Mathematical Problems in Engineering

Volume 2018, Article ID 9202986, 14 pages

https://doi.org/10.1155/2018/9202986

## A High-Speed Train Operation Plan Inspection Simulation Model

Correspondence should be addressed to Jiang Feng; moc.361@efilyawliar

Received 13 July 2017; Revised 16 October 2017; Accepted 10 December 2017; Published 1 February 2018

Academic Editor: Emilio Jiménez Macías

Copyright © 2018 Yang Rui et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We developed a train operation simulation tool to inspect a train operation plan. In applying an improved Petri Net, the train was regarded as a token, and the line and station were regarded as places, respectively, in accordance with the high-speed train operation characteristics and network function. Location change and running information transfer of the high-speed train were realized by customizing a variety of transitions. The model was built based on the concept of component combination, considering the random disturbance in the process of train running. The simulation framework can be generated quickly and the system operation can be completed according to the different test requirements and the required network data. We tested the simulation tool when used for the real-world Wuhan to Guangzhou high-speed line. The results showed that the proposed model can be developed, the simulation results basically coincide with the objective reality, and it can not only test the feasibility of the high-speed train operation plan, but also be used as a support model to develop the simulation platform with more capabilities.

#### 1. Introduction

The train operation plan (including the train rescheduling plan) is the most important plan in the daily operation of rail traffic and plays an important role in ensuring train operation safety and efficiency. Therefore, the train operation plan should be evaluated before being put into operation. The traditional ways, such as theoretical calculation, require a large computing time and are hard work for train traffic managers. Because the transport market demands rapid changes in China, the Chinese Railway Company needs to modify timetables frequently. This requires a fast and efficient way to test the operation plan. To meet this demand, we developed a simulation tool, to test the operation plan in a short time, and the simulation tests showed that the method could achieve high accuracy and a more reliable result.

Train operation plan simulation (TOPS) is the application of computer simulation technology in train operations; the purpose is to test whether the train can operate according to the planned timetable.

There are many studies on TOPS. In [1], the authors investigated energy-saving operation under disturbance, where the problem was described in a mathematical model and an optimization model of energy-saving train operation was applied, and the model was solved by a changeable chromosome-length genetic algorithm. Paper [2] considered the extra energy consumption caused by knock-on delays. It described a train trajectory optimization study considering the tradeoff between reductions in train energy usage against increases in the delay penalty in a delay situation with a fixed block signaling system, and a multitrain simulator was developed for the study. Reference [3] developed high-speed railway systems; the system described the automatic control system. In China, much research is focused on development of simulation tools, but most of it is mainly concerned with determining the simulated train operation paths [4–12].

Some literature sources applied Petri Net (PN) to simulate the train operation. Reference [13] used Petri Nets in modeling railway network and designing appropriate control logic for it to avoid collision; in the paper, the railway network was presented as a combination of the elementary models, the constraints at the points within the station were introduced, and the case study showed that the method can ensure once a track is occupied and no other train can enter into the same track so the collision can be avoided. Reference [14] applied the theory of supervisory control for discrete event systems to automatically design the system controller, where the Petri Nets are used, a modular representation of railway networks in terms of stations and tracks is provided, in the research, the railway network is described as a ES2PR (extended simple sequential process with resources) nets, and the global liveness was enforced by adding appropriate monitor places designed using siphon analysis. Reference [15] introduced the concept for a distributed railway control system and presented the specification and verification of the main algorithm used for safe distributed control, the approach was based on the RAISE method, by separating the system model into a domain model and a controller model, and the complexity was further reduced. Reference [16] implied Colored Petri Nets to model the switch control of a railway system, and the project is to teach students to model the railway with up to five trains. Reference [17] presented a simulation model based on hybrid Petri Nets, which is able to help transit authorities to carry out performance evaluation procedures in order to prevent, reduce, and if possible avoid accidents of transit authorities. Reference [18] used interval Colored-Timed Petri Nets to model and analyze railway stations; the method constructed a reduced reachability graph and exploited the fact that delays were described by an interval.

The existing models and tools are mainly about energy-saving and train operation simulation. Most of them are based on the signal type used to compute the location of trains, and the output is an analysis of different indexes which reflect the equipment features. As for the train operation, most researches focus on simulating the train according to the given operation plan strictly, which means seldom robust features are considered. However, when we consider the case of real-world train operation, there are some disturbances that will influence the operation of trains, like the random disturbance caused by rail workers. If we do not consider these disturbances, the simulation results can only check if the formed operation plan is conflict-free, but they cannot reflect real-world operation. Therefore, if we use these results to evaluate the train operation plan, we will obtain incorrect results because of the neglected disturbances.

Because the train operation plan has concurrent features, the dwell and arrival time at stations as well as the topology of the rail network fit the features of a Petri Net (PN). Thus, this paper applies an improved PN to model the train operation plan. During the modeling, we consider the objective and subjective disturbances using various distribution functions to describe the differences between the train operation plan and the real train operation track, applying an improved Colored-Timed Petri Net (CTPN) as the modeling tool. Therefore our mainly contribution is this model does not only simulate the train operation according to the given operation plan but also reflect the robust feature of the timetable. This benefits the railway company manager to evaluate the quality of train operation plan formed; the simulation results show that the model is an efficient tool to evaluate the train operation plan.

The outline of this paper is as below: Section 1 introduces the paper. Section 2 introduces the modeling process. In Section 3, we report the simulation results, and in Section 4 some conclusions are given.

#### 2. Modeling the Train Operation Plan Using CTPN

In this section, we introduce our train operation plan simulation model. A Colored-Timed Petri Net (CTPN) was used in the modeling. CTPN is an extension of Petri Net (PN). PN uses a TOKEN to represent the material or information source, while using PLACE to describe the place where the resources stored. In our research, TOKEN is applied to describe the trains and their operation, PLACE is applied to describe the stations and sectors between two stations, and the operation of trains are described by the transition. During our modeling, we first build the places that represent the stations and sectors, and then according to the topology of the railway network we use places and different kinds of transition to build the Petri Net. After the building of Petri Net, we decide the TOKENs that represent different trains according to the given train operation plan to initialize the net system, and then we drive the global timer to simulation by trigging different transitions.

We assume that readers have a basic knowledge of Colored-Timed Petri Nets (CTPN), and we refer readers to [19–21] for further details.

In this section, we first introduce the basic components used in the modeling process, then give the operation environment and train operation simulation method, after that introduce how to initialize the label, and, at last for detail simulation process, give an overall modeling steps.

##### 2.1. Train Abstract

In the train operation plan, the difference between trains is mainly about their speed, path and dwell, and arrival times. Meanwhile, as the trains are operated, the space location of the trains will change.

When we consider different trains, we need to describe whether they have different paths and different stop patterns. Also we should consider that, in daily operation, the dispatch department will adjust the train operation to absorb inevitable disturbances. It is clear that, during the operation, the order of stations a train should pass according to the plan and accurate arrival and departure time at a station are the key features to distinguish it from other trains. Therefore, we should subscribe these features when we describe a train.

Beyond the features mentioned above, because in China we operate different rains in a rail line, the operation speed and dwell time of trains can be differ. When the train operation does not fit the operation plan strictly, the dispatch department will adjust the operation situation according to the train operation speed. From this point of view, the train speed is taken as another feature as well.

The purpose of train operation plan simulation is to evaluate the possibility that the train operates according to the operation plan. To achieve this goal, we need to store the simulation data that reflect one train’s exact arrival and departure time at a station. We found that if we store the data in station and sector places, it would be difficult to handle the data structure and cause inefficiency during the simulation. So we just store the data in train TOKEN for faster data processing.

From the analyses above we can see that it is difficult to describe the train with single color; this means the traditional TOKEN is not suitable for our case. We use a multifeature TOKEN to represent train , in which is the speed of train ; is the operation state of train at station ; is the scheduled departure time of train from station ; is the scheduled arrival time of train at station ; is the simulated operation state of train at station ; is the simulated departure time of train at station ; is the simulated arrival time of train at station . Obviously, if train is scheduled not to stop at station , then we have equal to ; by analogy, if in the simulation train does not stop at station , then we have equal to . In our research, all the trains are operated with an EMU (Electronic Multiple Unit), which means the train unit has a fixed consist and its maintenance is integrated. The place where an EMU takes maintenance is called shunting yard; it is usually located in some large stations and takes reasonability for all the maintenance works. Because the shunting yard of an EMU can be regarded as a specific station, we assume that when an EMU reaches a station that is linked to a shunting yard, the operation of a train getting back to shunting yard is regarded as departure the station, while the leave of a train from shunting yard is regarded as arrival at the station. Therefore, under the assumption that the EMU’s times of entering and leaving the shunting yard are connected with the arrival and departure from the corresponding station, can be used to record the arrival time of train at station in the simulation when it leaves the shunting yard, while can be used to record the departure time of train at station in the simulation.

##### 2.2. Operation Environment

The operation environment includes the stations and track sections between stations that a train passes and the train operation constraints parameters. Among them, the station and track section are entity environments; they can carry a train and be expressed as a place; the parameters are the information environment, which contains various classes, and the data scale has a proportional relationship with the simulation scale. In this paper, we use the virtual place to express these environments.

###### 2.2.1. Train Place

During the simulation period, we need to inquire the train information continuously. As a public resource, we use a virtual place to store and manage the train data. In this place, in which is the departure time of train at station , its purpose is to improve the simulation efficiency.

###### 2.2.2. Station Place

A station can connect more than one direction; meanwhile, it contains several arrival and departure tracks to serve all kinds of operation, like arrival, departure, and passing of a train. Because the type and start time of operation as well as the connected direction are different for every station, the order of the arrivals and departures of trains is less connected, so we need to consider the operation of trains at a station and decide the departure order in all directions according to the planned and actual train operation situation. To fulfill this function, we use a station place to represent station , in which is the finish time of train at station and is the next train that departs on track section at station .

###### 2.2.3. Track Section Place

Because a track section can be seen as many connected block sections divided by the signal, among those sectors, trains must operate in the same order. In other words, trains cannot overtake each other on the same track section. So trains operating on the same track section must follow the “first arrive, first leave” rule. Besides, to avoid accidents and ensure that the station has enough time to prepare for the next train, the train dispatching system will adjust the trains’ operating speed to satisfy the minimum headway distance between trains. We use track section place to represent track section , in which is the estimated arrival time of the end of sector for train that is operating on track section and is the last train leaving in track section .

###### 2.2.4. Parameter Place

Although the speed of trains on a track section can be adjusted, it must follow specific rules, which include the headway determined by the features of the track, the train’s dynamic performance, and the signal system, while the operating time on the track section for different types of train has a standard. In real operation, because the train will be influenced by all kinds of disturbances, the real operating time usually deviates from the planned schedule (being earlier or delayed). This kind of deviation is random in nature, but it can be described by statistical laws. When a train departs from a station on time, the driver might relax because the time is sufficient, and this behavior can possibility cause a short delay during the operation (here we assume that the actual arrival time at next station is decided by the driver, where some Automatic Train Operation (ATO) systems also require final confirmation from the driver). In [22], a left partial function distribution is used to describe this behavior. When a train departs from a station with delay, because the driver is relatively focused on diminishing the delay, the possibility that real operating time in the next section is less than the planned one will increase. Therefore, a normal function can be used to describe this behavior [23]. Because the minimum headway and operation time and offset differ from track section to track section, we introduce a virtual place to store and manage these parameters. Here, means the station from which a train departs to track section ; means the station the train arrives at from track section ; means the maximum trains that can be contained on track section ; means the operating time standard of track section ; means the minimum headway time of track section ; means that a train arrives at track section on time, where the actual offset of the train operating obeys the function distribution; means that a train arrives at track section later than schedule, where the actual offset of the train operating obeys the normal function. By introducing and , we can simulate the train operation considering the actual disturbances; this will lead our simulation results more close to real-world case.

Similar to the train operating in track sections, the train operating at a station has different standards according to the type of operation. Considering that the operation process has a controlled random feature, we can still use the function and normal function to describe the actual offset in time, on time, and delay situations. More precisely, the train must wait for the route within a prepared station (switch shift and platform preparation), and then it is allowed to enter and leave the station. In other words, comparing the track headway between stations, there are specific station headway times that must be satisfied. Because these station headway times differ from station to station, we introduce a virtual place to represent and manage these data. Here, is the maximum number of trains contained at station ; is the arrival headway time at station ; is the departure headway time at station ; is the operation standard at station ; means that a train operation at station is on time, where the actual offset of the train operating obeys the function distribution; means that a train operation at station is later than scheduled, where the actual offset of the train operating obeys the normal function.

##### 2.3. Train Operation Simulation

The operation of a train can be described as a series of discrete events, and because the triggering mechanism is different for different events, the simulation process is step by step.

###### 2.3.1. Train Arrival Transition

When train operating on track section arrives at station , it will occupy the arrival and departure track to complete certain operations (e.g., passenger loading and alighting), and for station we need to supervise the operating process to arrange the departure from the station or entrance to the shunting yard. At this time, the operation of train is beyond , so the supervision of will end, but because of the station headway time, this train could affect other trains that are operating on , so we use to represent the trains that are entering the station and transition to simulate this behavior; then the train arrival can be described as Figure 1 shows.