A Novel Model for Train Operation Adjustment in High-Speed Railway based on Max-plus Algebra

The forecast of delay time is of great assistance to decision making in train operation adjustment when the schedule is disturbed either by infrastructure fault or natural hazard. This paper presents a railway delay propagation model to forecast the delay time, described by discrete event dynamic system (DEDS) and formulated by max-plus algebra theory. On the basis of the train operation regulations and headway constraints, a system matrix of max-plus algebra is acquired to illustrate the mechanism of delay propagation. And then a function to predict the delay time is proposed to solve the model, with two advantages: Firstly, the specific delay time is able to be calculated; secondly, the result of the prediction is comparatively precise due to the highly match of the model to the actual operation. Finally, by analysis of the prediction, this paper offers the decision support in train adjustment, from which the dispatcher can proactively conduct countermeasures to alleviate the propagation and even stop it.

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.

Tolerance types of interval eigenvectors in max-plus algebra

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.

China’s High-Speed Railway (HSR) has entered the era of networked operation. Unpredictable emergencies may disrupt the normal operation of the railway, resulting in train delays. The delays may even cause cascading delays due to the track constraint. This paper proposed a delay propagation model by max-plus algebra, considering the constraint of the HSR network, to predict the spatial-temporal range of cascading delays under emergencies. Moreover, the operation strategy re-management in sections and the re-timing strategy due to the station capacity constraint are studied under emergencies, forming a chain model of emergencies, primary delays, and secondary delays. Simulation results show that the proposed model could accurately predict the secondary delay under different emergencies.

In view of the existing high-speed railway train operation plan system cannot accurately, comprehensively and intuitively reflect the transport equipment operating load and ability to adapt to the situation, cannot reflect the train group operation, operation diagram, station work plan between the complex interactive relationship, a train operation simulation module is designed in this paper which through the construction of high-speed railway traffic related electronic map and technical standards database, computer simulation on the train diagram has been made. Then, a high-speed railway operation plan simulation system is developed, which includes train planning, traction calculation and train operation simulation. Finally, simulation results show that high-speed railway operation plan simulation system can accurately simulate the whole process technical operation of the train group operation, operation process, generate statistical analysis results, thus we can get real-time visual inspection of the adaptability of operating equipment ability in the operation scheme, and provide strong support for the work of high-speed train running organization. It is of great significance to improve the level of high-speed railway traffic organization.

A discrete event system is a system whose behavior is determined by events and their events change at discrete times. The eyelash production system at PT Bio Takara Purwokerto is a discrete event system problem and can be expresses in a max-plus linear problem. By using the power algorithm, it is determined eigen values ​​and eigen vectors over max-plus algebra which will be used as production time periodization. The results obtained that the periodic time for the eyelash production system at PT Bio Takara Purwokerto is 78.488 minutes. Based on this periodic time, we can then obtain the time each processing unit starts working to produce eyelashes.

Obtaining the eigenvalues and eigenvectors of large matrices is a key problem in electronic structure theory and many other areas of computational science. The computational effort formally scales as O(N3) with the size of the investigated problem, N (e.g. the electron count in electronic structure theory), and thus often defines the system size limit that practical calculations cannot overcome. In many cases, more than just a small fraction of the possible eigenvalue/eigenvector pairs is needed, so that iterative solution strategies that focus only on a few eigenvalues become ineffective. Likewise, it is not always desirable or practical to circumvent the eigenvalue solution entirely. We here review some current developments regarding dense eigenvalue solvers and then focus on the Eigenvalue soLvers for Petascale Applications (ELPA) library, which facilitates the efficient algebraic solution of symmetric and Hermitian eigenvalue problems for dense matrices that have real-valued and complex-valued matrix entries, respectively, on parallel computer platforms. ELPA addresses standard as well as generalized eigenvalue problems, relying on the well documented matrix layout of the Scalable Linear Algebra PACKage (ScaLAPACK) library but replacing all actual parallel solution steps with subroutines of its own. For these steps, ELPA significantly outperforms the corresponding ScaLAPACK routines and proprietary libraries that implement the ScaLAPACK interface (e.g. Intel’s MKL). The most time-critical step is the reduction of the matrix to tridiagonal form and the corresponding backtransformation of the eigenvectors. ELPA offers both a one-step tridiagonalization (successive Householder transformations) and a two-step transformation that is more efficient especially towards larger matrices and larger numbers of CPU cores. ELPA is based on the MPI standard, with an early hybrid MPI-OpenMPI implementation available as well. Scalability beyond 10 000 CPU cores for problem sizes arising in the field of electronic structure theory is demonstrated for current high-performance computer architectures such as Cray or Intel/Infiniband. For a matrix of dimension 260 000, scalability up to 295 000 CPU cores has been shown on BlueGene/P.

The paper deals with modeling and control of the real battery assembly system, which is under implementation in the RAFI GmbH Company (one of the leading Electronic Manufacturing Service Provider in Germany). To model the controlled battery assembly system a unified max-plus algebra and model predictive control framework is employed. The considered system belongs to some class of discrete event system, which contains a finite number of industrial tasks and a finite number of resources, which are utilised according to a mutual-exclusion protocol. The assembly task is organised in a completely automatic way, which involves a number of robots. Thus, the proposed computational framework is used to minimize robot energy consumption while satisfying the constraints imposed on the system.

This paper extends a rule-based controller formulation described in the references to include the maxplus formulation in the case of general Petri nets, not only event graphs. This potentially allows design of conflict resolution inputs (i.e. dispatching rules) for the re-entrant flow line and the job shop problem in the maxplus algebra, as well as in a new algebra being developed for discrete event dynamical systems in the references. >

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.

Model Predictive Control (MPC) is a model-based control method based on a receding horizon approach and online optimization. A key advantage of MPC is that it can accommodate constraints on the inputs and outputs. This paper proposes a max-plus general modeling framework adapted to the robust optimal control of air traffic flow in the airspace. It is shown that the problem can be posed as the control of queues with safety separation-dependent service rate. We extend MPC to a class of discrete-event system that can be described by models that are linear in the max-plus algebra with noise or modeling errors. Regarding the single aircraft as a batch, the relationships between input variables, state variables and output variable are established. We discuss some key properties of the system model and indicate how these properties can be used to analyze the behavior of air traffic flow. The model predictive control design problems are defined for this type of discrete event system to help prepare the airspace for various robust regulation needs and we give some extensions of the air traffic max-plus linear systems.

RELIABILITY CALCULUS USING MAX-PLUS ALGEBRA

Recently there has been increased research interest in the study of the hybrid dynamical systems (Sun & Ge, 2005) and (Li et al., 2005). These systems involve the interaction of discrete and continuous dynamics. Continuous variables take the values from the set of real numbers and the discrete variables take the values from finite set of symbols. The hybrid systems have the behaviour of an analog dynamic system before certain abrupt structural or operating conditions are changed. The event driven dynamics in hybrid control systems can be described using different frameworks from discrete event systems (Cassandras & Lafortune, 2008) such as timed automata, max-plus algebra or Petry nets. For dynamic systems whose component are dominantly discrete event, main tools for analysis and design are representation theory, supervisory control, computer simulation and verification. From the clasical control theory point of view, hybrid systems may be considered as a switching control between analog feedback loops. Generally, hybrid systems can achieve better performance then non-switching controllers because they can to reconfigure and reorganize their structures. For that is necessery correct coordination of discrete and analog control variables. The mathematical model for real process, generally, has the Hammerstein-Wiener form (Crama & Atkins, 2001) and (Zhao & Chen, 2006). It means that on the input and output of the process are present nonlinear elements (actuator and sensor). Here we will consider Hammerstein model which has the input saturation as nonlinear element. That is the most frequent nonlinearity encountered in practice (Hippe, 2006). Also, unmodeled dynamics with matching condition is present. As a control strategy will be used switching control. The switched systems can be viewed as higher abstraction of hybrid systems. The design of switching controllers having guaranted stability, known as the picewise linear LQ control (PLC), is first considered in (Wredenhagen & Belanger, 1994). The picewise linear systems are systems that have different linear dynamics in different regions of the continuous state space (Johansson, 2003). The PLC control has the associated switching surfaces in form of positively invariant sets and yields a relatively low-gain controller. In the LHG (low-and-high gain) design a low gain feedback law is first designed in such a way

This paper studies "fixed zeros" of solutions to the model matching problem for systems over a semiring. Such systems have been used to model queueing systems, communication networks, and manufacturing systems. The main contribution of this paper is the discovery of two fixed zero semimodules, which possess a connection with the extended zero semimodules of solutions to the model matching problem. Intuitively, the fixed zero semimodule provides an essential component that is obtained from the solutions to the model matching problem. For discrete event dynamic systems modeled in max-plus algebra, a common Petri net component constructed from the solutions to the model matching problem can be discovered from the fixed zero structure.