Pazoysky Yury Osharovich is the head of the department «Railway stations and hubs» of Moscow State University of Railway Engineering.

Shmal Vadim Nikolayevich is a senior professor of the department « Management of operational work and safety on transport» of Moscow State University of Railway Engineering.

Lanko Eugenia Vladimirovna is a student of the department «The organization of transportation and management on transport (railway transport)», Moscow State University of Railway Engineering.

Mathematical model of the elimination of the conflicting routes of trains in a yard neck

Elimination of the conflicting reception routes and departure routes (passing without stopping) of a train in a yard neck is a mandatory requirement of train protection at reception and departure of trains.

It is offered to use a station model which consists of the following main components: a yard neck (incoming routes and exit routes of the trains), station tracks, open-line tracks. All these components are interconnected.

This approach allows to pass from statics of an expert system to dynamics allowing to receive the actual decision (the model exists in time) in any simulated casual situation.

This model represents a problem of dynamic programming. With a certain extent of specification, it allows to simulate work of a station on reception, departure, shift of trains, closing of station tracks in connection with repair work. The model is universal for terminus stations, side stations and junctions.

Entrance information of the model is:

- train arrival and departure time from station or shunting movement;

- minimum stopping time of trains at the stations;

- train number;

- number of open - line tracks from which the train arrives and on which goes.

Output information of the model is:

- train number;

- actual time of the train arrival and departure;

- actual stopping time of the train at the stations;

- delay time of train arrival and train departure;

- number of a station track on which the train arrives ;

- route of the train arrival and train departure.

The interconnections of the components are presented as follows:

- number of station tracks and open-line tracks;

- the list of train arrival and departure routes (the route of reception and departure of a train represents a station track),an open-line track (or the first some block sections ) and a part of the yard neck connecting open-line tracks and station tracks).

- number of approaches to a station (to each yard neck);

- connections of mutual influence between routes both in a yard neck, and between yard necks which are presented in a table form of the route dependence (this table defines the station scheme).

The condition of the components is presented as follows:

- the schedule of the train arrival and departure at the station;

- occupation of the tracks by reception, departure, passing of trains, in connection with repair work and for other reasons;

- occupation of the reception routes and departure routes of the trains;

- train priorities on arrival and departure;

- priorities of the reception routes and departure routes of the trains;

- present moment of time.

Trains are compared on a total priority which is a sum of the following priorities:

- route priority. Arrival routes and departure routes are ranged depending on quantity of conflicts . The more the route causes conflicts, the less its priority is.

Arrival routes and departure routes are ranged separately.

- train priority (depends on a category of a train);

- an additional priority of a train according to a dispatcher instruction (serves for direct control, which train to stop and which train to send or to space);

- size of a departure priority over arrival (shows to which extent an arrival priority is higher than a departure priority or vice versa)

- priority of arrival sequence.

The size of the priorities is established in the course of the system training. Priorities of the objects in group and between groups are adjusted.

Indignation entering from outdoor environment , an emergence check of the conflicting routes of the train reception and departure is performed. In case of conflict emergence, an alternative of their elimination with the minimum sum temporary delays of train reception and train departure is calculated.

The calculation occurs for an interval which size is defined by accuracy of entrance information.

1) Pre settlement stage of initial information analysis.

For all trains, the arrival or departure of which coincides with a settled interval of time, the possibility of train occupation of the reception or departure route is checked. There is a selection of all possible routes of reception/departure of trains.

For each route the list of all trains which submitted demands for departure and (or) on arrival from station is formed.

Further assessment of the route guidance is paid off for all trains and for all routes.

2) First iteration.

Confirmation of the train claim for a route is analyzed for each pair (a considered route and a train).

Further a pair with the maximum sum priority is chosen. The demand of a train to which there corresponds this maximum value, is considered satisfied. The actual departure/ arrival time of a train at a station is fixed.

If the train arrived at the station, the appropriate station way becomes occupied. If the train left the station, the mark on release of the appropriate way is made as well as the mark that the appropriate boiling way or the first block section is occupied or vacant.

3) Subsequent iterations (check of the possibility of the parallel train reception or (and) parallel train departures).

After all iterations, for this moment of time, the satisfaction of all demands for train arrival (departure) is analyzed. The size of a departure/ arrival time delay, equal to considered intervals of time is added to trains, whose demands weren't satisfied.

If the train passes the station without stopping (duration of the stopping is equal to zero), there is a check of both arrivals at the station, and departures.

The accounting of a turn of passenger structures is possible. On the arrival of a train at the station and stay at the station of the train turn time, the train goes on a haul from which arrived and under a concrete train path.

The model training paradigm represents supervisory learning. Within such approach to the model the problem is set, and the decision on a known condition "input-output" is looked for. The dispatcher specifies, what should be the correct decision. That is, the operator specifies at the conflict emergence, which train is necessary for accepting (or to send) and which train is necessary to stop.

Learning consists in correction of the train scales and train routes in such a manner that at the next moment of time the exit calculation result of a network will be closer to the demanded answer.

The process of training is continuous (the database for possibility of a logic conclusion is collected) as the external conditions defining entrance and exit information, constantly change.

This model is flexible and adaptive to changes of the situation. The decision received with its help allows to facilitate essential problems of elimination of the conflicting routes and to increase traffic safety, quality of passenger service and efficiency of the use of railway transport technical means, taking into account possibilities of railway station track arrangement. This model can be used for automated management of train movement at a section.

Summary: the article represents a mathematical model of the elimination of the conflicting routes in a yard neck taking into account priorities of the trains and the minimum total delays of the trains.

Keywords: mathematical model, yard neck, route, traffic safety.