Simulation Of Stochastic Systems Research Articles

Water pathways: An open source stochastic simulation system for integrated water supply portfolio management and infrastructure investment planning

Financial risk, access to capital, regulatory processes, and regional competition for limited water sources represent dominant concerns in the United States as well as the broader global water supply sector. This work introduces the WaterPaths simulation software: a generalizable, cloud-compatible, open-source exploratory modeling system designed to inform long-term regional investments in water infrastructure while simultaneously aiding regions to improve their short-term weekly management decisions, often made in response to droughts. Uniquely, WaterPaths has the capability to identify coordinated planning and management for groups of water utilities sharing water resources. WaterPaths’ exploits dynamic and adaptive risk-of-failure (ROF) rules to trigger management and planning actions in temporally consistent pathways. The compact and efficient ROF-based representation of decision pathways allows WaterPaths to scale efficiently with the number of regional actors and their candidate actions. Lastly, as a platform for supporting decision making under deep uncertainty, WaterPaths accounts for a broad range of uncertainties including hydrological or climate extremes, permitting time, demand growth, effectiveness of water-use restrictions, construction costs, and financing uncertainties. To demonstrate the capabilities of WaterPaths, we introduce a new hypothetical water resources test case, the Sedento Valley. The Sedento Valley test case contains three resource-sharing water utilities that seek to regionally coordinate their policies for drought mitigation and infrastructure investment. The three utilities are challenged by a diverse set of deep uncertainties that encompass natural and human systems stressors. The Sedento Valley test case contributes a new opportunity for benchmarking decision-support tools and water-resources systems simulation software.

Arbitrary Polynomial Chaos for Uncertainty Propagation of Correlated Random Variables in Dynamic Systems

Dynamic simulation of stochastic systems requires uncertainty propagation. Traditional sample-based uncertainty propagation methods are often computationally intractable for online optimization-based estimation and control applications. Generalized polynomial chaos (gPC) is an efficient uncertainty propagation method that has been used for solving various nonlinear estimation and optimal control problems. However, gPC requires knowledge of the exact probability distribution of the random variables, and does not explicitly account for correlations between these random variables. This paper demonstrates the use of arbitrary polynomial chaos (aPC) for propagation of correlated multivariate random variables. aPC constructs orthogonal polynomial basis functions from only the raw moments of the random variables. Thus, aPC can be used for propagation of uncertainties with arbitrary probability distributions, even if their functional forms are unknown. The main contributions of this paper consist of presenting an algorithm for generating a set of orthogonal polynomial basis functions for correlated multivariate random variables and applying the Galerkin projection to compute closed-form expressions for the dynamics of the aPC expansion coefficients. An algorithm is also presented for efficient calculation of inner products between polynomial basis functions needed in the Galerkin projection. The error convergence properties of aPC are investigated and compared to that of gPC and Monte Carlo using a dynamic simulation case study.

Impacts of onsite greywater reuse on wastewater systems.

Together with significant water savings that onsite greywater reuse (GWR) may provide, it may also affect the performance of urban sewer systems and wastewater treatment plants (WWTPs). In order to examine these effects, an integrated stochastic simulation system for GWR in urban areas was developed. The model includes stochastic generators of domestic wastewater streams and gross solids (GSs), a sewer network model which includes hydrodynamic simulation and a GS transport module, and a dynamic process model of the WWTP. The developed model was applied to a case study site in Israel. For the validation of the sewer simulator, field experiments in a real sewer segment were conducted. The paper presents the integration and implementation of these modules and depicts the results of the effects of various GWR scenarios on GS movement in sewers and on the performance of the WWTP.

Chromatin computation: Epigenetic inheritance as a pattern reconstruction problem

Eukaryotic histones carry a diverse set of specific chemical modifications that accumulate over the life-time of a cell and have a crucial impact on the cell state in general and the transcriptional program in particular. Replication constitutes a dramatic disruption of the chromatin states that effectively amounts to partial erasure of stored information. To preserve its epigenetic state the cell reconstructs (at least part of) the histone modifications by means of processes that are still very poorly understood. A plausible hypothesis is that the different combinations of reader and writer domains in histone-modifying enzymes implement local rewriting rules that are capable of “recomputing” the desired parental modification patterns on the basis of the partial information contained in that half of the nucleosomes that predate replication.To test whether such a mechanism is theoretically feasible, we have developed a flexible stochastic simulation system (available at http://www.bioinf.uni-leipzig.de/Software/StoChDyn) for studying the dynamics of histone modification states. The implementation is based on Gillespie's approach, i.e., it models the master equation of a detailed chemical model. It is efficient enough to use an evolutionary algorithm to find patterns across multiple cell divisions with high accuracy.We found that it is easy to evolve a system of enzymes that can maintain a particular chromatin state roughly stable, even without explicit boundary elements separating differentially modified chromatin domains. However, the success of this task depends on several previously unanticipated factors, such as the length of the initial state, the specific pattern that should be maintained, the time between replications, and chemical parameters such as enzymatic binding and dissociation rates. All these factors also influence the accumulation of errors in the wake of cell divisions.

Simulation of stochastic systems via polynomial chaos expansions and convex optimization

Polynomial chaos expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and nontrivial manipulation of the model, or the computation of large numbers of simulation runs, rendering the approach too time consuming and impracticable for applications with more than a handful of random variables. We introduce a computationally tractable technique for computing the coefficients of polynomial chaos expansions. The approach exploits a regularization technique with a particular choice of weighting matrices, which allows to take into account the specific features of polynomial chaos expansions. The method, completely based on convex optimization, can be applied to problems with a large number of random variables and uses a modest number of Monte Carlo simulations, while avoiding model manipulations. Additional information on the stochastic process, when available, can be also incorporated in the approach by means of convex constraints. We show the effectiveness of the proposed technique in three applications in diverse fields, including the analysis of a nonlinear electric circuit, a chaotic model of organizational behavior, and finally a chemical oscillator.

Molecular stochastic simulations of chromatophore vesicles from Rhodobacter sphaeroides

A kinetic model is presented for photosynthetic processes under varying illumination based on the recently introduced steady state model of the photosynthetic chromatophore vesicles of the purple bacterium Rhodobacter sphaeroides. A stochastic simulation system is built up from independent copies of the different transmembrane proteins, each encapsulating its own set of binding sites and internal states. The proteins are then connected through pools for each of the metabolites. A number of steady state and time-dependent scenarios are presented showing that even under steady state conditions the stochastic model exhibits a different behavior than a continuous description. We find that the electronic coupling between the light harvesting complexes increases the efficiency of the core complexes which eventually allows the bacteria to bridge short illumination outages at already lower light intensities. Some new experiments are proposed by which the DeltapH dependent characteristic of the bc(1) complex or the proton buffering capacity of the vesicle could be determined.

Modelling the checkpoint response to telomere uncapping in budding yeast

One of the DNA damage-response mechanisms in budding yeast is temporary cell-cycle arrest while DNA repair takes place. The DNA damage response requires the coordinated interaction between DNA repair and checkpoint pathways. Telomeres of budding yeast are capped by the Cdc13 complex. In the temperature-sensitive cdc13-1 strain, telomeres are unprotected over a specific temperature range leading to activation of the DNA damage response and subsequently cell-cycle arrest. Inactivation of cdc13-1 results in the generation of long regions of single-stranded DNA (ssDNA) and is affected by the activity of various checkpoint proteins and nucleases. This paper describes a mathematical model of how uncapped telomeres in budding yeast initiate the checkpoint pathway leading to cell-cycle arrest. The model was encoded in the Systems Biology Markup Language (SBML) and simulated using the stochastic simulation system Biology of Ageing e-Science Integration and Simulation (BASIS). Each simulation follows the time course of one mother cell keeping track of the number of cell divisions, the level of activity of each of the checkpoint proteins, the activity of nucleases and the amount of ssDNA generated. The model can be used to carry out a variety of in silico experiments in which different genes are knocked out and the results of simulation are compared to experimental data. Possible extensions to the model are also discussed.

Fitting Time-Series Input Processes for Simulation

Providing accurate and automated input-modeling support is one of the challenging problems in the application of computer simulation of stochastic systems. The models incorporated in current input-modeling software packages often fall short because they assume independent and identically distributed processes, even though dependent time-series input processes occur naturally in the simulation of many real-life systems. Therefore, this paper introduces a statistical methodology for fitting stochastic models to dependent time-series input processes. Specifically, an automated and statistically valid algorithm is presented to fit autoregressive-to-anything (ARTA) processes with marginal distributions from the Johnson translation system to stationary univariate time-series data. ARTA processes are particularly well suited to driving stochastic simulations. The use of this algorithm is illustrated with examples.

Experimental Stochatics (2nd edition)

Otto Moeschlin and his co-authors have written a book about simulation of stochastic systems. The book comes with a CD-ROM that contains the experiments discussed in the book, and the text from the book is repeated on the CD-ROM. According to the authors, the aim of the book is to give a quick introduction to stochastic simulation for `all persons interested in experimental stochastics'. To please this diverse audience, the authors offer a book that has four parts. Part 1, called `Artificial Randomness', is the longest of the four parts. It gives an overview of the generation, testing and basic usage of pseudo random numbers in simulation. Although algorithms for generating sequences of random numbers are fundamental to simulation, it is a slightly unusual choice to give it such weight in comparison to other algorithmic topics. The remaining three parts consist of simulation case studies. Part 2, `Stochastic Models', treats four problems---Buffon's needle, a queuing system, and two problems related to the kinetic theory of gases. Part 3 is called `Stochastic Processes' and discusses the simulation of discrete time Markov chains, birth--death processes, Brownian motion and diffusions. The last section of Part 3 is about simulation as a tool to understand the traffic flow in a system controlled by stoplights, an area of research for the authors. Part4 is called `Evaluation of Statistical Procedures'. This section contains examples where simulation is used to test the performance of statistical methods. It covers four examples: the Neymann--Pearson lemma, the Wald sequential test, Bayesian point estimation and Hartigan procedures. The CD-ROM contains an easy-to-install software package that runs under Microsoft Windows. The software contains the text and simulations from the book. What I found most enjoyable about this book is the number of topics covered in the case studies. The highly individual selection of applications, which may serve as a source of inspiration for teachers of computational stochastic methods, is the main contribution of this electronic monograph. However, both the book and software suffer from several severe problems. Firstly, I feel that the structure of the text is weak. Probably this is partly the result of the text from the CD-ROM being put into a book format, but the short paragraphs and poorly structured sentences destroy the reading experience. Secondly, although the software is functional, I believe that, like me, many users will be disappointed by the quality of the user interface and the visualizations. The opportunities to interact with the simulations are limited. Thirdly, the presentation is slightly old fashioned and lacking in pedagogical structure. For example, flow charts and Pascal programs are used to present algorithms. To conclude, I am surprised that this electronic monograph warranted a second edition in this form. Teachers may find the examples useful as a starting point, but students and researchers are advised to look elsewhere.

Computational military tactical planning system

A computational system called fuzzy-genetic decision optimization combines two soft computing methods, genetic optimization and fuzzy ordinal preference, and a traditional hard computing method, stochastic system simulation, to tackle the difficult task of generating battle plans for military tactical forces. Planning for a tactical military battle is a complex, high-dimensional task which often bedevils experienced professionals. In fuzzy-genetic decision optimization, the military commander enters his battle outcome preferences into a user interface to generate a fuzzy ordinal preference model that scores his preference for any battle outcome. A genetic algorithm iteratively generates populations of battle plans for evaluation in a stochastic combat simulation. The fuzzy preference model converts the simulation results into a fitness value for each population member, allowing the genetic algorithm to generate the next population. Evolution continues until the system produces a final population of high-performance plans which achieve the commander's intent for the mission. Analysis of experimental results shows that co-evolution of friendly and enemy plans by competing genetic algorithms improves the performance of the planning system. If allowed to evolve long enough, the plans produced by automated algorithms had a significantly higher mean performance than those generated by experienced military experts.

Estimating the Optimum of a Stochastic System using Simulation

We incorporate new techniques for obtaining unbiased estimators of gradients from single simulations of stochastic systems in optimization procedures. We develop an "enhanced" least squares estimator of the optimum which incorporates information about both the function and its gradient and improves substantially on techniques which use only the function. We also propose a sequential design to use with the enhanced least squares estimator to optimize a regression function when it is evaluated by simulation.

Importance Sampling and the Cyclic Approach

The method of importance sampling is widely used for efficient rare-event simulation of stochastic systems. This method involves simulating the system under a new distribution that accentuates the ...

Importance Sampling and the Cyclic Approach

The method of importance sampling is widely used for efficient rare-event simulation of stochastic systems. This method involves simulating the system under a new distribution that accentuates the probability along the most likely paths to the rare event. Traditionally, insights from large deviations theory are used to identify the distribution emphasizing these most likely paths. In this paper we develop an intuitive cyclic approach for selecting such a distribution. The key idea is to select a distribution under which the event of interest is no longer rare and the probability of occurrence of a cycle in any sample path remains equal to the original probability of that cycle. We show that only an exponentially twisted distribution can satisfy this equiprobable cycle condition. Using this approach we provide an elementary derivation of the asymptotically optimal change of measure for level crossing probability for Markov-additive processes. To demonstrate its ease of use for more complex stochastic systems, we apply it to determine the asymptotically optimal change of measure for estimating buffer overflow probability of a single-server queue subject to server interruptions.

A multi-criterion approach for Kanban allocations

In this paper, a single-item, multi-stage, serial production system is considered. Materials in the system are controlled by Kanban discipline. A fixed total number of Kanbans over a given number of serial workstations is allocated. Three conflicting objectives, the average throughput rate (to be maximized), the average work-in-process (to be minimized), and the average flow time (to be minimized) are considered. Stochastic system simulation is used to generate the efficient set of Kanban allocations. Then the analytic hierarchy process (AHP) is utilized to identify the most-preferred allocation. An illustrative example is given.

Cell Growth Simulation (CGS): The Simulator

Cell Growth Simulation (CGS) is a software package that sinlulates the growth of cultured cells. and the effects of different types of agents on the cell populations in vitro. It is a stochastic simulation system and is based on the cell cycle kinetics. Experiments involving DNA synthesis, blocking. mitosis inhibition. labeling and cell kill can be simulated by imitating application of drugs such as thymidine. aphidicoline, hydroxyurea. vincristine. finblistine. colcemid and others. The model to be simulated is described by the user according to his theoretical convictions. The system provides numerous facilities to help the user describe an experiment and examine the simulation results. A menu driven interactive scheme is used to communicate with the user. CGS is implemented on AT type personal computers with hard disks. This paper focuses on the simulator modules of CGS. It is an event dliven simulator which follows the individual cells through their life cycles. General structure of the simulator. primary events and their attributes. chain operations. culture initializations. imitation of cell maturation and DNA synthesis are explained in the text as well as collection of statistics from the simulated experiments.

Manufacturing blocking discipline: A multi-criterion approach for buffer allocations

In this paper, a single-item, multi-stage, serial production system is considered. Materials in the system are controlled by manufacturing blocking discipline (MBD). A fixed total number of buffers over a given number of serial workstations is allocated. Three conflicting objectives, the average throughput rate (to be maximized), the average work-in-process (to be minimized), and the average system time (to be minimized) are considered. Stochastic system simulation is used to generate the efficient set of buffer allocations. Then analytic hierarchy process (AHP) is utilized to identify the most-preferred allocation. Sensitivity analysis for allocating buffer with respect to the three conflicting objective is also investigated. An illustrative example is given.

Fuzzy-Markov Simulation Technique for Product Testing Equipment

A novel intelligent simulation technique is proposed for testing of automatic control systems. The technique combines fuzzy reasoning and Markov modelling for stochastic system simulation purposes. A learning problem is also discussed with an example of a digital test-bed.

Analog simulation of stochastic systems in a metastable piecewise quasilinear potential driven by band-limited white noise.

Stochastic dynamics in a metastable potential that is linear except for finite curvatures at the bottom and barrier top has been treated using an analog simulator. Band-limited white noise is applied and the response of the system is observed as the bandwidth is increased until the noise becomes effectively white. Supplementary computer simulations have also been carried out. In the oscillation regime, i.e., for low noise intensities, the power spectrum exhibits significant deviation from that for the harmonic oscillator. Average amplitudes of the driving force have been calibrated so that peak positions of the power spectrum may produce identical results for the two simulations. The amplitude distribution has been consistent among the analog simulation, the computer simulation, and the Boltzmann distribution. For higher noise intensities, the Arrhenius plot from the analog and computer simulations has reproduced a correct barrier height, but the pre-exponential factor is about one-sixth of that obtained from Kramers's formula.

Cell Growth Simulation (CGS): the design philosophy

Cell Growth Simulation (CGS) is a software package that simulates the growth of cell cultures, and the effects of different types of agents on the cell populations in vitro. It is a stochastic simulation system based on the cell cycle kinetics. Experiments involving DNA synthesis blocking, mitosis inhibition, labelling and cell kill can be simulated by imitating agents such as thymidine, aphidicoline, hydroxyurea, vincristine, vinblistine, colcemid and others. The model to be simulated is described by the user according to his theoretical convictions, The system provides numerous facilities to help the user describe an experiment and examine the simulation results. A menu driven interactive scheme is used to communicate with the user. CGS has a modular structure and its general structure, design philosophy and capabilities are presented. The system has been developed through the cooperation of industrial engineering, cell biology, medical oncology and computer programming disciplines. It is implemented on...

Simulation of stochastic systems : Sheldon M. Ross, College of Engineering, Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, U.S.A.

Simulation of stochastic systems : Sheldon M. Ross, College of Engineering, Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, U.S.A.