Stochastic Discrete Event Research Articles

Optimizing cardiology capacity to reduce emergency department boarding: A systems engineering approach

Patient safety and emergency department (ED) functionality are compromised when inefficient coordination between hospital departments impedes ED patients' access to inpatient cardiac care. The objective of this study was to determine how bed demand from competing cardiology admission sources affects ED patients' access to inpatient cardiac care. A stochastic discrete event simulation of hospital patient flow predicted ED patient boarding time, defined as the time interval between cardiology admission request to inpatient bed placement, as the primary outcome measure. The simulation was built and tested from 1 year of patient flow data and was used to examine prospective strategies to reduce cardiology patient boarding time. Boarding time for the 1,591 ED patients who were admitted to the cardiac telemetry unit averaged 5.3 hours (median 3.1, interquartile range 1.5-6.9). Demographic and clinical patient characteristics were not significant predictors of boarding time. Measurements of bed demand from competing admission sources significantly predicted boarding time, with catheterization laboratory demand levels being the most influential. Hospital policy required that a telemetry bed be held for each electively scheduled catheterization patient, yet the analysis revealed that 70.4% (95% CI 51.2-92.5) of these patients did not transfer to a telemetry bed and were discharged home each day. Results of simulation-based analyses showed that moving one afternoon scheduled elective catheterization case to before noon resulted in a 20-minute reduction in average boarding time compared to a 9-minute reduction achieved by increasing capacity by one additional telemetry bed. Scheduling and bed management practices based on measured patient transfer patterns can reduce inpatient bed blocking, optimize hospital capacity, and improve ED patient access.

Safe Diagnosability of Stochastic Discrete Event Systems

Recently, safe diagnosability of discrete event systems (DESs) was investigated by Paoli and Lafortune, which was viewed as the first necessary step of fault-tolerant supervision. In this paper, we consider the problem of safe diagnosability in the framework of stochastic discrete event systems (SDESs). We define the notion of safe diagnosability for stochastic automata, in which fault detection occurs before any given forbidden string in the failed mode of system is executed. The relationship between diagnosability and safe diagnosability for SDESs is analyzed. In particular, a necessary and sufficient condition for safe diagnosability of SDESs is presented by constructing the recognizer of illegal language and the safe diagnoser. Some examples are described to illustrate the results.

Decentralized Diagnosis of Stochastic Discrete Event Systems

We investigate the decentralized diagnosis of stochastic discrete event systems (SDESs) by using multiple local stochastic diagnosers, each possessing its own sensors to deal with different information. We formalize the notions of decentralized diagnosis for SDESs by defining the concept of codiagnosability for stochastic automata, in which any communication among the local stochastic diagnosers or to any coordinators is not involved. These notions are weaker than the corresponding notions of decentralized diagnosis of classical DESs. A stochastic system being codiagnosable means that a fault can be detected by at least one local stochastic diagnoser within a finite delay. We construct a codiagnoser from a given stochastic system with a finite number of projections whose each diagnosis component uses the complete model of the system. We also deal with a number of basic properties of the codiagnoser. In particular, a necessary and sufficient condition of the codiagnosability for SDESs is presented, which generalizes the corresponding results of centralized diagnosis for SDESs. Also, we give a computing method in detail to check the codiagnosability of SDESs. As an application of our results, some examples are described.

Pathway Complexity of Model Virus Capsid Assembly Systems

As computational and mathematical studies become increasingly central to studies of complicated reaction systems, it will become ever more important to identify the assumptions our models must make and determine when those assumptions are valid. Here, we examine that question with respect to viral capsid assembly by studying the ‘pathway complexity’ of model capsid assembly systems, which we informally define as the number of reaction pathways and intermediates one must consider to accurately describe a given system. We use two model types for this study: ordinary differential equation models, which allow us to precisely and deterministically compare the accuracy of capsid models under different degrees of simplification, and stochastic discrete event simulations, which allow us to sample use of reaction intermediates across a wide parameter space allowing for an extremely large number of possible reaction pathways. The models provide complementary information in support of a common conclusion that the ability of simple pathway models to adequately explain capsid assembly kinetics varies considerably across the space of biologically meaningful assembly parameters. These studies provide grounds for caution regarding our ability to reliably represent real systems with simple models and to extrapolate results from one set of assembly conditions to another. In addition, the analysis tools developed for this study are likely to have broader use in the analysis and efficient simulation of large reaction systems.

Holding time estimation for reactions in stochastic event-based simulation of complex biological systems

The complexity of biological systems motivate the use of an “in silico” stochastic discrete event simulation methodology. This method can incorporate the effects of the recently identified stochastic resonance of a biological system and is computationally capable to process the dynamic interactions of different pathways in the cell. The main requirement for this technique is the event time models for the discrete events of the biological system. Currently such models do not exist for biological functions and this paper proposes one such event model – the biochemical reactions between the molecules inside the cytoplasm of a cell where the reaction environment is highly chaotic. We present a mathematical formulation for the estimation of the reaction time between two molecules within a cell based on the discrete system states. In particular, we propose two models: (1) The reactant molecules enter the system one at a time to initiate reactions, and (2) The reactant molecules arrive in batches of a certain size. We derive expressions for the average and second moment of the time for reaction. This random time is used by our stochastic event-based simulation. Unlike rate equations, the proposed model does not require the assumption of concentration stability for multiple molecule reactions. Also the models incorporate many structural and functional parameters of the biological function, that are lacking in the currently used rate equation model. The parametric nature of the model makes it generic and useful for diverse studies.

Active Acquisition of Information for Diagnosis and Supervisory Control of Discrete Event Systems

This paper considers the problems of fault diagnosis and supervisory control in discrete event systems through the context of a new observation paradigm. For events that are considered observable, a cost is incurred each time a sensor is activated in an attempt to make an event observation. In such a situation the best strategy is to perform an "active acquisition" of information, i.e. to choose which sensors need to be activated based on the information state generated from the previous readings of the system. Depending on the sample path executed by the system, different sensors may be turned on or off at different stages of the process. We consider the active acquisition of information problem for both logical and stochastic discrete event systems. We consider three classes of increasing complexity: firstly, for acyclic systems where events are synchronized to clock ticks; secondly, for acyclic untimed systems; and lastly, for general cyclic automata. For each of these cases we define a notion of information state for the problem, determine conditions for the existence of an optimal policy, and construct a dynamic program to find an optimal policy where one exists. For large systems, a limited lookahead algorithm for computational savings is proposed.

An ordinal optimization based evolution strategy to schedule complex make-to-order products

This paper considers the problem of planning and scheduling a complex make-to-order product with multiple levels of product structure. The work assumes finite capacity constraints and uncertain processing times. For planning such systems we define a schedule as a set of planned operation start times together with a set of priority rules (for individual resources) that are followed in implementing the schedule. An optimal schedule is determined by minimizing the expected total cost (the sum of work in progress holding costs, product earliness costs and product tardiness costs). A Stochastic Discrete-Event Based Evolution Strategy (SDEES) is first introduced to tackle the scheduling problem. However, SDEES is computationally demanding due to the multiplicative effect of the number of search iterations and the size of the evaluation samples required at each stage in the search. To reduce computation and improve search speed, an Ordinal Optimization Based Evolution Strategy (OOES) is developed. Quantitative examples covering a range of uncertainty levels are used to illustrate the effectiveness of the methods. Further, a case study using data from a collaborating company demonstrates the practical effectiveness. The Ordinal Optimization Evolutionary Strategy achieves a performance similar to the SDEES whilst reducing the computational time by around 60%.

Opportunistic scheduling for streaming multimedia users in high-speed downlink packet access (HSDPA)

High-speed downlink packet access (HSDPA) achieves high data rates and high spectral efficiency by using adaptive modulation and coding schemes and employing multicode CDMA. In this paper, we present opportunistic algorithms for scheduling HSDPA users and selecting modulation/coding and multicode schemes that exploit channel and buffer variations to increase the probability of uninterrupted media play-out. First, we introduce a stochastic discrete event model for a HSDPA system. By employing the discrete event model, we transform the scheduling problem of providing uninterrupted play-out to a feasibility problem that considers two sets of stochastic quality-of-service (QoS) constraints: stability constraints and robustness constraints. A methodology for obtaining a feasible solution is then proposed by starting with a so-called stable algorithm that satisfies the stability QoS constraints. Next, we present stochastic approximation algorithms that adapt the parameters of the stable algorithm in a way that a feasible point for the robustness QoS is reached within the feasibility region of the stability QoS

Automated Statistical Analysis in Stochastic Project Scheduling Simulation

This paper describes a stochastic simulation-based scheduling system (S3) that: (1) integrates the deterministic critical path method (CPM), the probabilistic program evaluation and review technique (PERT), and the stochastic discrete event simulation (DES) approaches into a single system and lets the scheduler make an informed decision as to which method is better suited to the company’s risk-taking culture; (2) automatically determines the minimum number of simulation runs in DES mode and therefore optimizes the simulation process; and (3) provides a terminal method that tests the statistical significance of the differences between simulations, hence eliminating outliers and therefore increasing the accuracy of the DES process. The system is based on an earlier version of the system called stochastic project scheduling simulation and makes use of all the capabilities of this system. The study is of value to practitioners because S3 produces a realistic prediction of the probability of completing a proje...

Raw material release time control for complex make-to-order products with stochastic processing times

This paper considers a make-to-order manufacturing system producing complex products with multiple resource constraints, multiple levels of product structures, and stochastic processing times. The objective is to find the optimal raw material release times by minimising the expected sum of work-in-progress holding costs, product earliness costs and product tardiness costs. An evolution strategy-based planning tool is developed, in which the performance measure is evaluated by stochastic discrete event simulation. The tool is applied to an illustrative example that includes wide, deep and complex product structures and to a case study using data obtained from an industrial company that manufactures capital goods. It is demonstrated that the solutions produced perform substantially better than those produced by the backward scheduling based on infinite capacity, and also significantly better than those produced by the same search method based on deterministic processing times. More benefit can be achieved if the system has a higher degree of uncertainty.

Pathogen dissemination in health care facilities: what to do when traditional assumptions fail

A burgeoning population, more rapid travel, and the ongoing evolution of bacterial and viral pathogens create increasing concerns regarding our ability to respond to novel or emerging agents of disease. Although many elegant models have been developed addressing pathogen dissemination in the general population, less attention has been paid to modeling or quantitating the spread of pathogens through health care institutions, such as intensive care units, hospitals, or clinics. As the recent severe acute respiratory syndrome outbreaks demonstrated, health care facilities can be important elements in the dynamics of pathogen dissemination. Quantitative models of pathogen dissemination within health care institutions could be used to optimize control policies, an application whose importance is amplified because of the increasingly limited resources for health care in general. Health care facilities are spatially intricate, inhomogeneous, and dynamically complex ecosystems because of the intensity, heterogeneity, and regional nature of interactions between disparate sets of individuals. In the inpatient setting, patients are seen relatively frequently, and there are multiple classes and subgroups of caretakers. A given patient is usually seen by a subset of the nurses, primary physicians and consultants, and the bcaregiver domainsQ (assigned patients) of different caregivers usually overlap. These limited but overlapping domains create a highly heterogeneous contact network that can interact with the number and distribution of colonized patients to modulate pathogen dissemination. In addition, the order in which patients are seen can strongly modulate the dissemination of pathogens, and the pattern of contacts is often partially stochastic (because of random ordering of visits or unanticipated contacts), and even a blargeQ hospital represents a statistically small population. Traditional methods of modeling pathogen dissemination are based on representing the venue of dissemination as a spatially and temporally well-mixed environment and using differential equation approaches to describe the growth of the infected population. For reasons enumerated above, health care facilities significantly violate such assumptions, rendering the applicability of traditional techniques suspect. In contrast to more traditional equation-based approaches, conceptually simple discrete element (agentor individual-based) models can readily and explicitly address bgeographicQ considerations, temporal elements of transmission, and probabilistic transmission dynamics germane to the spatially intricate environments and small population sizes characteristic of health care institutions. We have developed stochastic discrete event models of pathogen transmission that explicitly account for temporal and spatial factors in the dissemination of pathogens through the hospital, the intensive care unit, the emergency department, and the outpatient clinic. Results generated using Monte Carlo simulations for each of these venues demonstrate common themes. First, there is tremendous variability in the levels of pathogen transmission from simulation to simulation within each venue, suggesting that interventional clinical trials will need to be very large to adequately test predictive models. Second, spatial heterogeneity can dramatically reduce the dissemination of pathogens at a constant level of transmissibility. This finding suggests that spatial factors could be important considerations in models for optimizing control strategies, and that well-mixed (homogeneous) models that are parameterized with population-level epidemiological data might underestimate the risk of person-to-person transmission. Supported by NIH NIAID R21A155818-02 (JRH).

Control of Markov Chains With Safety Bounds

In an earlier paper, the authors introduced the notion of control of stochastic discrete event systems (DESs), modeled as controlled Markov chains. Safety was specified as an upper bound on the components of the state probability distribution, and the class of irreducible and aperiodic Markov chains were analyzed relative to this criterion. Under the assumption of complete state observations: 1) the authors identified the set of all state-feedback controllers that enforce the specification, for all safe initial probability distributions and 2) for any given state-feedback controller, the authors constructed the maximal invariant safe set (MISS). In this paper, the authors extend the work in several ways: 1) is specified in terms of both upper and lower bounds; 2) we consider a larger class of Markov chains that includes reducible and periodic chains; 3) we present a more general iterative algorithm for computing the MISS, which is quite flexible in its initialization; 4) we obtain an explicit upper bound for the number of iterations needed for the algorithm to terminate. Note to Practitioners-The paper studies safety control of stochastic systems modeled as Markov chains. Safety is defined as a requirement that the probability distribution in each state remain bounded between an upper and a lower bound. For example, a financial investment policy should be such that the probability of ever being bankrupt is bounded below by a positive number. Prior works on control of Markov chains have addressed optimality but not safety. A condition is obtained under which a controlled Markov chain is guaranteed to be safe at all times. For those chains that do not satisfy such a condition, a maximal subset of the safe set of distributions is computed so that if the chain is initialized with a distribution in that maximal subset, it remains safe all the times. A condition is obtained under which such a maximal set is nonempty. The computation of such a maximal set is iterative and we provide a condition under which the computation terminates in a finite number of iterations. Manufacturing system examples are included to illustrate the results.

Application des BDSPNs à la modélisation et à l'évaluation de performances des chaînes logistiques

Batch deterministic and stochastic Petri nets (BDSPNs) are a class of Petri nets developed for modelling, analysis and performance evaluation of supply chains and more generally stochastic discrete event systems with batch behaviour. BDSPNs extends DSPNs by introducing batch places and batch tokens, which permit it to efficiently model batch behaviours of batch discrete event processes appeared often in production systems, inventory systems, and supply chains. In those systems, materials are processed in batches (finite discrete quantities) and many operations such as inventory replenishment, manufacturing and distribution operations are usually performed in batch mode to take advantages of the economies of scale or because of the batch nature of customer orders. In this paper, the model and its dynamical behaviour are defined formally. Methods for analysis and evaluation of the performance of the model are then developed. As applications, the performances of an inventory system and of a supply chain are evaluated analytically and by simulation, respectively, by using the BDSPN modelling and analysis tool. The applications demonstrate the advantages of BDSPNs as a tool for modelling, analysis and performance evaluation of supply chains.

Stochastic discrete event simulation of germinal center reactions

We introduce a generic reaction-diffusion model for germinal center reactions and perform numerical simulations within a stochastic discrete event approach. In contrast to the frequently used deterministic continuum approach, each single reaction event is monitored in space and time in order to simulate the correct time evolution of this complex biological system. Germinal centers play an important role in the immune system by performing a reaction that aims at improving the affinity between antibodies and antigens. Our model captures experimentally observed features of this reaction, such as the development of the remarkable germinal center morphology and the maturation of antibody-antigen affinity in the course of time. We model affinity maturation within a simple affinity class picture and study it as a function of the distance between the initial antibody-antigen affinity and the highest possible affinity. The model reveals that this mutation distance may be responsible for the experimentally observed all-or-none behavior of germinal centers; i.e., they generate either mainly output cells of high affinity or no high-affinity output cells at all. Furthermore, the exact simulation of the system dynamics allows us to study the hypothesis of cell recycling in germinal centers as a mechanism for affinity optimization. A comparison of three possible recycling pathways indicates that affinity maturation is optimized by a recycling pathway that has previously not been taken into account in deterministic continuum models.

Performance evaluation of non markovian stochastic discrete event systems - a new approach

In this work, we address the problem of transient and steady-state analysis of a stochastic discrete event system which includes non Markovian distributions with a finite support. Rather than computing an approximate distribution of the model (as done in the previous methods), we develop an exact analysis of an approximate model. The design of this method leads to a uniform handling for the computation of the transient and steady-state behaviour of the model. We have evaluated our method on a standard benchmark (the queuing model Our results demonstrate that: in most of the cases the solution of the approximate model converges quickly to the solution of the exact model, in the difficult cases (e.g. an heavy load on the queue) our method is more robust than the previous ones.

Stochastic discrete event model of a multi-robot team playing an adversarial game

This paper introduces a method to model multi-robot teams using stochastic discrete event system techniques. The environment state space and robot behaviours are discretised and modelled by modular finite state automata (FSA). Then, all the FSA are composed to obtain the complete model of the team situated in its environment. Controllable and uncontrollable events are identified. Exponential distributions are assigned to the interevent times for uncontrollable events and stochastic dynamic programming is applied to the optimal selection of the controllable events. The method is illustrated by its application to a robotic football game. Simulation results are presented.

A virtual server queueing network method for component based performance modelling of metacomputing

In this paper, we introduce a virtual server queueing network concept to evaluate the performance of metacomputing systems. It adds a virtual server concept to the existing queueing network theory. It enables us to effectively and accurately evaluate the performance of metacomputing systems. Component based software development now gains much interest and is especially regarded as very useful and necessary in the area of metacomputing. We find that the virtual server queueing network concept is well suited for a component based performance modelling and evaluation approach. In this paper, we have derived component based performance models of a metacomputing environment using the virtual server queueing network concept and validated them through measurement. With it, we quantitatively characterize the file access performance of caching in the metacomputing environment. We used a stochastic discrete event simulation as the main methodology to solve the models.

Control of stochastic discrete event systems modeled by probabilistic languages

In Garg et al. (1999) and Garg (1992) the formalism of probabilistic languages for modeling the stochastic qualitative behavior of discrete event systems (DESs) was introduced. In this paper, we study their supervisory control where the control is exercised by dynamically disabling certain controllable events thereby nulling the occurrence probabilities of disabled events, and increasing the occurrence probabilities of enabled events proportionately. This is a special case of "probabilistic supervision" introduced in Lawford and Wonham (1993). The control objective is to design a supervisor such that the controlled system never executes any illegal traces (their occurrence probability is zero), and legal traces occur with minimum prespecified occurrence probabilities. In other words, the probabilistic language of the controlled system lies within a prespecified range, where the upper bound is a "nonprobabilistic language" representing a legality constraint. We provide a condition for the existence of a supervisor. We also present an algorithm to test this existence condition when the probabilistic languages are regular (so that they admit probabilistic automata representation with finitely many states). Next, we give a technique to compute a maximally permissive supervisor online.

Modeling the Ultimate Seaweed Expansion

Since 1984 the green tropical alga Caulerpa taxifolia (Chlorophyta), of aquarium origin, has spread rapidly along the north-western Mediterranean sea coast. This alga was recently discovered on the Mediterranean south coast (Tunisia) and the west coast of the United States. This paper presents modeling efforts to simu late Caulerpa taxifolia expansion. Three different mod els were built; the first model is based on stochastic discrete event simulation coupled with a geographical information system. The second model uses a neural network, trained with simulation data and is consid ered as a metamodel. The third is a multimodel de signed to simulate a biocontrol. Indeed, to control Caulerpa overhang, it may be possible to use special ized predator of C. taxifolia such as Elysia subornata (Mollusca, Ascoglossa). Simulation was mandatory before any introduction to estimate the potential re duction of the colonization by C. taxifolia. Encourag ing results concerning the use of E. subornata are pre sented.

Wedding connectionist and algorithmic modelling towards forecasting Caulerpa taxifolia development in the north-western Mediterranean sea

We discuss the use of supervised neural networks as a metamodelling technique for discrete event stochastic simulation in order to reduce significantly the computational burden involved by discrete simulations. A sophisticated computer model, coupling a geographical information system with a stochastic discrete event simulator, has been developed to anticipate the propagation of the green alga Caulerpa taxifolia in the north-western Mediterranean sea. The simulation model provides reliable predictions, a couple of years in advance, of: (i) the local expansion patterns of the alga; (ii) the increase of C. taxifolia biomass and (iii) the covered surfaces. However because the algorithmic model accounts for spatial interactions and anthropic dispersion/activities such as eradication, introduction of specific predators etc., simulations are extremely time and memory consuming. Therefore, to reduce the computational burden, a neural network was successfully trained on artificially generated data provided by the simulation runs to provide accurate forecasts 12 years in advance along with associated confidence intervals. The ability of the neural networks to capture the underlying physics of the phenomena is clearly illustrated by several preliminary experiments on a large coastal area. The neural network is able to construct, on this site, estimates of the Caulerpa taxifolia expansion 12 years in advance in good agreement with the simulation trajectories.