Stochastic Discrete Event Research Articles

Bounded Synthesis and Reinforcement Learning of Supervisors for Stochastic Discrete Event Systems With LTL Specifications

Bounded Synthesis and Reinforcement Learning of Supervisors for Stochastic Discrete Event Systems With LTL Specifications

Stochastic Simulation of Construction Methods for Multi-purpose Utility Tunnels

The traditional method of installing underground utilities (e.g., water, sewer, gas pipes, electrical cables) by burying them under roads has been used for decades. However, the repeated excavations related to this method cause problems, such as traffic congestion and business disruption, which can significantly increase financial and social costs. Multi-purpose Utility Tunnels (MUTs) are a good alternative for buried utilities. Although the initial cost of MUTs is higher than that of the traditional method, social cost savings make them more feasible, especially in dense urban areas. Different factors, such as the specifications of utilities, the location of the MUTs, and the construction method, should be investigated to determine if MUTs can be an economical and practical alternative. The construction method is one of the most important factors to assess to have a successful MUT project and reduce its impact on the surrounding area. Simulation can be used to investigate the different construction methods of MUTs. In this paper, two Stochastic Discrete Event Simulation models depicting two MUT construction methods (i.e., microtunneling and cut-and-cover) are developed to analyze the duration and cost of the MUT projects. Also, 4D simulation models of these methods are developed for constructability assessment of these projects.

Identification of unobservable behavior in stochastic discrete event systems with a low number of sensors

Dynamic discrete event systems (DDES) are systems that evolve from the asynchronous occurrence of discrete events. Their versatility has become a critical modeling tool in different applications. Finding models that define the behavior of DES is a topic that has been addressed from different approaches, depending on the type of system to be modeled and the model's objective. This article focuses on the identification of timed models for stochastic discrete event systems. The identified model includes both observable and unobservable behavior. The objective of the method is achieved through the following steps:•Identifying the sequences of events observed at different time instances during the closed-loop operation of the system (observed language),•Inferring the stochastic behavior of time between events and modeling the observable behavior as a stochastic timed Interpreted Petri Net (st-IPN),•and finally, inferring the non-observable behavior using the language projection operation between the observed language and the language generated by the st-IPN.This method has novel aspects because it uses timed events, can be applied to systems with a low number of sensors and can infer unobservable behavior for any sequence of events.

Integrating information, financial, and material flows in a chemical supply chain

We address the flows involved in a real supply chain and discuss how they can be integrated for supply chain management. A scheduling model is proposed based on a State-Task Network representation to schedule order transactions and manufacturing operations in a make-to-order chemical plant. The proposed model is compared to scheduling models that focus on either the order transactions or the manufacturing operations. The advantage of the integrated approach is found in the accuracy of the solutions attained, whereas the siloed models produce suboptimal or infeasible solutions. Each model is compared in a stochastic discrete event simulation environment. An integrated scheduling model is also presented, which includes information, financial, and material flows along a three-echelon supply chain. This integrated model serves as a starting point for developing decision-support systems that take a more comprehensive view of the complex relationships amongst the different flows involved in real supply chains.

Online prognosis of stochastic discrete event systems with guaranteed performance bound

In this paper, we consider the online prognosis of stochastic discrete event systems. Even though it is easy to predict the occurrence of faults in advance accurately for a prognosable discrete event system, it is much more difficult to do so for systems that are not prognosable. In this paper, we solve the online prognosis problem in a stochastic discrete event system framework. Our idea is to calculate the probability of the occurrence of faults in the future when a no-fault observable string is observed. We say an observable string is no-fault if no faults have occurred when it is observed. We then compare the probability with a pre-set threshold to decide whether to issue an alert or not. We develop a method to calculate the lower bound for possible thresholds, which has the fewest false alerts and no missed alerts of faults. For a given threshold, we use the rate of missed fault alerts and the rate of false fault alerts to evaluate the performance of fault prognosis. We formally define these two rates and develop algorithms to calculate them. These results can guide us in choosing a proper threshold to achieve the best trade-off between false fault alerts and missed alerts of faults.

Probabilistic verification of diagnosability for a certain class of timed stochastic systems

This paper addresses diagnosability for a class of timed stochastic discrete event systems that are modeled with labeled continuous time Markov models. A large variety of fault patterns is considered and the paper aims to define and propose conditions for weak notions of diagnosability of fault patterns in a time stochastic framework. The proposed approach is based on a state isolation perspective. Logical and probabilistic verifiers that result by first taking the product of the system with the fault pattern, followed by the parallel composition of the resulting structure with its logical observer are designed in this perspective. The advantage of this schema is to separate explicitly the system from the pattern we are interested in, as well as from the sensoring and observational aspects. Consequently, the verifiers allow the explicit tracking of the information about the first occurrence of a fault pattern and the preservation of not only the logical information provided by the labeling function but also the timing aspects imposed by the dynamics of the system.

Simulation optimization for stochastic casualty collection point location and resource allocation problem in a mass casualty incident

After a severe disaster strikes, a large number of casualties in need of urgent treatment, known as a mass casualty incident (MCI) event, arise from multiple disaster areas in a very short period of time and overwhelm available resources of the local healthcare system. This paper focuses on the effective design of casualty collection point (CCP) locations and the efficient allocation of limited emergency medical service (EMS) resources to transport casualties quickly to appropriate hospitals and increase the survival rate of casualties. A hybrid simulation–optimization approach to optimize the CCP location and EMS resource allocation problem over mixed binary and integer feasible domains for the minimization of expected complete delivery time of all casualties from disaster region to hospitals is presented in this work due to the stochastic and dynamic nature of the MCI logistics environment. A high-resolution stochastic discrete event simulation model considering time-varying stochastic casualty arrivals, random triage service times, and stochastic travel times caused by road network vulnerability is first constructed to describe a more detailed modeling of comprehensive MCI humanitarian logistics from the disaster regions to the hospitals. Then, a novel two-stage sequential algorithm, namely a combination of optimal computing budget allocation-based rapid-screening algorithm and adaptive particle global and hyperbox local search (ORSA-APGHLS), is developed to speed up convergence to near-optimal solutions compared to three common existing algorithms (Genetic Algorithm, Tabu Search and Stochastic Nelder-Mead Algorithm) under a limited simulation budget. We collaborate with the National Science and Technology Center for Disaster Reduction (NCDR) in Taiwan to conduct computational experiments to demonstrate the efficiency and efficacy of the proposed two-stage ORSA-APGHLS algorithm according to a potential earthquake scenario occurring in Tainan City, Taiwan. Through sensitivity analysis, the influence of different levels of scarce emergency medical resources and degrees of road damage on the expected complete delivery time of all casualties and the location-allocation decisions are investigated.

Robustness Evaluation Process for Scheduling under Uncertainties

Scheduling production is an important decision issue in the manufacturing domain. With the advent of the era of Industry 4.0, the basic generation of schedules becomes no longer sufficient to face the new constraints of flexibility and agility that characterize the new architecture of production systems. In this context, schedules must take into account an increasingly disrupted environment while maintaining a good performance level. This paper contributes to the identified field of smart manufacturing scheduling by proposing a complete process for assessing the robustness of schedule solutions: i.e., its ability to resist to uncertainties. This process focuses on helping the decision maker in choosing the best scheduling strategy to be implemented. It aims at considering the impact of uncertainties on the robustness performance of predictive schedules. Moreover, it is assumed that data upcoming from connected workshops are available, such that uncertainties can be identified and modelled by stochastic variables This process is supported by stochastic timed automata for modelling these uncertainties. The proposed approach is thus based on Stochastic Discrete Event Systems models and model checking techniques defining a highly reusable and modular process. The solution process is illustrated on an academic example and its performance (generecity and scalability) are deeply evaluated using statistical analysis. The proposed application of the evaluation process is based on the technological opportunities offered by the Industry 4.0.

Metamodel optimization of a complex, rural–urban emergency medical services system

Complex simulation systems, such as those involving emergency medical services (EMS), are often too computationally demanding to be used in optimization problems. Metamodeling is an attractive alternative, in which a sample of system configurations is evaluated using simulation, and a fast predictive model is developed as a surrogate for the slow simulator. Though the metamodeling literature is extensive, there has been little exploration of how much data is required to construct metamodels that can be used to solve optimization problems effectively, particularly in the context of a complicated rural–urban EMS system environment. In this work, the EMS system in northern St. Louis County, Minnesota is studied, with the goal of discovering station configurations with improved response times. The underlying physical system is complex, with 12 stations spread across both rural and urban areas and a fairly large geographic footprint. A decade of call data is used to develop and validate a stochastic discrete event simulator (DES) for this system, and then the simulator and raw data are used to select realistic station configurations to train the metamodel. Results are first given for just a single station within the system, and then increasingly complex settings are examined culminating with consideration of all 12 stations. Overall, though the metamodeling approach was effective for simpler cases, it requires a tremendous amount of data for larger settings. Specifically for the St. Louis County example, improved configurations were found for the one- and two-station cases, but the amount of data required to produce effective metamodels for the five- and twelve-station versions of the system was computationally infeasible given current DES and optimization heuristic implementations.

Diagnosability of fault patterns with labeled stochastic Petri nets

This paper is about the diagnosability of fault patterns in timed stochastic discrete event systems. For this purpose, the diagnosability problem is formulated with labeled stochastic Petri net models and pure logical fault pattern nets. A particular composition of a labeled stochastic Petri net with a fault pattern net is proposed and is shown to characterize in an explicit way the fault patterns, including the timing and probabilistic aspects of the underlying system. Logical and probabilistic verifiers are derived, and used to establish a set of conditions to check not only the strong diagnosability property but also weaker notions of diagnosability.

Developing a framework to enhance the seismic resilience of the electricity distribution system feeding the healthcare system

Delivering electricity to hospitals is vital for maintaining hospitals' functionality. Given the seismic vulnerability of electrical substations, providing effective rehabilitation plans for repairing these systems seems necessary for a resilient healthcare system. Studies concerning interdependent systems' functionality have not thoroughly addressed the interdependency of healthcare and electrical distribution systems. A framework to identify the effectiveness of different post-disaster rehabilitation plans for electrical substations to enhance the resilience of the healthcare system electricity is developed in this study, which increases the recoverability of the healthcare system after an earthquake. The vulnerability analysis for electrical facilities is done using modified fragility functions, considering the effects of aging as well. The geographical information system is used for assigning patients to hospitals given several patients' decision criteria. The framework uses a stochastic discrete event simulation to determine the effectiveness of different rehabilitation scenarios for five days after an earthquake occurs while using patients’ waiting time as the performance measure. Finally, the proposed framework is applied to Ghazvin city in the north-west of Iran. The results show that the best scenario would increase system resilience by 85%, highlighting the importance of identifying and implementing the best scenario.

Abstract executions of stochastic discrete event systems

Stochastic discrete event systems play a steadily increasing role in reliability engineering and beyond in systems engineering. Designing stochastic discrete event systems presents however well-known difficulties: models are hard to debug and to validate because of the existence of infinitely many possible executions, itself due to stochastic delays, which are possibly intertwined with deterministic ones. In this article, revisiting ideas introduced in the framework of model-checking of timed and hybrid systems, we show that it is possible to abstract the time in stochastic discrete event systems. More specifically, we show that schedules of transitions can be abstracted into systems of linear inequalities and that abstract and concrete executions are bisimilar. The result presented in this article represents thus a very important step forward in quality assurance of stochastic models of complex technical systems. We illustrate the potential of the proposed approach by means of AltaRica 3.0 models.

Abstract executions of stochastic discrete event systems

Abstract executions of stochastic discrete event systems

Simulation with Fuzzy Durations

Traditional stochastic discrete event simulation method requires the users to fit the task duration data with an empirical probability function or a theoretical probability density function. This has limited the application of discrete event simulation techniques from research stage to construction practice due to the tedious data fitting tasks required for the construction operation planners lacking of statistical background. On the other hand, usually the activity duration estimated by practitioners contains some kind of vagueness caused by estimator's subjective judgment. This type of vagueness may be more appropriate to be modeled by fuzzy numbers that can be assessed without data fitting. This paper proposes a new mechanism where fuzzy duration modeled by fuzzy numbers can be used in discrete event simulation. Consequently, the tedious data fitting tasks are eliminated but the uncertainty of task duration is still taken into account.

Exposure and Revelation Times as a Measure of Opacity in Timed Stochastic Discrete Event Systems

Opacity is a security notion that focuses on determining whether a given system's behavior is kept secret to intruders. Various notions of opacity have received significant attention during the last decade including current state opacity and initial state opacity, which have been studied for deterministic and probabilistic systems in untimed contexts. In timed systems, opacity requirements may vary with time and one could also be interested in knowing the time duration for which opacity requirements are violated or preserved. The main contribution of this article is to introduce and analyze opacity exposure and opacity revelation times as measures of vulnerability in timed discrete event system (DES) that behave according to Markovian dynamics (i.e., at any given time, all enabled events are independent and distributed in time with exponential probability density functions). Labeled stochastic Petri nets (LSPNs) are used to model timed stochastic DESs, and appropriate constructions (involving current and initial state observers) are used to evaluate exposure and revelation times for a given LSPN.

Diagnosis of Structural and Temporal Faults for $k$ -Bounded Non-Markovian Stochastic Petri Nets

This paper concerns the diagnosis of faults for stochastic discrete event systems that behave according to non-Markovian dynamics. ${k}$ -bounded partially observed Petri nets are used to model the system structure and the sensors. Stochastic processes with probability density functions (pdf) of finite support define the dynamics. Structural and temporal faults are considered. Structural faults correspond to specific sequences of events that should satisfy precedence conditions defined with patterns. Temporal faults are defined with time constraints that must be fulfilled by the firing durations. The probabilities of consistent trajectories are computed with a numerical scheme from the collected timed measurements. The advantage of the proposed scheme is that it can be used for a large variety of pdf that may be defined either with an analytical or a numerical description. It works also for various time semantics. Diagnosis in terms of probability for faulty patterns and temporal constraints is established as a consequence.

COVID-19 scenario modelling for the mitigation of capacity-dependent deaths in intensive care.

Managing healthcare demand and capacity is especially difficult in the context of the COVID-19 pandemic, where limited intensive care resources can be overwhelmed by a large number of cases requiring admission in a short space of time. If patients are unable to access this specialist resource, then death is a likely outcome. In appreciating these ‘capacity-dependent’ deaths, this paper reports on the clinically-led development of a stochastic discrete event simulation model designed to capture the key dynamics of the intensive care admissions process for COVID-19 patients. With application to a large public hospital in England during an early stage of the pandemic, the purpose of this study was to estimate the extent to which such capacity-dependent deaths can be mitigated through demand-side initiatives involving non-pharmaceutical interventions and supply-side measures to increase surge capacity. Based on information available at the time, results suggest that total capacity-dependent deaths can be reduced by 75% through a combination of increasing capacity from 45 to 100 beds, reducing length of stay by 25%, and flattening the peak demand to 26 admissions per day. Accounting for the additional ‘capacity-independent’ deaths, which occur even when appropriate care is available within the intensive care setting, yields an aggregate reduction in total deaths of 30%. The modelling tool, which is freely available and open source, has since been used to support COVID-19 response planning at a number of healthcare systems within the UK National Health Service.Electronic supplementary materialThe online version of this article (10.1007/s10729-020-09511-7) contains supplementary material, which is available to authorized users.

Privacy and safety analysis of timed stochastic discrete event systems using Markovian trajectory-observers

Various aspects of privacy and safety in many application domains can be assessed based on proper analysis of successive measurements that are collected about a given system. This work is devoted to such issues in the context of timed stochastic discrete event systems (DES) that are modeled with partially observed timed stochastic Petri net models. The first contribution is to introduce a k-step trajectory-observer, which is a construction that captures all possible k-suffixes of the trajectories that are consistent with a given sequence of measurements that has been recorded. When the system behaves according to Markovian dynamics (i.e., all event occurrences are distributed in time with exponential probability density functions), a parallel-like composition of the timed system with the resulting observer is proposed that leads to a Markovian process. The second contribution is to take advantage of the Markovian analysis to compute certain important characteristic times during which the underlying system should satisfy a given property (based on the suffixes of length k of a given trajectory). To illustrate the approach, we consider two particular properties, namely k-suffix language opacity and k-diagnosability, which can be studied in a stochastic timed context using the Markovian trajectory observer.

Pattern diagnosis for stochastic discrete event systems

In this paper, pattern diagnosis problem in stochastic discrete event system (SDES) is investigated. In a system, an abnormal state may be caused by the occurrence of several normal events. This kind of fault is called fault pattern. The diagnosis problem of fault pattern is defined as pattern diagnosis. Based on the notions of A-diagnosability and AA-diagnosability in SDES, the definitions of PA-diagnosability and PAA-diagnosability for pattern diagnosability in SDES are presented in this paper. In addition, a necessary and sufficient condition for an SDES to be PA-diagnosable is proposed. The goal of this paper is diagnosing fault pattern in the real systems. Three-Tank Water Level Control System and Heating, Ventilation, and Air-conditioning System are described to illustrate our algorithm. Experimental results demonstrate that pattern diagnosability in SDES is more accurate than that in DES.

Development and Initial Validation of a Stochastic Discrete Event Simulation to Assess Disaster Preparedness

Introduction:Assessing disaster preparedness in a given region is a complex problem. Current methods are often resource-intensive and may lack generalizability beyond a specific scenario. Computer-based stochastic simulations may be an additional method but would require systems that are valid, flexible, and easy to use. Emergo Train System (ETS) is an analog simulation system used for disaster preparedness assessments.Aim:To digitalize the ETS model and develop stochastic simulation software for improved disaster preparedness assessments.Methods:A simulation software was developed in C#. The simulation model was based on ETS. Preliminary verification and validation (V&V) tests were performed, including unit and integration testing, trace validation, and a comparison to a prior analog ETS disaster preparedness assessment exercise.Results:The software contains medically validated patients from ETS and is capable of automatically running disaster scenarios with stochastic variations in the injury panorama, available resources, geographical location, and other variables. It consists of two main programs: an editor where scenarios can be constructed and a simulation system to evaluate the outcome. Initial V&V testing showed that the software is reliable and internally consistent. The comparison to the analog exercise showed a general high agreement in terms of patient outcome. The analog exercise featured a train derailment with 397 injured, of which 45 patients suffered preventable death. In comparison, the computer simulation ran 100 iterations of the same scenario and indicated that a median of 41 patients (IQR 31 to 44) would suffer a preventable death.Discussion:Stochastic simulation methods can be a powerful complement to traditional capability assessments methods. The developed simulation software can be used for both assessing emergency preparedness with some validity and as a complement to analog capability assessment exercises, both as input and to validate results. Future work includes comparing the simulation to real disaster outcomes.