Forecast of Train Delay Propagation Based on Max-Plus Algebra Theory

Max-Plus algebra has been used to model and analyze network problems, such as railway networks, project scheduling, queuing systems, and production systems. In this network problem, Max-Plus Algebra is used for scheduling analysis. The assumption used in this analysis is a normal situation, there are no changes in the system that affect scheduling. One factor that is important and needs to be considered is the occurrence of delays in the system which affect scheduling. The objectives of this research are 1) to analyze the effect of system delays on scheduling, and 2) to determine interventions in the form of switching on the server to overcome delay propagation due to schedule delays at certain stages in the system. The simple production system in this research involves 3 servers. The arrangement of the three servers is a combination of parallel and series arrangements. The simulation in this research uses the Scilab. The switching carried out in this research is by speeding up the process on the server by 1 unit of time. The results of this research are 1) direct delay propagation occurs if the delay occurs on the server that contains the eigenvalues. If a delay occurs on a server that does not contain eigen values ​​then there will be no delay propagation provided that the amount of delay on that server does not exceed (t – 1) where t is the time required for the entire process from that server to the next server. If the delay exceeds (t – 1) then delay propagation will occur. 2) Based on simulations using Scilab, delay propagation can be overcome by switching one or more servers according to the delay point. Delays on the server containing the eigenvalues ​​can only be resolved by switching the server. Meanwhile, on servers that do not contain eigenvalues, switching can be done using a combination of these servers.

The running time of high-speed train is generally not late, and it can run normally in most cases. However, when severe weather conditions, train components and equipment, accidents or emergencies occur, it will lead to train operation delay and traffic congestion. Therefore, when an accident occurs, we need to adjust the train time or route timely and accurately. As an important algebraic system, max-plus algebra is widely used in the field of industrial production control. In industrial production, the most production mode is the discrete system , but the characteristics and the ability of discrete systems depends on the periodic of system and the number of workpiece produced by the system in unit time, and the characteristics of the system are closely related to the properties of the matrix, especially, the eigenvalues and eigenvectors of the matrix in the sense of max-plus algebra. Therefore, this paper studies the max-plus algebra theory and the solution of eigenvalues and eigenvectors of matrices in the sense of max-plus algebra, establish the operation time matrix to optimize the train operation adjustment model of high-speed railway, and analyze the failure propagation model.

Discrete event dynamic systems (DEDS), are systems, which change state over time, based on current state and state transition rules. Each state is separated from its neighbour by a step rather than a continuum of infinitesimal states. This continuum in DEDS needs a representation between 0 and 1. The application of fuzzy logic in defining and modelling the DEDS is suggested as a possible solution because the nature of DEDS may be asynchronous, distributed, parallel, non-deterministic and/or stochastic. This results in the generalisation of crisp finite automata into fuzzy automata for a DEDS. In this paper, a DEDS in the form of hopper feed system is considered. The system is reformulated using state vectors and event transition matrices and is extended to fuzzy vectors and matrices. An algorithm is proposed for the final control action to be implemented using a programmable logic controller (PLC).

ABSTRACTIn this paper, the static output feedback stabilisation of discrete event dynamic systems (DEDSs) is investigated via the semi-tensor product (STP) of matrices. Firstly, the dynamics of DEDSs modelled by deterministic Moore-type finite automata are converted into an matrix expression in the STP frame. Secondly, necessary and sufficient conditions for the existence of a static output feedback control pattern, stabilising the controlled discrete event dynamic systems to some equilibrium point, are given, and constructive algorithms to seek the static output feedback control pattern including an effective specific solution algorithm and an analytic solution algorithm are proposed. Thirdly, the equilibrium-based static output feedback stabilisation of DEDSs is extended to the set-based static output feedback stabilisation and necessary and sufficient conditions and constructive algorithms to seek the corresponding control pattern are provided. Finally, some examples are presented to illustrate the effectiveness of the proposed approach.

Algebraic Characteristics and Structure Decomposition for “Linear” Discrete Event Dynamic Systems

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.

Discrete event dynamic systems (DEDS) are prevalent in many areas of engineering, like manufacturing, maintenance, distributed computing, etc. Activities or discrete events in DEDS are generally large in numbers, highly parallel, distributed, and highly intertwined. Modeling DEDS systems are further complicated by the fact that the decisions to be made from the model may incorporate inference engines that uses advanced statistical analysis on massive data and may also include fuzzy decisions. This paper talks about development of a new tool for modeling and simulation of DEDS that can satisfy the characteristics mentioned above; the new tool is called General purpose Petri net Simulator (GPenSIM). This paper further presents a recent extension to the new tool, which is the real-time simulation capability.

In order to study the issue of train operation adjustment of high-speed rail, the method of train operation adjustment based on conflict resolution is proposed. The procedure of train operation adjustment is divided into two steps, namely train paths self-recovery and train operation conflicts resolution. The characteristics of train operation conflicts resolution such as rigid constraints, dynamic and real-time, and combinatorial optimization are analyzed. Based on the analysis of the functions of the time costs and the after-effects of the conflict resolution, the calculation of conflict resolution cost for high-speed rail is studied. The procedure of train operation conflicts resolution and train operation adjustment based on conflict resolution for high-speed rail are given.

ALGEBRAIC CHARACTERISTICS AND STRUCTURE DECOMPOSITION FOR “LINEAR” DISCRETE EVENT DYNAMIC SYSTEMS

Discrete Event Dynamic System (DEDS) is a dynamic system in which unexpected events take place at irregular intervals. Such systems can describe many different real phenomena occurring in transport networks, technological processes and computer systems and also in examples of design systems presented in this article. This article describes methods to support managing the design of IT infrastructure as a DEDS dealing with the allocation of human resources, the synchronisation of tasks and risk management. These methods are based on the max-plus system modelling theory , while the example uses a schedule of managing the design, implementation and deployment of software which helps monitor and control complex technological processes. The proposed solution can be used in both standard and agile & lean management principles promoted in recent years.

Rule-based Composable Modelling of Industrial Automation Automata under Nominal and Faulty Conditions

Because the classical control theory does not give satisfactory results in the DEDS (discrete event dynamic systems) control systems synthesis, especially in analytical terms, and because such systems are very important in human life-e.g. flexible manufacturing systems (FMS), transport systems, communications systems, etc.-another approaches are wanted. The main aim of this paper is to point out a simple approach leading to a very simple dealing with the FMS (as a kind of the DEDS) modelling and intelligent control problems solving. On that way imbedding some results of applied artificial intelligence, especially the rule-based knowledge representation and simple form of automatic reasoning, is used.

Investigated the environmental assessment from the point of system simulation, the environment assessment system belongs to the discrete event dynamic system. According to the comparison between the environment assessment system and the military command automation system, there are many common grounds in essence. Therefore, in order to solve the problems exist in environmental assessment field nowadays, the relative theories of the military command automation system (C4ISR) were transplanted to environmental assessment field. Finally, based on the information technology and the simulation technology one solution was constructed named Environmental Assessment Automation System-C4ISRE (Command, Control, Communications, Computer, Intelligence, Surveillance, Reconnaissance, Environmental Assessment). The relative theories of C4ISRE including Discrete Event Dynamic Systems (DEDS), the technology of using Petri Net (PN) to analyze and model the DEDS, Distributed Virtual Reality (DVR), Computer Generated Forces (CGF), Synthetic Natural Environment (SNE), Dynamic Environment Simulation (DSE), Environmental Assessment(EA). The integration of upper contents constructs the theory frame of Informatization Environmental Assessment (IEA?and also makes a stable theoretical base for IEA’s further research.

THE SUPERVISORY CONTROL PROBLEM SOLVED VIA PETRI NETS

Discrete event dynamical systems are used to model a number of engineering applications ranging from communication networks, distributed computing systems to manufacturing systems. A new analytical model is proposed for the analysis of asynchronous, optimistic distributed simulation of discrete event dynamical systems. The performance of traditional timewarp algorithms and that of a new rollback algorithm, Wolf, are examined in this framework and a comparison is attempted. A few preliminary implementations of Wolf on a distributed computing system confirm analytical results predicting a considerable reduction in error propagation, a decrease in the number of cancellations and an enhancement in the forward computation.