, particle fluidization and bubble formation. The dimensions of the simulation domain are similar to Link et al. (2005) but with different stiffness of particles. The higher velocity of gaseous fluid relative to particles entering through a jet causes the particles to fluidize. The particles behavior, fluidization, bubble formation and the velocity vectors of particles show a good agreement with the literature. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Assessment of a 7-day turn-around for the reporting of cervical smear results using discrete event simulation

A discrete event simulation (DES) model has been used to analyse options with the potential to facilitate a 7-day turn-around of cervical screening results in England, with the aim of reducing the anxiety experienced by the participants. Detailed information regarding the cervical screening process collected from the NHS Cancer Screening Programme, research papers, current national guidelines and five cytology laboratories in England was used to inform a DES model representing a typical laboratory. A number of options for change were evaluated. The simulation model suggested that it would be feasible to improve the result turn-around times from 95% within 11 weeks to 95% within 2 weeks; and from an average current result turn-around time of around 6 weeks, to over 50% within 7 days. Moreover, the options for change should be cost saving in the long term.     

A discrete event simulation of the adult trabecular skeleton

A verified, but unvalidated discrete event computer simulation of the adult bone remodeling system is presented. It implements the unit-based theory of adult skeletal remodeling proposed by Frost. The simulation allows a scientist to design trials involving the adult skeleton by inputting the times of administration, and effects (remodeling cycle initiation, activity, lifespan, proliferation) on bone cells of drugs, according to his current understanding of their mechanisms of action. The simulation constantly tracks the contents and age of all bone structural units, updating each every 2.5 days, to reflect ongoing bone resorption, osteoid formation, osteoid mineralization, and the passage of time. In reality, the simulation tabulates the results of remodeling cycles which take place during the trial. The investigator may receive histomorphometric, densitometric, and biochemical data, as indicators of skeletal status, as often as every 2.5 days during the trial, far more frequently than is usually done in real experiments. At the conclusion of a trial, he may plot/review time-related graphs of the interim data. Validation trials of aging, “activation,” and clodronate administration, are presented. This simulation, when validated, could be a cost-saving device because it can increase the chance for success of any adult skeletal experiment by guiding investigators toward taking fewer, better selected measurements. Furthermore, when refined to include color graphics display of skeletal structure, it could be the basis for an educational device. This could help both the medical community and the public by providing a more ready understanding than can currently be had of adult skeletal remodeling, its relationship to adult metabolic bone disease, and the prevention/treatment of adult metabolic bone disease (e.g. osteoporosis).     

Demand uncertainty in construction supply chains: a discrete event simulation study

The delivery of construction projects is typically an assembly operation involving a high number of subassemblies and materials brought on site by the supply chain. However, although supply chain management in construction has attracted significant attention, paradoxically little focus has been placed on construction supply networks and operations. This paper places emphasis on supply chain operations by looking at the logistics function of construction material suppliers. Specifically, the paper examines the impact of demand uncertainty on supply chain performance in order to assess the capacity of material distribution companies to provide a timely and cost-efficient service to the construction industry. The study adopts a discrete event simulation approach to assess the impact of demand fluctuations on two crucial logistics performance measures; lead time and cost efficiency. The results show that lead times are particularly sensitive to fluctuations under conditions of low demand. The findings also reveal that, although transport is a significant cost element for lower demand levels, higher inventory costs result in a negative exponential relationship between increasing demand and cost efficiency.     

A discrete event simulation model in the case of managing a software project

The design and development of large-scale software projects is a complex endeavor, often facing problems like cost and schedule overruns as well as low quality. Over the last years the management of software development projects has been recognized as the cornerstone point of seeking improvement and solutions. Simulation modeling of the software project process is gaining interest among academics and practitioners, as a method to tackle the complex questions with which relevant enterprises are confronted. It offers support on several issues, such as defining software product development strategies, decision-making regarding process improvement and training, in a time span ranging from a short portion of the life cycle to long term product evolution, with organization-wide implications. The aim of this work is to implement a model simulating a core part of a software project process, enabling the estimation of several project development details such as delivery times and quality metrics. The purpose of the model is to assist project managers in control and monitoring, but also in identifying the best planning alternatives. The model scope covers a portion of the life cycle of an incremental software development venture.     

Evaluating the quality of online optimization algorithms by discrete event simulation

A key feature of dynamic problems which offer degrees of freedom to the decision maker is the necessity for a goal-oriented decision making routine which is employed every time the logic of the system requires a decision. In this paper, we look at optimization procedures which appear as subroutines in dynamic problems and show how discrete event simulation can be used to assess the quality of algorithms: after establishing a general link between online optimization and discrete event systems, we address performance measurement in dynamic settings and derive a corresponding tool kit. We then analyze several control strategies using the methodologies discussed previously in two real world examples of discrete event simulation models: a manual order picking system and a pickup and delivery service.     

Numerical simulation of scour around a submarine pipeline using computational fluid dynamics and discrete element method

Scour under a submarine pipeline can lead to structural failure; hence, a good understanding of the scour mechanism is paramount. Various numerical methods have been proposed to simulate scour, such as potential flow theory and single-phase and two-phase turbulent models. However, these numerical methods have limitations such as their reliance on calibrated empirical parameters and inability to provide detailed information. This paper investigates the use of a coupled computational fluid dynamics-discrete element method (CFD-DEM) model to simulate scour around a pipeline. The novelty of this work is to use CFD-DEM to extract detailed information, leading to new findings that enhance the current understanding of the underlying mechanisms of the scour process. The simulated scour evolution and bed profile are found to be in good agreement with published experimental results. Detailed results include the contours of the fluid velocity and fluid pressure, particle motion and velocity, fluid forces on the particles, and inter-particle forces. The sediment transport rate is calculated using the velocity of each single particle. The quantitative analysis of the bed load layer is also presented. The numerical results reveal three scour stages: onset of scour, tunnel erosion, and lee-wake erosion. Particle velocity and force distributions show that during the tunnel erosion stage, the particle motion and particle–particle interactive forces are particularly intense, suggesting that single-phase models, which are unable to account for inter-particle interactions, may be inadequate. The fluid pressure contours show a distinct pressure gradient. The pressure gradient force is calculated and found to be comparable with the drag force for the onset of scour and the tunnel erosion. However, for the lee-wake erosion, the drag force is shown to be the dominant mechanism for particle movements.     

Efficient simulation of discrete stochastic reaction systems with a splitting method

Stochastic reaction systems with discrete particle numbers are usually described by a continuous-time Markov process. Realizations of this process can be generated with the stochastic simulation algorithm, but simulating highly reactive systems is computationally costly because the computational work scales with the number of reaction events. We present a new approach which avoids this drawback and increases the efficiency considerably at the cost of a small approximation error. The approach is based on the fact that the time-dependent probability distribution associated to the Markov process is explicitly known for monomolecular, autocatalytic and certain catalytic reaction channels. More complicated reaction systems can often be decomposed into several parts some of which can be treated analytically. These subsystems are propagated in an alternating fashion similar to a splitting method for ordinary differential equations. We illustrate this approach by numerical examples and prove an error bound for the splitting error.     

Convergence properties of ordinal comparison in the simulation of discrete event dynamic systems

Recent research has demonstrated that ordinal comparison has fast convergence despite the possible presence of large estimation noise in the design of discrete event dynamic systems. In this paper, we address the fundamental problem of characterizing the convergence of ordinal comparison. To achieve this goal, an indicator process is formulated and its properties are examined. For several performance measures frequently used in simulation, the rate of convergence for the indicator process is proven to be exponential for regenerative simulations. Therefore, the fast convergence of ordinal comparison is supported and explained in a rigorous framework. Many performance measures of averaging type have asymptotic normal distributions. The results of this paper show that ordinal comparison converges monotonically in the case of averaging normal random variables. Such monotonicity is useful in simulation planning.The author would like to thank C. G. Cassandras, X. Chao, S. G. Strickland, X. Xie, and the reviewers for their helpful suggestions.     

Enabling better management of patients: discrete event simulation combined with the STAR approach

Squeezed budgets and funding cuts are expected to become a feature of the healthcare landscape in the future, forcing decision makers such as service managers, clinicians and commissioners to find effective ways of allocating scarce resources. This paper discusses the development of a decision support toolkit (DST) that facilitates the improvement of services by identifying cost savings and efficiencies within the pathway of care. With the help of National Health Service and commercial experts, we developed a discrete event simulation model for deep vein thrombosis (DVT) patients and adapted the socio-technical allocation of resources (STAR) approach to answer crucial questions like what sort of interventions should we spend our money on? Where will we get the most value for our investment? How will we explain the choices we have made? The DST enables users to model their own services by working with the DST interface allowing users to specify local DVT services. They can input local estimates, or data of service demands and capacities, thus creating a baseline discrete event simulation model. The user can then compare the baseline with potential changes in the patient pathway in the safety of a virtual environment. By making such changes key decision makers can easily understand the impact on activity, cost, staffing levels, skill-mix, utilisation of resources and, more importantly, it allows them to find the interventions that have the highest benefit to patients and provide best value for money.     

DEVS approximation of infiltration using genetic algorithm optimization of a fuzzy system

The infiltration process is generally described by a nonlinear differential equation, which can be solved by iteration methods such as a Newton-Raphson method. In this paper we propose a Discrete Event System Specification (DEVS) model for Green-Ampt infiltration. We show that this model can be approximated using Genetic Algorithm optimization of a fuzzy system. The fuzzy approximation is shown to be more accurate than the Taylor series approximation recently proposed.     

Numerical solution of bed load transport equations using discrete least squares meshless (DLSM) method

The discrete least squares meshless (DLSM) method is extended in this paper for solving coupled bedload sediment transport equations. The mathematical formulation of this model consists of shallow water equations for the hydrodynamical component and an Exner equation expressing sediment continuity for the bedload transport. This method uses the moving least squares (MLS) function approximation to construct the shape functions and the minimizing least squares functional method to discretize the system of equations. The method can be viewed as a truly meshless method as it does not need any mesh for both field variable approximation and the construction of system matrices; it also provides the symmetric coefficient matrix. In the present work, several benchmark problems are studied and compared with the work of other researchers; the proposed method shows good accuracy, high convergence rate, and high efficiency, even for irregularly distributed nodes. At the end, a real test problem is performed to show and verify the main benefit and applicability of the proposed method to cope with complex geometry in practical problems.     

Parametric modeling of protein–DNA binding kinetics: A discrete event based simulation approach

To understand the stochastic behavior of biological systems, we adopt an “in silico” stochastic event based simulation methodology that can determine the temporal dynamics of different molecules. The main requirement for this technique is the event execution time models for the different biological functions of the system. This paper presents a parametric model to determine the execution time of one such biological function: protein–DNA binding. This biological function is modeled as a combination of microlevel biological events using a coarse-grained probability measure to estimate the stochastic parameters of the function. Our model considers the actual binding mechanism along with some approximated protein and DNA structural information. We use a collision theory based approach to transform the thermal and concentration gradients of this biological function into their corresponding probability measure. This information theoretic approach significantly removes the complexity of the classical protein sliding along the DNA model, improves the speed of computation and can bypass the speed-stability paradox. This model can produce acceptable estimates of DNA–protein binding time necessary for our event based stochastic system simulator where the higher order (more than second order statistics) uncertainties can be ignored. The results show good correspondence with available experimental estimates. The model depends very little on experimentally generated rate constants and brings the important biological parameters and functions into consideration. We also present some “in silico” results showing the effects of protein–DNA binding on gene expression in prokaryotic cells.     

Mathematical model of an optical antenna based on the discrete sources method

We consider an optical antenna that is a linear cluster of nanoparticles inside a metal film on a substrate. Based on discrete sources method has been developed and implemented a mathematical model of the optical antenna. Numerical results demonstrate the ability to control the width of the lobe, and directionality of the antenna radiation.     

Mathematical description of a charged-particle system near a porous membrane

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 40, No. 1, pp. 114–117, January–February, 1988.     

NFFT-based extension of a particle simulation method using multigrid

In the calculation of electrostatic problems using multigrid methods, computationally the most expensive part is often the charge assignment to a grid. We show how to improve an existing multigrid method by using an NFFT-based scheme for this task. Numerical tests show that the new method outperforms the direct charge assignment schemes for the case where smooth charge distributions with large support are considered. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of powder mixed electric discharge machining (PMEDM) using finite element method

In the present paper, an axisymmetric two-dimensional model for powder mixed electric discharge machining (PMEDM) has been developed using the finite element method (FEM). The model utilizes the several important aspects such as temperature-sensitive material properties, shape and size of heat source (Gaussian heat distribution), percentage distribution of heat among tool, workpiece and dielectric fluid, pulse on/off time, material ejection efficiency and phase change (enthalpy) etc. to predict the thermal behaviour and material removal mechanism in PMEDM process. The developed model first calculates the temperature distribution in the workpiece material using ANSYS (version 5.4) software and then material removal rate (MRR) is estimated from the temperature profiles. The effect of various process parameters on temperature distributions along the radius and depth of the workpiece has been reported. Finally, the model has been validated by comparing the theoretical MRR with the experimental one obtained from a newly designed experimental setup developed in the laboratory.