CN107284480A - A kind of automatic preparation method of route map of train being multiplexed based on underbody - Google Patents

A kind of automatic preparation method of route map of train being multiplexed based on underbody Download PDF

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CN107284480A
CN107284480A CN201710428127.7A CN201710428127A CN107284480A CN 107284480 A CN107284480 A CN 107284480A CN 201710428127 A CN201710428127 A CN 201710428127A CN 107284480 A CN107284480 A CN 107284480A
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train
station
route map
underbody
time
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CN107284480B (en
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王义惠
宁滨
唐涛
宿帅
廖志斌
张瞄
罗依梦
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Beijing Jiaotong University
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Abstract

The embodiments of the invention provide a kind of automatic preparation method of route map of train being multiplexed based on underbody, it is related to Train Operation Control Technology field, comprises the following steps：Underlying parameter needed for configuration establishment route map of train；Train running scheme is configured according to the underlying parameter；Route map of train Optimized model is set up according to the underlying parameter and train running scheme；Using route map of train Optimized model described in MILP Algorithm for Solving, the route map of train based on the underbody quantity put into effect is obtained.The present invention improves the establishment efficiency of service chart, automatically the route map of train worked out can meet the constraintss such as reciprocal time, personal distance, train order, rolling stock, ensure the feasibility of service chart, cut operating costs, passenger waiting time is reduced, the need for the frequent adjustment of urban rail system fine-grained management Train service chart can be met.

Description

A kind of automatic preparation method of route map of train being multiplexed based on underbody
Technical field
Compiled automatically the present invention relates to Train Operation Control Technology field, more particularly to based on the route map of train that underbody is multiplexed Method processed.
Background technology
With continuing to develop for City Rail Transit System, road network structure is gradually increasingly sophisticated.By in July, 2015, warp The urban track traffic general planning mileage of State Council approved is more than 7300 kilometers, it is contemplated that to the year two thousand twenty, in urban track traffic is total Journey can reach 7395 kilometers.
In the case where Urban Rail Transit Development scale is increasingly huge, the establishment of route map of train is handed over as city rail One key technology of logical operation management plays an important roll, and it implements each ring that quality directly influences rail transportation operation Section.
At the same time, rolling stock and urban track traffic operation are also closely connected, in service chart, the hair of train Car gap size directly affects the underbody quantity put into effect, and whether train turns back in terminus also directly affects each station to when sending out Between.
On the other hand, existing train diagram establishment method is not taken into consideration by rolling stock.In view of this, to carry High urban track traffic operation management level, route map of train is realized in the urgent need to a kind of optimization method for considering rolling stock Automatic establishment.
The content of the invention
Train diagram establishment efficiency can be improved The embodiment provides one kind, urban rail system is met and becomes more meticulous Regulatory requirement, improves the feasibility of route map of train, reduces train operation cost, reduce passenger waiting time based on underbody The automatic preparation method of route map of train of multiplexing.
To achieve these goals, this invention takes following technical scheme.
A kind of automatic preparation method of route map of train being multiplexed based on underbody, including：
Underlying parameter needed for configuration establishment route map of train；
Train running scheme is configured according to the underlying parameter；
Route map of train Optimized model is set up according to the underlying parameter and train running scheme, the route map of train is excellent Changing model includes：Train departure interval calculation model, train arrival and leaving moment computation model, train sequence binding model, underbody fortune With restricted model, target function model；
Using route map of train Optimized model described in MILP Algorithm for Solving, obtain what is be multiplexed based on underbody Route map of train.
Further, described underlying parameter includes：
Underlying parameter according to needed for train actual track and traffic-operating period configuration establishment route map of train, the underlying parameter Including line information, station information, stand between run time, stand in down time, train operation beginning and ending time, first final vehicle hour Point, minimum departure interval, maximum departure interval, minimum reciprocal time, maximum reciprocal time；
There is J station on urban rail circuit, be expressed as Ssta={ 1,2 ..., J }, and rolling stock section is connected with station 1, and it is fixed Justice is up direction from station 1 to station J traffic direction, is down direction from station J to the traffic direction at station 1.
Further, the configuration train running scheme includes：
By train operation beginning and ending time [tstart, tend] it is divided into K period, i.e. T1=[t0, t1], T2=[t1, t2] ..., Tk=[tK-1, tK], wherein t0=tstart, tK=tend；
Each period need to complete IkIndividual train number, and have train number total quantityCollect where train number It is combined into Sservice={ 1,2 ..., Itotal}。
Further, described train departure interval calculation model includes：
Adjacent two train has the departure interval within each period, and the departure interval of k-th period is：AndWherein, hmin、hmaxMinimum departure interval and maximum departure interval are represented respectively.
Further, described train arrival and leaving moment computation model includes：
Arriving and leaving moment calculation formula for the up train in each platform is：
Wherein,The train number i j AT STATION up time of departure is represented,Represent train number i being up at j AT STATION Up to the time,The up dwell time of train number i AT STATION at j is represented,Represent train number i from station j to next stop j+1's Up run time；
Arriving and leaving moment calculation formula for down train in each platform is：
Wherein,The train number i j AT STATION descending time of departure is represented,Represent train number i going downwards at j AT STATION Up to the time,The descending dwell time of train number i AT STATION at j is represented,Represent train number i from station j to next stop j-1's Descending run time；
The first and last order of classes or grades at school train departure time is obtained according to described first and last regular bus time point, its calculation formula is,
The time of departure of first train in initiating station：
The time of departure of last train in initiating station：
Wherein, the arriving and leaving moment of adjacent two train meets conditionTo ensure synchronization turn back line A upper only train；
If J is turns back to train AT STATION behind station, the reciprocal time of train AT STATION at JMeet following condition：
Wherein,WithThe train minimum reciprocal time in J places and maximum reciprocal time AT STATION are represented respectively；
Further, described train sequence binding model includes：
Based on the basic principle of train sequence constraint, the two car time of departures of 1 train and station J train are full AT STATION It is enough lower constraint：
Further, described train circulation plan computation model includes：
Train circulation plan computational methods are as follows：
αiRepresent whether train number i is sent by rolling stock section：
βiRepresent whether train number i returns to rolling stock section：
γI, i 'Represent whether train number i and train number i ' uses same underbody：
Further, described train circulation plan calculating meets following constraints：
Whether whether the train number sent depending on train number i ' and above by rolling stock section uses same underbody to train number i, that is, meets Relation：
Whether train number i, which returns to rolling stock section, depends on using same underbody with the presence or absence of train number i ' and train number i below, that is, meets Relation：
When train number i and i' uses same underbody, train number i is not returned to rolling stock section, train number i ' nor being sent by rolling stock section, That is αi′、βiAnd γI, i 'Meet following relation：
αi′+βi≤2+M(1-γI, i '),
αi′+βi≥2-M(1-γI, i ')；
If train behind station AT STATION 1 to turn back, (i is train number above, i ' by front and rear two train numbers i, i ' AT STATION at 1 For train number below) should meet following relation to the hair time：
Wherein,WithThe minimum reciprocal time of train AT STATION at 1 and maximum reciprocal time are represented respectively； Two adjacent trains meet following condition of turning back to the hair time at 1 AT STATION：
Further, described target function model includes：
Minimize object functionWherein, w1、w2And w3For weight, fObj, 1, nomFor and the nominal value of departure interval deviation that provides of service mode, fObj, 2, nomFor using same The number of the train number of one underbody, fObj, 3, nomFor the penalties of interval variation；
F in object functionObj, 1It is pair and part that departure interval deviation that service mode is provided is minimized, its expression For：
F in object functionObj, 2It is the part minimized to the number of allocated passenger trains that operation stage puts into effect, i.e., to operation rank Section is maximized using the train number number of same underbody, and it is expressed as：
F in object functionObj, 3It is the part limited the interval variation of neighbouring train number, the change at this interval is by working as Space before represents with the poor absolute value of the average value at neighbouring train number interval, i.e.,：
Further, route map of train Optimized model described in described use MILP Algorithm for Solving, is obtained The route map of train based on the underbody quantity put into effect is taken, including：
Step 1, integral ring is multiplied by real number linearizes：During at two described adjacent trains AT STATION 1 to hair Between in the constraint of turning back that meetsPart is linearized, and concrete methods of realizing isIts In,
zI, i '≤tKγI, i ', ZI, i '≥t0γI, i ',
Step 2, to fObj, 1In absorption part linearized：Concrete methods of realizing is
Wherein,
Step 3, to fObj, 3In absorption part linearized：Concrete methods of realizing is
Wherein,
Step 4, output optimal solution：Configuration parameter is inputted, MIXED INTEGER is used to described route map of train Optimized model Linear programming algorithm is solved, and auxiliary picture route map of train.
Beneficial effect of the present invention：The embodiment of the present invention improves the establishment efficiency of service chart, the train operation worked out automatically Figure can meet the constraintss such as reciprocal time, personal distance, train order, rolling stock, it is ensured that the feasibility of service chart, reduction Operation cost, reduces passenger waiting time, the need for can meeting the frequent adjustment of urban rail system fine-grained management Train service chart.
Brief description of the drawings
In order to illustrate the technical solution of the embodiments of the present invention more clearly, being used required in being described below to embodiment Accompanying drawing be briefly described, it should be apparent that, drawings in the following description are only some embodiments of the present invention, for this For the those of ordinary skill of field, without having to pay creative labor, other can also be obtained according to these accompanying drawings Accompanying drawing.
Fig. 1 is a kind of processing for the automatic preparation method of route map of train being multiplexed based on underbody provided in an embodiment of the present invention Flow chart；
Fig. 2 is a kind of route map of train worked out according to the method for the embodiment of the present invention；
Fig. 3 is that a kind of underbody worked out according to the method for the embodiment of the present invention uses figure；
Fig. 4 is a kind of interval figure for the uplink and downlink train worked out according to the method for the embodiment of the present invention；
Fig. 5 is a kind of route map of train worked out according to the method for the embodiment of the present invention；
Fig. 6 is that a kind of underbody worked out according to the method for the embodiment of the present invention uses figure；
Fig. 7 is a kind of interval figure for the uplink and downlink train worked out according to the method for the embodiment of the present invention.
Embodiment
Embodiments of the present invention are described below in detail, the example of the embodiment is shown in the drawings, wherein from beginning Same or similar element or element with same or like function are represented to same or similar label eventually.Below by ginseng The embodiment for examining accompanying drawing description is exemplary, is only used for explaining the present invention, and is not construed as limiting the claims.
For ease of the understanding to the embodiment of the present invention, done below in conjunction with accompanying drawing by taking several specific embodiments as an example further Explanation, and each embodiment does not constitute the restriction to the embodiment of the present invention.
Embodiment one
This embodiment offers a kind of process chart for the automatic preparation method of route map of train being multiplexed based on underbody such as Shown in Fig. 1, mainly include the following steps that：
Step S110：The actual track underlying parameter needed for drawing is configured, including：Line information, station information, stand between transport The minimum departure interval that row time, respectively station dwell time, the beginning and ending time of train operation, first and last regular bus time point, system allow The minimum reciprocal time allowed with maximum departure interval, system and maximum reciprocal time.Such as：There is J station on urban rail circuit, It is expressed as Ssta={ 1,2 ..., J }, and rolling stock section is connected with station 1, and define from station 1 to station J traffic direction and be Up direction, is down direction from station J to the traffic direction at station 1.
Step S120：The train number completed in train running scheme, i.e. configuration operation period is configured according to the underlying parameter Number.
By train operation beginning and ending time [tstart, tend] it is divided into K period, i.e. T1=[t0, t1], T2=[t1, t2] ..., Tk=[tK-1, tK], wherein t0=tstart, tK=tendEach period need to complete IkIndividual train number, and have train number total quantityCollection is combined into S where train numberservice={ 1,2 ..., Itotal}。
Step S130：Route map of train Optimized model is set up according to above-mentioned underlying parameter and the train number number provided, the optimization Model includes following five submodels of C1, C2, C3, C3 and C5, wherein,
C1, train departure interval calculation：The urban rail railroad embankment period is divided into by K period, wherein k ∈ according to step 2 { 1,2 ..., K }, then k-th of period [tk-1, tk] departure interval calculated with following equation：
And meet
C2, train arrival and leaving moment are calculated：If up direction of the train on urban rail circuit, it arrives the calculating of hair time such as Under：
Wherein,The train number i j AT STATION up time of departure is represented,Represent train number i being up at j AT STATION Up to the time,The up dwell time of train number i AT STATION at j is represented,Represent train number i from station j to next stop j+1's Up run time；
If train is in the down direction of urban rail circuit, it is calculated as follows to the hair time：
Wherein, whereinThe train number i j AT STATION descending time of departure is represented,Under representing train number i AT STATION at j Row arrival time,The descending dwell time of train number i AT STATION at j is represented,Represent train number i from station j to next stop j- 1 descending run time；
And the operation beginning and ending time [t of known urban rail circuitstart, tend], then first train number and last train number are rising The time of departure of initial station is calculated as follows：
Following condition should be met for two trains that are connected to hair time：
If J is turns back to train AT STATION behind station, the reciprocal time of train AT STATION at JFollowing condition should be met：
Wherein,The requirement of minimum reciprocal time and maximum reciprocal time need to be met；
C3, train sequence constraint:Sequence constraint principle for continuous two train is not allow overtaking, i.e., sent out from station 1 Che Hou, the train set out below is no more than the train above set out.Then 1 and station J AT STATION, the time of departure of two cars should Meet following constrain：
C4, rolling stock constraint:Introduce three binary variable αi, βi, γI, i 'To represent train in rolling stock section and underbody With related different conditions, wherein,
αiRepresent whether train number i is sent by rolling stock section：
βiRepresent whether train number i returns to rolling stock section：
γI, i 'Represent whether train number i and train number i ' uses same underbody：
Train number i ' whether by rolling stock section send depending on its whether with a certain train number above use same underbody, i.e. physics Same train in meaning, need to meet relation：
Whether train number i, which returns to rolling stock section, depends on using same underbody with the presence or absence of train number i ' and train number i below, that is, meets Relation：
When train number i and i' uses same underbody, train number i is not returned to rolling stock section, train number i ' nor being sent by rolling stock section, That is αi′、βiAnd γI, i 'Meet following relation：
αi′+βi≤2+M(1-γI, i ')
αi′+βi≥2-M(1-γI, i '),
If train behind station AT STATION 1 to turn back, (i is train number above, i ' by front and rear two train numbers i, i ' AT STATION at 1 For train number below) should meet following relation to the hair time：
Wherein,WithThe minimum of train AT STATION at 1 and maximum reciprocal time are represented respectively.
And two connected trains should meet following condition of turning back to the hair time at 1 AT STATION：
C5, target function model：Influence in view of train departure interval and train circulation plan to service chart, the target Function model will minimize such as minor function：
Wherein, w1、w2And w3For weight, fObj, 1, nomFor and the nominal value of departure interval deviation that provides of service mode, fObj, 2, nomFor by the number of two train numbers using same underbody, fObj, 3, noM is the penalties of interval variation.
F in object functionObj, 1It is pair and part that departure interval deviation that service mode is provided is minimized, its expression For：
F in object functionObj, 2It is the part minimized to the number of allocated passenger trains that operation stage puts into effect, in other words, Operation stage is maximized using the train number number of same underbody, it is expressed as：
F in object functionObj, 3It is the part limited the interval variation of neighbouring train number, the change at this interval is by working as Space before represents with the poor absolute value of the average value at neighbouring train number interval, i.e.,：
In above-mentioned C1, C2, C3, C4, C5 Optimized model, C1-C4 is the constraints of the optimization problem, and C5 is that the optimization is asked The object function of topic.
Step S140：The Optimized model is solved using MILP, the train for being related to rolling stock is obtained Service chart.
Algorithm above can be realized using MATLAB, CPLEX and solved.
Embodiment two
In the implementation process of present invention method, if maximum, minimum interval is 660s and 120s, weight takes Value is respectively 4103, 20,5104, the train number number that each period need to complete is with preferable interval as shown in table one, two：
Table one
Table two
According to above-mentioned steps, the Optimized model that route map of train is worked out automatically is set up, and use MILP Algorithm is solved to problem, and obtained route map of train is as shown in Fig. 2, Fig. 5, and underbody uses figure as shown in Fig. 3, Fig. 6, upper, The interval of down train is as shown in Fig. 4, Fig. 7.
Abscissa is the urban rail circuit pack service time in Fig. 2, and from 5:00 AM half to, ordinate is car thirty in the morning 10 Stand, the train number indication marked in figure using the same line style of type uses same underbody.Abscissa is the time in Fig. 3, and ordinate is The underbody numbering used, the square of wherein same horizontal line represents the train number using same underbody.Abscissa is made for train in Fig. 4 Industry number, ordinate is that the round dot in the interval (unit is the second) of train, figure marks the point with square marks to represent respectively Row and the current train of down direction and the interval of previous train.Fig. 5 transverse axis is the urban rail circuit whole day operation period, is indulged Axle is station, and same underbody is used using the train number indication of identical lines type mark.Fig. 6 abscissa is time, ordinate It is that underbody uses the square in numbering, same horizontal line to represent the train number using same underbody.Fig. 7 is the urban rail railroad embankment period The up train departure interval figure that part is obtained is intercepted for round-the-clock, transverse axis is train number, and the longitudinal axis is interval time.By Fig. 2, Fig. 3, Fig. 5 and Fig. 6 can be seen that after the related constraint of rolling stock is taken into account, underbody is fully used, and slow down because of passenger flow The problem of underbody is not enough caused by the increase of sharp increase train number.It can be seen that Train Interval tends to regularization by Fig. 4 and Fig. 7, it is full Foot operation demand, reduces passenger waiting time.
In summary, the embodiment of the present invention is realized the route map of train being multiplexed based on underbody and worked out automatically, and with such as Lower advantage：
1st, the route map of train worked out automatically can meet the constraint such as reciprocal time, personal distance, train order, rolling stock Condition, it is ensured that the feasibility of service chart, reduces operation cost, reduces passenger waiting time；
2nd, the automatic establishment of route map of train is greatly improved the establishment efficiency of service chart, can meet urban rail system and become more meticulous The need for managing the frequent adjustment of Train service chart.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited thereto, Any one skilled in the art the invention discloses technical scope in, the change or replacement that can be readily occurred in, It should all be included within the scope of the present invention.Therefore, protection scope of the present invention should be with scope of the claims It is defined.

Claims (10)

1. a kind of automatic preparation method of route map of train being multiplexed based on underbody, it is characterised in that including：
Underlying parameter needed for configuration establishment route map of train；
Train running scheme is configured according to the underlying parameter；
Route map of train Optimized model is set up according to the underlying parameter and train running scheme, the route map of train optimizes mould Type includes：Train departure interval calculation model, train arrival and leaving moment computation model, train sequence binding model, rolling stock are about Beam model, target function model；
Using route map of train Optimized model described in MILP Algorithm for Solving, the train being multiplexed based on underbody is obtained Service chart.
2. the route map of train automatic preparation method according to claim 1 being multiplexed based on underbody, it is characterised in that described Underlying parameter include：
Underlying parameter according to needed for train actual track and traffic-operating period configuration establishment route map of train, the underlying parameter includes Line information, station information, stand between run time, stand in down time, the train operation beginning and ending time, first and last regular bus time point, Minimum departure interval, maximum departure interval, minimum reciprocal time, maximum reciprocal time；
There is J station on urban rail circuit, be expressed as Ssta={ 1,2 ..., J }, and rolling stock section is connected with station 1, and define from Station 1 to station J traffic direction is up direction, is down direction from station J to the traffic direction at station 1.
3. the route map of train automatic preparation method according to claim 1 being multiplexed based on underbody, it is characterised in that described Configuration train running scheme includes：
By train operation beginning and ending time [tstart, tend] it is divided into K period, i.e. T1=[t0, t1], T2=[t1, t2] ..., Tk= [tK-1, tK], wherein t0=tstart, tK=tend；
Each period need to complete IkIndividual train number, and have train number total quantityCollection is combined into where train number Sservice={ 1,2 ..., Itotal}。
4. the route map of train automatic preparation method according to claim 3 being multiplexed based on underbody, it is characterised in that described Train departure interval calculation model include：
Adjacent two train has the departure interval within each period, and the departure interval of k-th period is：And hmin≤Hk≤hmax,Wherein, hmin、hmax Minimum departure interval and maximum departure interval are represented respectively.
5. the route map of train automatic preparation method according to claim 3 being multiplexed based on underbody, it is characterised in that described Train arrival and leaving moment computation model include：
Arriving and leaving moment calculation formula for the up train in each platform is：
Wherein,The train number i j AT STATION up time of departure is represented,Represent train number i AT STATION at j be up to up to when Between,The up dwell time of train number i AT STATION at j is represented,Represent train number i from station j to the up of next stop j+1 Run time；
Arriving and leaving moment calculation formula for down train in each platform is：
Wherein,The train number i j AT STATION descending time of departure is represented,Represent train number i AT STATION at j go downwards to up to when Between,The descending dwell time of train number i AT STATION at j is represented,Represent train number i from station j to the descending of next stop j-1 Run time；
The first and last order of classes or grades at school train departure time is obtained according to described first and last regular bus time point, its calculation formula is,
The time of departure of first train in initiating station：
The time of departure of last train in initiating station：
Wherein, the arriving and leaving moment of adjacent two train meets condition
If J is turns back to train AT STATION behind station, the reciprocal time of train AT STATION at JMeet following condition：
Wherein,WithThe train minimum reciprocal time in J places and maximum reciprocal time AT STATION are represented respectively.
6. the route map of train automatic preparation method according to claim 3 being multiplexed based on underbody, it is characterised in that described Train sequence binding model include：
Based on the basic principle of train sequence constraint, AT STATION the two car time of departures of 1 train and station J train meet with Lower constraint：
。
7. the route map of train automatic preparation method according to claim 3 being multiplexed based on underbody, it is characterised in that described Train circulation plan computation model include：
Train circulation plan computational methods are as follows：
αiRepresent whether train number i is sent by rolling stock section：
βiRepresent whether train number i returns to rolling stock section：
γI, i 'Represent whether train number i and train number i ' uses same underbody：
8. the route map of train automatic preparation method according to claim 7 being multiplexed based on underbody, it is characterised in that described Train circulation plan calculating meet following constraints：
Whether whether the train number sent depending on train number i ' and above by rolling stock section uses same underbody to train number i, that is, meets relation：
Whether train number i, which returns to rolling stock section, depends on using same underbody with the presence or absence of train number i ' and train number i below, that is, meets and close System：
When train number i and i' uses same underbody, train number i is not returned to rolling stock section, train number i ' nor being sent by rolling stock section, i.e., αi′、βiAnd γI, i 'Meet following relation：
αi′+βi≤2+M(1-γI, i '),
αi′+βi≥2-M(1-γI, i ')；
If train behind station AT STATION 1 to turn back, (i is train number above, after i ' is by front and rear two train numbers i, i ' AT STATION at 1 The train number in face) should meet following relation to the hair time：
Wherein,WithThe minimum reciprocal time of train AT STATION at 1 and maximum reciprocal time are represented respectively；It is adjacent Two trains meet following condition of turning back to the hair time at 1 AT STATION：
9. the route map of train automatic preparation method according to claim 3 being multiplexed based on underbody, it is characterised in that described Target function model include：
Minimize object functionWherein, w1、w2With w3For weight, fObj, 1, nomFor and the nominal value of departure interval deviation that provides of service mode, fObj, 2, nomTo use same underbody Train number number, fObj, 3, nomFor the penalties of interval variation；
F in object functionObj, 1It is pair and part that departure interval deviation that service mode is provided is minimized, it is expressed as：
F in object functionObj, 2It is the part minimized to the number of allocated passenger trains that operation stage puts into effect, i.e., operation stage is made Maximized with the train number number of same underbody, it is expressed as：
F in object functionObj, 3It is the part limited the interval variation of neighbouring train number, the change at this interval is between currently Every representing with the poor absolute value of the average value at neighbouring train number interval, i.e.,：
10. the route map of train automatic preparation method according to claim 1 being multiplexed based on underbody, it is characterised in that institute Route map of train Optimized model described in the use MILP Algorithm for Solving stated, is obtained based on the underbody put into effect The route map of train of quantity, including：
Step 1, integral ring is multiplied by real number linearizes：To expiring at two described adjacent trains AT STATION 1 to the hair time In the constraint of turning back of footPart is linearized, and concrete methods of realizing isWherein,
zI, i '≤tK γ i, i ', zI, i '≥t0 γ i, i ',
Step 2, to fObj, 1In absorption part linearized：Concrete methods of realizing is
Wherein,
Step 3, to fObj, 3In absorption part linearized：Concrete methods of realizing is
Wherein,
Step 4, output optimal solution：Configuration parameter is inputted, it is linear using MIXED INTEGER to described route map of train Optimized model Planning algorithm is solved, and auxiliary picture route map of train.
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