Discrete Event Dynamic Systems Research Articles

Modeling and Analysis of Protein Synthesis and DNA Mutation Using Colored Petri Nets

In molecular biology, protein synthesis is an essential biological process of generating specific proteins in living systems. Many mathematical models are designed to characterize the process of the flow of genetic information from deoxyribonucleic acid (DNA) to protein; however, most of them cannot provide detailed and observed steps to describe and analyze this fundamental biological process. Colored Petri Net (CPN), as a mathematical method widely applied in the process analysis of discrete event dynamic systems, has increasingly become an innovative and efficient theoretical approach for exploring the biological processes. Aiming at describing the entire process of protein synthesis, a CPN-based model has been designed that successfully and intuitively represents the flow of genetic information involving transcription and translation. DNA mutations are permanent alterations in the nucleotide sequence of the DNA strand, while different types of mutations have various effects on the synthesized proteins. Based on the proposed protein synthesis model, we put forward a new CPN model to identify the type of mutation, which is beneficial for analyzing whether the mutation has impacts on the structure or function of the produced protein. The mutation position and bases mutated rate are obtained by contrasting the nucleobases on DNA sequences, while the mutation type is determined via the alignment of the amino acids in the polypeptide chain. The model’s effectiveness and accuracy are illustrated by biological mutation examples, indicating this method offers great superiority in modeling and analyzing the complex biological processes.

A Two-level Traffic Light Control Strategy for Preventing Incident-Based Urban Traffic Congestion

This work designs a two-level strategy at signalized intersections for preventing incident-based urban traffic congestion by adopting additional traffic warning lights. The first-level one is a ban signal strategy that is used to stop the traffic flow driving toward some directions, and the second-level one is a warning signal strategy that gives traffic flow a recommendation of not driving to some directions. As a visual and mathematical formalism for modeling discrete-event dynamic systems, timed Petri nets are utilized to describe the cooperation between traffic lights and warning lights, and then verify their correctness. A two-way rectangular grid network is modeled via a cell transmission model. The effectiveness of the proposed two-level strategy is evaluated through simulations in the grid network. The results reveal the influences of some major parameters, such as the route-changing rates of vehicles, operation time interval of the proposed strategy, and traffic density of the traffic network on a congestion dissipation process. The results can be used to improve the state of the art in preventing urban road traffic congestion caused by incidents.

A Behavioural Analysis of Complexity in Socio-Technical Systems under Tension Modelled by Petri Nets

Complexity analysis of dynamic systems provides a better understanding of the internal behaviours that are associated with tension and efficiency, which in the socio-technical systems may lead to innovation. One of the popular approaches for the assessment of complexity is associated with self-similarity. The dynamic component of dynamic systems represents the relationships and interactions among the inner elements (and its surroundings) and fully describes its behaviour. The approach used in this work addresses complexity analysis in terms of system behaviour, i.e., the so-called behavioural analysis of complexity. The self-similarity of a system (structural or behavioural) can be determined, for example, using fractal geometry, whose toolbox provides a number of methods for the measurement of the so-called fractal dimension. Other instruments for measuring the self-similarity in a system, include the Hurst exponent and the framework of complex system theory in general. The approach introduced in this work defines the complexity analysis in a social-technical system under tension. The proposed procedure consists of modelling the key dynamic components of a discrete event dynamic system by any definition of Petri nets. From the stationary probabilities, one can then decide whether the system is self-similar using the abovementioned tools. In addition, the proposed approach allows for finding the critical values (phase transitions) of the analysed systems.

Accelerated Simulation of Discrete Event Dynamic Systems via a Multi-Fidelity Modeling Framework

Simulation analysis has been performed for simulation experiments of all possible input combinations as a “what-if” analysis, which causes the simulation to be extremely time-consuming. To resolve this problem, this paper proposes a multi-fidelity modeling framework for enhancing simulation speed while minimizing simulation accuracy loss. A target system for this framework is a discrete event dynamic system. The dynamic property of the system facilitates the development of variable fidelity models for the target system due to its high computational cost; and the discrete event property allows for determining when to change the fidelity within a simulation scenario. For formal representation, the paper defines several key concepts such as an interest region, a fidelity change condition, and a selection model. These concepts are integrated into the framework to allow for the achievement of a condition-based disjunction of high- and low-fidelity simulations within a scenario. The proposed framework is applied to two case studies: unmanned underwater and urban transportation vehicles. The results show that simulation speed increases at least 1.21 times with a 5% accuracy loss. We expect that the proposed framework will resolve a computationally expensive problem in the simulation analysis of discrete event dynamic systems.

Instruction-throughput regulation in computer processors with data-center applications

This paper tests a recently-proposed technique for regulating output performance of Discrete Event Dynamic Systems and Stochastic Hybrid Systems. The controller is based on an integrator with a variable gain, adjusted so as to guarantee wide stability margins of the closed-loop system. The gain is adjusted by estimating, in real time, the derivative of the plant function via approximations to its IPA derivative. The technique is robust to computational errors in the loop, and hence these approximations are designed for fast computation rather than precision. The development of the regulation technique has been motivated by applications in computer processors, and extensively tested in the past on a cycle-level, full system simulator. In this paper we describe implementations of the regulator on an Intel machine based on the Haswell processor, and apply it to control the instructions’ throughput of various industry program-benchmarks as well as data-center applications.

Perturbation Analysis: A Framework for Data-Driven Control and Optimization of Discrete Event and Hybrid Systems

The history of Perturbation Analysis (PA) is intimately related to that of Discrete Event Dynamic Systems (DEDS), starting with a solution of a long-standing problem in the late 1970s and continuing today with the control and optimization of Hybrid Systems and the emergence of event-driven control methods. We review the origins of the PA theory and how it became part of a broader framework for models, control and optimization of DEDS. We then discuss the theoretical underpinnings of Infinitesimal Perturbation Analysis (IPA) as a data-driven stochastic gradient estimation method and how it has been applied over the past few decades. We explain how IPA offers a basis for general-purpose stochastic optimization of Markov systems through the notion of the performance potential and how it has evolved beyond DEDS and now provides a framework for control and optimization of Hybrid Systems and, more generally, event-driven methodologies.

An Iterative Approach to Reduce Systemic Risk among Financial Institutes

Financial institutions are interconnected by holding debt claims against each other. The interconnection is a key contributing factor to the past worldwide financial crisis. A default bank may cause its creditors to default, and the risk may be further propagated to up-stream institutes. We study how the mechanism of default liquidation affects the total wealth of the financial system and curbs the risk contagion. We formulate this problem as a nonlinear optimization problem with equilibrium constraints and propose an optimal liquidation policy to minimize the system’s loss without changing the partition of default and non-default banks. We show that the optimization problem resembles a Markov decision problem (MDP) and therefore we can apply the direct-comparison based optimization approach to solve this problem. We derive an iteration algorithm which combines both the policy iteration and the gradient based approach. Our work provides a new direction in curbing the risk contagion in financial networks; and it illustrates the advantages of the direct-comparison based approach, which originated in the field of discrete event dynamic system, in nonlinear optimization problems.

An approach to distinguishing the levels of free-labeled $L$-type Petri net languages in the Chomsky hierarchy

Petri nets (PNs) and automatic machines are two approaches to modeling discrete event dynamic systems. The relationship between these approaches is important for controlling discrete event dynamic systems. This paper investigates the relationship between these approaches from the formal language point of view, i.e., we introduce an approach to distinguishing the levels of free-labeled $L$-type PN languages in the Chomsky hierarchy. To characterize PNs from the formal language point of view, the concepts of increaser, valid increaser, and linearer are introduced. For a PN with no valid increaser, its PN language is regular. For a PN with a valid increaser with at least two linearers, its PN language is context-sensitive. For a PN in which each valid increaser has only one linearer, assuming only one increaser in the PN, the PN language is context-free. If the PN has more than one increaser, the corresponding PN language is context-sensitive when valid increasers and their linearers can be fired currently or crossed. The language is context-free when the increasers and their linearers are fired alternatively, or an increaser and its linearer are fired sequentially relative to other increasers and their linearers, or when firing occurs after an increaser and before its linearer.

Performance regulation in discrete event and hybrid dynamical systems using IPA

This paper considers a performance regulation technique for a class of timed discrete-event and hybrid dynamical systems, aimed at an output tracking of a given setpoint reference. The regulator, designed for simplicity and efficiency of computation, consists of a variable-gain integrator that yields effective tracking despite abrupt changes to the system. The gain is computed in real time by infinitesimal perturbation analysis, and the resultant control system displays wide stability margins as well as considerable robustness to modeling and computing errors. In particular, we consider errors resulting from approximations that are made to the controller’s gains in order to speed up their computations. Previous analysis was carried out under assumptions of differentiable sample-performance functions which serve to approximate a steady-state (expected-valued) function. We dispense with these two assumptions which often are unrealistic in time-varying systems. The paper proves convergence of the regulation technique and demonstrates the results on simulation examples.

A sample gradient-based algorithm for a multiple-OR and PACU surgery scheduling problem

ABSTRACTIn this article, we study a surgery scheduling problem in multiple Operating Rooms (ORs) constrained by the Post-Anesthesia Care Unit (PACU) capacity within the block-booking framework. With surgery sequences predetermined in each OR, a Discrete-Event Dynamic System (DEDS) is devised for the problem. A DEDS-based stochastic optimization model is formulated in order to minimize the cost incurred from patient waiting time, OR idle time, OR blocking time, OR overtime, and PACU overtime. A sample gradient-based algorithm is proposed for the sample average approximation of our formulation. Numerical experiments suggest that the proposed method identifies near-optimal solutions and outperforms previous methods. We also show that considerable cost savings (11.8% on average) are possible in hospitals where PACU beds are a constraint.

Modeling and Simulation of Metallurgical Process Based on Hybrid Petri Net

In order to achieve the goals of energy saving and emission reduction of iron and steel enterprises, an increasing number of modeling and simulation technologies are used to research and analyse metallurgical production process. In this paper, the basic principle of Hybrid Petri net is used to model and analyse the Metallurgical Process. Firstly, the definition of Hybrid Petri Net System of Metallurgical Process (MPHPNS) and its modeling theory are proposed. Secondly, the model of MPHPNS based on material flow is constructed. The dynamic flow of materials and the real-time change of each technological state in metallurgical process are simulated vividly by using this model. The simulation process can implement interaction between the continuous event dynamic system and the discrete event dynamic system at the same level, and play a positive role in the production decision.

Performance regulation of event-driven dynamical systems using infinitesimal perturbation analysis

This paper presents a performance-regulation method for a class of stochastic timed event-driven systems aimed at output tracking of a given reference setpoint. The systems are either Discrete Event Dynamic Systems (DEDS) such as queueing networks or Petri nets, or Hybrid Systems (HS) with time-driven dynamics and event-driven dynamics, like fluid queues and hybrid Petri nets. The regulator, designed for simplicity and speed of computation, is comprised of a single integrator having a variable gain to ensure effective tracking under time-varying plants. The gain’s computation is based on the Infinitesimal Perturbation Analysis (IPA) gradient of the plant function with respect to the control variable, and the resultant tracking can be quite robust with respect to modeling inaccuracies and gradient-estimation errors. The proposed technique is tested on examples taken from various application areas and modeled with different formalisms, including queueing models, Petri-net model of a production-inventory control system, and a stochastic DEDS model of a multicore chip control. Simulation results are presented in support of the proposed approach.

STP Approach to Model Controlled Automata with Application to Reachability Analysis of DEDS

AbstractThis paper introduces semi‐tensor product of matrices (STP), a new matrix analysis tool, into the field of discrete event dynamic system (DEDS). Using STP, the dynamics of controlled automaton are modelled as an algebraic expression of the states, events and control specification. Based on this algebraic description, a sufficient and necessary condition is proposed to check whether any two states of a DEDS are reachable or not. The condition suggests an algorithm which can discover all the event strings by which a controlled automaton can move to one state from another one if they are reachable. All the results can be used to analyze corresponding problems of finite automata after simple modification. Finally, illustrative examples examine the correctness of the presented results/algorithm and demonstrate the modification after which the results are suitable for finite automata. The approach of this paper provides a new angle and means to understand and analyze the dynamics of DEDS.

Stability of Dynamical Systems-On the Role of Monotonic and Non-Monotonic Lyapunov Functions [Bookshelf

The contents of the book are a review of dynamical systems,the principal stability and boundedness results on metric spaces, specialized stability and boundedness results on metric spaces, applications to discrete-event systems, stability results for finite-dimensional dynamical systems, applications to the stability of finite-dimensional dynamical systems, and stability results for infinite-dimensional systems. Each chapter ends with three final sections: Notes and References, Problems, and Bibliography; these sections are welcome additions that provide insights and perspectives beyond the main content of the chapters. This second edition provides more emphasis on the stability of discrete-event and hybrid systems than the first edition [1] (see [2] for an earlier review), and it emphasizes the use of non-monotonic Lyapunov functions, which the authors developed in their recent research publications. In the Preface, the authors motivate the introduction of non-monotonic Lyapunov functions; this generalization is used to derive a general form of Lyapunov stability results. Further, in the case that the Lyapunov functions are monotonic, standard Lyapunov stability results are obtained. In practice, this extension is primarily motivated by discrete event and hybrid dynamical systems. These new features add significant material to the first edition. This new edition of the book provides a scholarly and comprehensive view of Lyapunov stability that should be accessible to mathematically inclined graduate students and to many researchers in the control field. It is a welcome addition to the published literature.

Planned Traffic Stability on a Rail Network

Impetuous multiplication of mobility and road traffic proliferation lead to concerns for increasing the attractiveness of urban public transport. Compared to private car use, urban public transport attractiveness is conditioned, in particular, by travel times and certainty of respecting the transport schedules, meaning planned traffic stability. Traffic schedules are considered to be more stable as the primary delays from the announced schedule have low probabilities and values and their propagation as repeated delays is least noticed in time and space. Solutions for assuring traffic stability must take into consideration contradictory aspects, because introducing time reserves in the schedules means time travel extensions. In order to assure the stability of planned traffic, present paper develops studies of various models and methods that aim to reduce inherent primary delays. Thereby, for studying repeated delays on a complex network, a mathematical model adequate to a Discrete Event Dynamic System (DEDS), that in MAX-PLUS algebra becomes a linear system, was used. The paper concludes with a case study on an integrated network resulted from the superposition of Bucharest’s existing suburban rail network with the underground network designed for 2030, being identified measures for improving the stability indicators. Traffic stability is assessed on the basis of two indicators: instability coefficient and delay elimination rate. Main measure for improving stability indicators is the growth of time reserves taking into consideration the quality requirements resulting from the condition of maintaining a reduced planned travel time.

Mobile Robot Lab Project to Introduce Engineering Students to Fault Diagnosis in Mechatronic Systems

This paper proposes lab work for learning fault detection and diagnosis (FDD) in mechatronic systems. These skills are important for engineering education because FDD is a key capability of competitive processes and products. The intended outcome of the lab work is that students become aware of the importance of faulty conditions and learn to design FDD strategies for a real system. To this end, the paper proposes a lab project where students are requested to develop a discrete event dynamic system (DEDS) diagnosis to cope with two faulty conditions in an autonomous mobile robot task. A sample solution is discussed for LEGO Mindstorms NXT robots with LabVIEW. This innovative practice is relevant to higher education engineering courses related to mechatronics, robotics, or DEDS. Results are also given of the application of this strategy as part of a postgraduate course on fault-tolerant mechatronic systems.

Diagnosability of Petri nets with observation graphs

This paper addresses the problem of diagnosability for dynamic discrete event systems modeled with bounded or unbounded Petri nets that are deadlock-free and monitored with sensor configurations with marking and event measurements. The proposed method gives necessary and sufficient conditions for diagnosability. It is based on the transformation of the coverability graph into an observation graph that encodes all observation sequences of measured markings and events with respect to the sensor configuration. This graph also encodes all sequences of transitions that may fire from any reachable marking of the Petri net. Diagnosability is determined by analyzing the paths and circuits in the observation graph. The method is illustrated with several examples of bounded or unbounded Petri nets.

A Branch and Bound Algorithm for Cyclic Scheduling of Timed Petri Nets

A timed Petri net (TPN) has been widely used for modeling, scheduling, and analyzing discrete event dynamic systems. This study examines cyclic scheduling problems of a TPN to minimize the cycle time especially for automated manufacturing systems. Appropriate token routing at each conflict place can make a TPN repeat an identical firing sequence. We propose a systematic procedure to transform a TPN with such cyclic token routing into an equivalent timed event graph (TEG) for which the cycle time and firing schedules can be evaluated by a linear programming (LP). Based on the transformation procedure, we develop an efficient branch and bound algorithm to solve the scheduling problem. A partial solution is defined as a partial token route that has only a subset of token routes for determining the complete schedule. The lower bound of a partial solution is determined by the cycle time of a TEG that has the partial token route. The cycle time of a TEG with an additional token route for a new partial solution is computed by a dual-simplex algorithm which avoids solving the LP completely again. A dynamic branching strategy that prevents unnecessary branching for the scheduling decision is also proposed. We demonstrate the computational efficiency through intensive experiments of cluster tools and robotic flow shops.

Hybrid and Hybrid Adaptive Petri Nets: On the computation of a Reachability Graph

Petri Nets (PNs) constitute a well known family of formalisms for the modelling and analysis of Discrete Event Dynamic Systems (DEDS). As general formalisms for DEDS, PNs suffer from the state explosion problem. A way to alleviate this difficulty is to relax the original discrete model and deal with a fully or partially continuous model. In Hybrid Petri Nets (HPNs), transitions can be either discrete or continuous, but not both. In Hybrid Adaptive Petri Nets (HAPNs), each transition commutes between discrete and continuous behaviour depending on a threshold: if its load is higher than its threshold, it behaves as continuous; otherwise, it behaves as discrete. This way, transitions adapt their behaviour dynamically to their load. This paper proposes a method to compute the Reachability Graph (RG) of HPNs and HAPNs.

Modeling of Warehouse System with RFID Based on Petri Net

Technology of RFID has been widely used in modern warehouse system, with which systems’ working efficiency was improved and error rate was reduced. This paper is aimed at providing a new warehouse operation procedure which take technology of RFID into concern. The new warehouse operation procedure is implemented using the Petri net method which is suitable to the needs of the system being a discrete event dynamical system.