Theoretical Background and Software Support for ...

Theoretical Background and Software Support for Creation of Railway Transport Model in Crisis Situations Zdenek Dvorak, Bohus Leitner, Ivo Milata, Ladislav Novak and Radovan Sousek University of Zilina, Slovakia: Zdenek.Dvorak@fsi,uniza.sk, Universtiy of Liberec, Czech Republic: Pavel.Fuchs.tul.cz, University of Zilina, Slovakia: [email protected], [email protected], [email protected], University of Pardubice, Czech Republic: [email protected]

ABSTRACT The paper describes issues connected to theoretical assumptions for operational planning in rail transport. It also deals with mathematical model of planning in rail transport as well as it describes draft software support, which was designed by University of Žilina for operational planning of rail transport, especially in crisis situations. KEY WORDS Crisis situations in rail transport, Simulation of rail traffic, Software support for operational planning of rail traffic.

1. INTRODUCTION Occurrence of crisis situation in rail transport and elimination of its consequences can be influenced up to certain point by applying technological procedures and proper preparations. This is valid also in railway transport and in its technological processes. Decision process is represented by railway transport on route sectors and its organisation in case of violation by diverse haphazard – stochastic impacts. Number, size and impacts of crisis situations which are occurring in the society are still growing. Their occurrence is caused by natural factors and anthropogenic factors. Very serious are human activities like environmental pollution or international terrorism, which play the most important role. These impacts take place in railway transport and they bring need to develop preventive measures for solution of arisen crisis situation and for elimination of their impacts. One of the limiting factors in work of crisis manager or dispatching site is to obtain sufficient amount of exact and fast information and sufficient computer support to decision process. Programme ASTRA+ can be used to provide above mentioned missing information support. 2. THEORETICAL AND METHODOLOGICAL ASPECTS OF THE PROBLEM SOLUTION Now, at the beginning of the 21st century, the rail transport is crucial amongst all used transport means. Comparing to other transport means in cases of crisis situations and their solutions, rail transport has many advantages: • it has high transport capacity; • it is highly reliable; it does not depend on day time or weather; • it is suitable for public transport and material transport on medium and large distances; • it reaches high sector (or maximal) speed. On the other hand, it has also some disadvantages: • Transport speed is relatively low (from the moment of loading of goods to the moment of unloading), • In case of transport infrastructure damage its renewal requires lot of time and lot of money, • It requires especially trained employees,

•

It requires powerful machines consequences of accident. [17]

for

removal

of

The experience shows that in cases of crisis situations of wide ranges, when the road transport was passed away or its capacity was low, the railways were working without limits. Especially in cases of huge evacuations the rail transport was the most important transport mean. Crisis and extraordinary situations in transport infrastructure can cause violation or abruption of transport. In cases of transport infrastructure violation the transport can be started immediately. In case of transport abruption, the renewal has to be proceeded to provide basic transport capacity. In both cases the transport could be done in limited range according to not usual organisation. [5] In present time there is a plan to prepare a number of actions focused on transport route renewal which should help in removing of negative aspects in railway transport. Unfortunately, there exists no unique method, aimed on providing required transport capacity by effective way in conditions of limited transport capacity, which could create functional technology for railway transport. [2] Due to mentioned facts and issues the project realised following actions: • Elaboration and application of modern management methods on chosen problems. • Theoretical investigation in the area of interest based on testing by the computer program ASTRA as well as it’s practical usage in cases of crisis situations. • Defining of management algorithms for managing of railway transport in limited conditions. • Testing of possible evaluations of transport situation on route sector or whole route. • Creating of general theory as a base for future research and solution finding for transport technology problems in crisis situations. • Creating of the crisis train diagram in railway transport. Above mentioned procedure was a base for creation of algorithms and models. Using created algorithms and models we created individual sub-programs what led to creation of program product, which is dedicated to operational planning in railway transport. [3] [4] Our institution is working on issues of modelling in railway transport in a long-term horizon. In past we were owner of sufficient programming environment as well as high performance computers. After year 2000 we started with development of our own theoretical models, which were based on huge statistical investigation. We investigated in detail what are the connections and dependences of travelling time on twenty track sectors. We processed more than 30 thousands of data sets about real time for individual trains to pass the route. [4] [13][18] We designed our own algorithms based on those findings. Mathematical support was based on many well-known mathematical and statistical methods. First real results show the impeachment of well-known division of probabilities. We were forced to find different variations of probabilities.

The results of our research were applied into created program product ASTRA (Fig.1).

Relay A - D Route sector A-B

Station A

Route sector B-C

Station B

Route sector C-D

Station C

Station D

Fig. 1 The first window of ASTRA programme

Fig. 2 Graphical description of train-created stations

Research in this field is connected to many problems. One of them was that it is not possible to apply chosen theory on mathematical models for all situations. Therefore we changed applied theoretical apparatus. We also changed methodology of calculation for simulations and we modified designed program. We designed ASTRA+, which is able to model and simulate problems also on one track routes. [7]

Significant part of crisis situations leads into lowering of number of route tracks. If there is only one track available, instead of two route tracks it changes technology of railway transport rapidly. Incoming flow of requirements – trains are originating in train generating stations on direction tracks. Generated trains are waiting for departure in outgoing set of tracks where they can create queue. The tracks in selected train stations are used for train journey, but they can be also used for train stopping while waiting. Due to the limitation of track number there are also limits for queue – number of trains waiting. [11], [12], [14] It is not possible to prepare the train transport diagram with consideration of floating displayed actions (train journey, station intervals, train and station measures and action etc.). Time needed for these actions has to be constant. Duration of train passing the same route sector has to be planned as fixed, despite the fact it is not like this. The fact is that the program ASTRA+ does not offer constant time duration of activities, so it will be essential to add this function. The main problem is which value should be used. Erlang’s distribution is sidelong to the right. [10]

3. USED MATHEMATICAL APPARATUS The railway transport in route sectors is possible to understand as bulk service system and it considers railway route as a service line. It is a system, which is also wellknown as M/M/1, where there are no limits in requirements, stations of services are limited (in our case it is one service station) and waiting for service requirements. The simulation of traffic in railway route sectors depends on three parameters: • Time interval of train entrance to the route sector, • Time of route sector occupancy, • Number of route and station tracks, on which the traffic will be done and can be possibly used for waiting of trains. [12] During evaluation of transport capacity of route sector we did not consider only route sector between two neighbouring train stations, but we evaluated route sectors between so called train-created (arrange, configure, create) stations. Such sectors are for instance relay ZILINA (Station A) – Vrútky (Station B) – Poprad (Station C) – KOŠICE (Station D). Railway route sector can consist from different number of partial route sectors (Fig.2).

Station A Route group of rails

f ( x) =

b a ( y − y 0 ) a −1 exp [− b ( y − y 0 )] (a − 1)!

b a ( y − y0 ) y0 (a − 1)!

Fx = ∫

y

a −1

exp[− b( y − y 0 )]dy

Station B

Outgoing group of rails

Creating of trains

Movement

(2)

After announcing of one of the crisis states, the Railways of Slovak Republic can organize railway transport according to “crisis train diagram of railway transport”. This train diagram is based on “list of passenger trains for crisis situation period”. Example case of such situation is shown on Fig.3. [13] [14] Route sector A -B

Queue– waiting for trains departure

(1)

Queue –Waiting for carriageway

Movement

Fig. 3 Graphical description of train-created stations

Queue – waiting for trains arrival

Movement

The dilemma was whether we should use average of generated values, or median of maximal and minimal generated value. Decision variable for simulations in railway transport is the time of occupying of route sector, [12]

tobs =

tj

+

τn.,

(3)

where interval τnj is generally considered to be random variable. Therefore we can consider travelling time t j also to be random variable. The best description of travelling time is by Erlang’s distribution of random variable, which uses two parameters a and b. Parameter a is in all cases constant a = 16. Parameter b is dependent on median of travelling time tj,p and it is calculated from ratio b = a/ t j,p. Above mentioned solutions are valid only for two track routes. The solution in their case is usually quite simple.

4. SOFTWARE SUPPORT FOR RAILWAY TRAFFIC PROCESSES SIMULATION In Slovak Republic the total constructed length of railway routes is 3 658 km. Single track routes has length of 2 640km, which 72% of total route length. Double and more tracked routes have length 1019 km, which is 72% of total route length. In railway network of ZSR there are 8 767 railswitches, 2 283 railway bridges and 76 railway tunnels. [16] According to this statistics we can assume that the most probable decrease in transport capacity is in case of single track route. Solution of such problem is much more problematic task than it was in previous case. The most crucial issue connected to this task is the fact that if the transport is organised on single track route, trains are entering route sector from both sides. Therefore it is needed to evaluate train’s position and based on this to recalculate their passing in railway stations. Condition of determined inputs of trains is in this case much more serious, because it is not possible to overcharge route sector. Trains can enter only if the situation at least theoretically enables their continuous ride. These situations will be always managed by operators and therefore we can not define it as stochastic inputs of trains. According to change in theoretical apparatus was program ASTRA redesigned into ASTRA +, which is able to model and simulate railway traffic on double track routes, on single track routes including the cascade traffic on single track routes. Solution of this kind of problem was solved in program product ASTRA+ (Fig.4).

Fig.4 The splash screen of software ASTRA +

4.1 Input and verification of data The practical part of solution was realised for several years. The matter of program product is based on detailed database data about stations, tracks, railway bridges and tunnels.

Participants on this project were working with original technical details gained in previous projects. Based on digitalisation in creating train transport diagram and onward filling in of databases about particular railway objects by data from modern measuring devices, present data metafile was imported directly from railway infrastructure provider. Basic algorithm of program structure is shown on Fig. 5. Start Data input (Stations, Inter-station sectors, Motive vehicles, Carriage train, Length of train, Weight of train)

1. 2. 3. 4.

Comparison of: Length of train and norm for train sector. Weight of train and norm for train sector. Recounting by motive vehicles. Recounting by motive vehicles.

1. 2. 3. 4.

Amount of: Distance of stations. Holding time of sectors. Data for selected train sector. Recounting by adhesion rate.

Sub-program SIMULATION

Sub-program TIMERUN

Sub-program ACCESIBLE SPEED

End

Fig. 5 Scheme of data input - software ASTRA

Fig. 6 Window for data input The input of data is preceded through the roll bars (Fig.6). Roll bar ROUTE (in Slovak TRAT) – gives a possibility to choose from any railway route that operate by Railways of the Slovak Republic (next ZSR). The roll bar motive vehicle offers all possible vehicles for selected route.

After choosing the route and selection of database fields, real data for route segment are loaded into window for data input. It is possible to change some of the data in mentioned detailed data fields. This can lead to change in transport capacity. Mentioned changes will be shown in note column and will be highlighted in red (Fig. 7).

Displaying of graphical simulation is shown on Fig.9. This simulation is preceded in real time with focus on technological solution of problem object.

Fig.9 Window of graphical simulation Other real output of simulation is overview table, which displays all needed data (Fig.10). Fig. 7 Window showing real data in database The work and proceeding of real data was very important part of the project. Problematic objects were shown in red colour in output window (Fig.8).

Fig. 10 List of simulation Fig. 8 Window output data For everyday work in transport railway companies it is important to bring new technical or technological solutions with paying attention to these objects. [7], [8], [9]

Due to the fact, that detailed list of all results was too detailed for practical using by experts in field, therefore programmers of ASTRA decided to create summary output of simulation results (Fig. 11). This window is designed to evaluate projected state, state after violation and state after application of measures.

4.2 Process of computer simulation Graphical visualisation is based on displaying of computer simulation calculated values in form of agreed signs in real time according to selected time scale. The stations of simulation model are displayed by graphical signs on monitor in dependence to their position on selected scale. The trains are displayed by black spots according to time and location. Displaying consists from: • Static objects as stations, tracks, station rails, security systems characterised by their location and distance in kilometres, state and number of tracks, • Dynamical objects such as train sets which are characterised by location and speed. Displaying is proceeded in: • Moments of timer violation (violation of timer is done in given time intervals, which can be changed during simulation). • Moment, when new requirement (train) enters the simulation model.

Fig. 11 Results of simulation

8. CONCLUSION In praxis in railway network there could appear some situations when, compared to usual situations, some limitations in the transport capacities on certain sectors appear. [15], [19] Organisation of the railway transport in this sector is crucial for the transport capacity of the whole route. The methods of management work are in this case totally different from the usual methods. The most significant contribution of program product is its specific and original usage of processes for calculation of minimal time interval for train ride in real route sectors. The aim of this article is to explain new knowledge from field of railway transport planning theories in specific conditions and to present created software product ASTRA+.

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T HIS WORK WAS SUPPORTED BY THE M INISTRY OF T RANSPORT OF THE C ZECH REPUBLIC, PROJECT N O. CG742-015-030.