CN111178697A - Method and system for calculating passing capacity of high-speed railway - Google Patents

Method and system for calculating passing capacity of high-speed railway Download PDF

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CN111178697A
CN111178697A CN201911284084.5A CN201911284084A CN111178697A CN 111178697 A CN111178697 A CN 111178697A CN 201911284084 A CN201911284084 A CN 201911284084A CN 111178697 A CN111178697 A CN 111178697A
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station
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吕苗苗
倪少权
陈钉均
张�杰
潘金山
李雪婷
吕红霞
徐长安
郭秀云
陈韬
廖常宇
谢春
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Beijing Shanghai High Speed Railway Co Ltd
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Southwest Jiaotong University
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Abstract

The invention relates to the technical field of railway operation management, in particular to a method and a system for calculating the passing capacity of a high-speed railway. The method comprises the following steps: s1, listing a train stop time difference matrix; s2, judging whether the column workshop has an overstepping relation, if not, entering S3, and if so, entering S4; s3, calculating the occupation time of the train group and the extra occupation time of the train when the train stops under the condition of no crossing relationship; s4, calculating a train crossing station; s5, calculating the occupation time of the train group and the extra occupation time of the train when the train stops under the condition that the train workshop has an overrun relationship; and S6, judging the influence of the train stop scheme on the passing capacity according to the extra occupied time of the train stop, wherein the shorter the train operation diagram time which is additionally occupied by the train stop is, the smaller the passing capacity deducted by the train stop is. The invention can directly calculate the extra occupied time of the train stop station in the train operation diagram under the non-overrun condition and the overrun condition, visually reflect the influence of the train stop station on the passing capacity, and ensure the accuracy and the rationality of the calculation result.

Description

Method and system for calculating passing capacity of high-speed railway
Technical Field
The invention relates to the technical field of railway operation management, in particular to a method and a system for calculating the passing capacity of a high-speed railway.
Background
The capacity resources of the high-speed railway in China are short, the main purpose of the passing capacity research is to exert the capacity of railway equipment facilities to the maximum extent, the stop scheme of the high-speed railway train is an important factor influencing the passing capacity, on one hand, the stop time and the starting and stopping additional time are generated when the high-speed railway train stops at each time, the occupied time can generate adverse influence on the passing capacity, and on the other hand, different stop schemes have different influences on the passing capacity. Currently, there is relatively little research on the quantitative relationship between high-speed train stop schedules and capacity.
The high-speed railway passing capacity refers to that: under the condition of adopting a certain type of motor train unit and a certain running organization method, various fixed equipment of the high-speed railway can pass the maximum number of trains in unit time (generally, one day and one night).
The train stop scheme specifies the stop and stop time of the train. The railway train operation diagram (operation diagram for short) is a technical file for representing the operation of trains in railway sections and the arrival and departure or passing time of trains in stations, and is the basis for organizing the operation of trains on the whole road. It specifies the procedures for each train number for the section occupied by the train, the arrival and departure (or passage) times of the train at each station, the train's travel time in the section, the stop time of the train at the station, and locomotive traffic, train weight and length, etc. The train running time table is a diagram for a train running time table, and each train is specified to run in an interval and arrive, send and pass at a station at a certain time. The train operation diagram is a diagram of the relation between time and space of train operation, and it represents a two-dimensional line diagram of the train operation in each section and the stop or passing state at each station.
The train tracking interval time is in an automatic block section, two or more trains can be arranged in the same direction in an inter-station interval, and the trains run at block subarea intervals, which is called tracking running. The minimum interval time between running trains is tracked and is called train tracking interval time. The train tracking interval time is determined by the interval distance of trains in the same direction, the running speed of the trains and the type of the communication and closing equipment. The overtaking refers to that the train which arrives first stops at the station and starts after the train which arrives at the same direction passes through the station or arrives at the station to stop, and the overtaking is called overtaking.
At present, the method for calculating the passing capacity of the high-speed railway is improved on the basis of methods such as an existing line deduction coefficient method, an average minimum train interval method and a computer simulation method.
The existing method for calculating the passing capacity of the high-speed railway mainly comprises the following steps:
(1) and the deduction coefficient method is that the highest-grade non-stop high-speed train is used as the basic train, and the number of the pairs or the rows of the low-grade passenger trains and the stop trains which need to be deducted from the parallel train operation diagram is laid.
However, the key of the deduction coefficient method lies in the value of the deduction coefficient, and different line sections are different in the deduction coefficient due to different distribution of train operation lines, and even if the train operation diagrams of different structures in the same line section are different, the passenger train deduction coefficient is also different, and the structure of the train operation diagram of the high-speed railway has larger change compared with the existing line, if the existing deduction coefficient is still used, the accuracy and the rationality of the calculation result are difficult to guarantee.
(2) Average minimum train spacing method: the method for calculating the passing capacity adopted by Germany comprises the steps of firstly analyzing the actual running state of each section of train, and then jointly determining the average necessary buffering time in a train running diagram according to the conditions of the probability of the late point of the train, the time of allowing the late point of the train under certain quality requirements, the average minimum train interval time of various train types, the average time of the late point train entering the late point, the total value of the time of allowing the late point of the train to reflect the requirement level of the running quality of the train and the like, thereby determining the value of the passing capacity of the section.
However, the average minimum train spacing method must be used after operating for a period of time in the same line or in the same transportation organization mode as the train spacing method itself, obtaining a certain number of sample values, and calculating representative parameter values. The high-speed railway in China adopts a transportation organization mode that trains with different speed grades run in a collinear way, time difference and train stop generated by the trains with different speeds in the mode are the two main factors influencing the passing capacity of the high-speed railway, and if the time difference and the train stop are calculated by an average minimum interval method, how the two factors influence the passing capacity cannot be reflected in the process, so the method still has certain limitation in actual application at present.
(3) Computer simulation: and simulating manual map laying by using a computer, and compiling a saturated train operation map by closely laying and drawing various train operation lines according to the technical standard of the train operation map, thereby obtaining the maximum passing capacity of the high-speed railway.
However, the computer simulation method generally has a large number of feasible solutions for computer layout, and when comparing, selecting and optimizing among the various feasible solutions, the computer simulation method is relatively complex and has a high redundancy, and generally only can apply an expert system method or seek an approximately optimal solution or a satisfactory solution by means of a man-machine conversation.
Disclosure of Invention
The invention provides a method and a system for calculating the passing capacity of a high-speed railway, which solve the technical problem that the deduction of the passing capacity of a stop station cannot be directly calculated by a train stop station scheme in the prior art.
The technical scheme adopted by the invention is as follows:
in one aspect, the invention provides a train passing capacity calculation method, which comprises the following steps:
s1, acquiring train stop time in a train operation diagram, listing a train stop time difference matrix at each station according to a train departure sequence, wherein rows and columns of the matrix s represent trains L at the stationsiWith adjacent train LjDifference of station stop;
s2, judging whether the train workshops have an overtravel relationship, and if the train workshops do not have the overtravel relationship, entering the step S3; if the train has an overrun relationship, the process proceeds to step S4;
s3, calculating the time of the train group occupying the running chart under the condition that the train workshop does not have the crossing relation and the time of the train running chart additionally occupied by the train stopping station;
s4, calculating a train crossing station;
s5, calculating the time of the train group occupying the running chart under the condition that the train workshop has an overrun relation and the time of the train running chart additionally occupied by the train stopping station;
s6, judging the influence of the train stop scheme on the passing capacity according to the train operation diagram time additionally occupied by the train stop; the shorter the train diagram time that is additionally occupied for train stopping, the less the capacity of the train to be deducted by the train stopping.
Further, in step S3, the method for calculating the time of the train diagram occupied by the train group and the time of the train diagram additionally occupied by the train stopping includes the following steps:
s101, arranging a train LiAt ZsHas a stop time of Δ tisAccording to the train LiWith adjacent train LjConstructing a train stop time difference value matrix at stop time of each stationWhere i ═ 1, 2., M-1}, j ═ 2., M }, and the matrix s rows and i columns represent the train L at s stationsiWith adjacent train LjDifference in station stopping time;
s102, setting a train group train LiAnd adjacent rear ranks vehicle LjDeparture interval I at the departure stationi-j＝ΔTi-j+ I, wherein Δ Ti-jDue to the train stop scheme, the train LiExtra time is needed in the operation diagram, the initial value of i is 1, and the initial value of j is i + 1;
s103, setting delta T from the train stop difference matrix i columni-j0, accumulated value βi-j0, according to train LiAnd a train LjThe station stop difference value matrix of each station is accumulated from the first row of the i columns of the matrix to the back, if the accumulated value is up to the s rows of the i columns of the matrix
Figure BDA0002317530900000041
Record Δ Ti-j＝βi-jand is provided with βi-jif it is 0, the process proceeds to step S104, where the accumulated value β is addedi-jIs always negative or zero, then Δ Ti-jKeeping the matrix unchanged, sequentially accumulating backwards until the last row of the matrix is N rows, and calculating Ii-jI +1, the process proceeds to step S105;
s104, accumulating from the i column s +1 row of the matrix backwards in sequence, if meeting beta againi-jIf > 0, update the delta Ti-j＝β+ΔTi-jSequentially accumulating the signals backwards according to the method in the step S103 until the last row of the matrix I is N, and calculating Ii-j，i＝i+1；
S105, judging whether i is equal to M-1, if so, entering a step S106, otherwise, repeating the step S103 and the step S104;
s106, calculating a train group L1～LMTime spent in train diagram
Figure BDA0002317530900000051
And can know the occupied time T of the train stop station in the train operation diagramParking space＝TAccount for-(M-1)I。
Further, in step S4, the method for determining an overrun station includes the following steps:
s201, setting a high-grade train LkLower-grade train L next to the preceding train and being crossedjMinimum inter-arrival time at an overrun station is Ij-kThen, Ij-k＝max{I,tStop+IGo toIn which IGo toThe train-to-pass interval;
s202, as the cross-over relationship does not exist between the equal-level trains, the equal-level train Li、LjInter-originating interval time Ii-jThrough the calculation of steps S102 to S104, the high-grade train L is obtained under the condition of tight departurekWith low-grade train LiMinimum departure interval I betweeni-k＝∑Ii-j+Ij-k；
S203, when the low-grade train LiIs covered by a high-grade train LkWhen the station is overtaking, the sum of the station stop time difference value of the two stations before the overtaking station and the minimum arrival interval time of the two stations at the overtaking station is more than LiAnd LkThe starting interval time between the two trains is obtained by the formula (2-1)iStation when crossed:
Figure BDA0002317530900000052
in the formula (2-1), YLiIs a low-grade train LiStation, Δ t, when being crossedizIs a train LiAt YLiA stop time before the station.
Further, in step S5, the method for calculating the time of the train diagram occupied by the train group and the time of the train diagram additionally occupied by the train stopping in the crossing relationship among the trains includes the following steps:
s301, sorting the overtaking stations Y according to the station reverse sequence, wherein Y is {1,2,. and.. Y }, the station sequence corresponds to the front and back sequence of the overtaken trains, namely according to the time sequence, the overtaking stations of the first lower-level train which is overtaken in the train group are sorted into 1, and the overtaking stations of the last lower-level train which is overtaken in the train group are sorted into Y, so that the overtaken lower-level trains share Y columns;
s302, the first-train crossed low-grade train L in the train group1To high-grade train LkTime T occupied in train operation diagramAccount forCalculated by the following formula:
Figure BDA0002317530900000061
in the formula (2-2), the first two terms are the first train L of the train group1To high-grade train LkInter-originating interval time of, wherein the first item
Figure BDA0002317530900000062
Is a train of the same class L1And LYInter-originating interval time, second item Ij-kFor the last lower-grade train L to be crossedYAnd high grade LkThe originating interval of (a) can be calculated as shown in the formula (2-3), where tGo toThe minimum time interval from the arrival of a train at a station in one direction to the stop of the train passing another train in the same direction from the station is called the arrival time interval of the train in the same direction, and the third term
Figure BDA0002317530900000063
Is LYAt an overrun station and LkDeparture Interval of, item four
Figure BDA0002317530900000064
Is LYFrom the passing station YLYThe sum of the stop time from the next station to the end station to the station, and a fifth term tGet upAnd adding time for train departure.
IY-k＝max(I,tStop+tGo to) (2-3)
S303, setting a low-grade train LiIs covered by a high-grade train LkThe station of the cross is y, and L is at the y stationiDeparture time and LkThe departure time interval is
Figure BDA0002317530900000065
Then it is firstOne-train overtaking low-grade train L1At the passing station YL11 and high-grade train LkThe time interval of departure time is
Figure BDA00023175309000000611
Wherein t isHair smoothing deviceThe minimum interval time from the time when a train in a certain direction passes through a station to the time when the train is sent from the station to another train in the same direction is recorded as the train sending time interval in the same direction;
Figure BDA0002317530900000066
is a train LkAnd L1Departure interval at an overrun station due to train L1By train LkAfter the two trains are overtravel, the two trains do not have an overtravel relationship, and L1Starting after the vehicle stops at the overpass station 1, then
Figure BDA0002317530900000067
Wherein
Figure BDA0002317530900000068
Is a train LiAnd a train LkDeparture intervals when the overtaking stations 1 are all originated;
s304. the second row of crossed low-grade trains L2At the passing station YL22 and high-grade train LkThe time interval of departure time is Iy-kIn which Iy-kIs a train L1And L2Departure interval at the passing station 1, L1At the passing station YL11 Biba, L2At the passing station YL1When 1 is stopped or passed, then
Figure BDA0002317530900000069
As shown in the formula (2-4),
Figure BDA00023175309000000610
is as a train L2Train L when stopping at an overrun station1And L2At the passing station YL11, the same reason is L2At the passing station YL1When 1 is stopped or passed, then
Figure BDA0002317530900000071
As shown in formula (2-5);
Figure BDA0002317530900000072
Figure BDA0002317530900000073
s305. sequentially calculating train LkAnd LYAt the passing station YLYDeparture interval of Y
Figure BDA00023175309000000710
As shown in formula (2-6);
Figure BDA0002317530900000074
L(Y-1)at the passing station YL(Y-1)Y-1 Bi che, LYAt the passing station YL(Y-1)When Y-1 stops or passes, then
Figure BDA0002317530900000075
As shown in formulas (2-7), wherein
Figure BDA0002317530900000076
Is a train LYTrain L when stopping at an overrun station(Y-1)And LYAt the passing station YL(Y-1)Departure interval of Y-1, also due to LYAt the passing station YL(Y-1)When Y-1 stops or passes, then
Figure BDA0002317530900000077
As shown in formulas (2-8):
Figure BDA0002317530900000078
Figure BDA0002317530900000079
s306, calculating the occupied time of the train in the operation diagram due to the influence of the stop of the train through the following formula;
Tparking space＝TAccount for-YI (2-9)。
In another aspect, the present invention provides a train passing capacity calculating system, where the system is configured to implement the train passing capacity calculating method described above, and the system includes:
the first calculation module is used for acquiring train stop time in a train operation diagram and listing a train stop time difference matrix according to a train departure sequence;
the second calculation module is used for judging whether the train workshops have the crossing relationship, and if the train workshops do not have the crossing relationship, the third calculation module is started; otherwise, entering a fourth calculation module;
the third calculation module is used for calculating the time of the train group occupying the operation diagram under the non-crossing relation of the train workshops and the time of the train operation diagram additionally occupied by the train stopping station, and the time enters the sixth calculation module;
the fourth calculation module is used for calculating the train overtaking station;
the fifth calculation module is used for calculating the time of the train operation diagram occupied by the train group under the condition that the crossing relationship exists among the trains and the time of the train operation diagram additionally occupied by the train stop;
and the sixth calculation module is used for judging the influence of the train stop scheme on the passing capacity according to the train working diagram time additionally occupied by the train stop, wherein the shorter the train working diagram time additionally occupied by the train stop is, the smaller the passing capacity deducted by the train stop is.
Further, the third computing module comprises:
a first calculating unit for setting a train LiAt ZsHas a stop time of Δ tisAccording to the train LiWith adjacent train LjAnd constructing a train stop time difference matrix at the stop time of each station, wherein i is {1, 2., M-1} and j is { 2., M } and rows and columns of the matrix represent the train L at the station siWith adjacent train LjDifference in station stopping time;
a second calculation unit for setting a train group train LiAnd adjacent rear ranks vehicle LjDeparture interval I at the departure stationi-j＝ΔTi-j+ I, wherein Δ Ti-jDue to the train stop scheme, the train LiExtra time is needed in the operation diagram, the initial value of i is 1, and the initial value of j is i + 1;
a third calculation unit for setting delta T from the train stop difference matrix i columni-j0, accumulated value βi-j0, according to train LiAnd a train LjThe station stop difference value matrix of each station is accumulated from the first row of the i columns of the matrix to the back, if the accumulated value is up to the s rows of the i columns of the matrix
Figure BDA0002317530900000081
Record Δ Ti-j＝βi-jand is provided with βi-jif the accumulated value is equal to 0, the fourth calculation unit is entered, if the accumulated value is equal to betai-jIs always negative or zero, then Δ Ti-jKeeping the matrix unchanged, sequentially accumulating backwards until the last row of the matrix is N rows, and calculating Ii-jEntering a fifth calculation unit if i is i + 1;
a fourth calculation unit for accumulating backward in sequence starting from the i column s +1 row of the matrix, if again meeting betai-jIf > 0, update the delta Ti-j＝β+ΔTi-jSequentially accumulating backwards according to the method of the third calculation unit until the last row of the matrix I and the last N rows, and calculating Ii-j，i＝i+1；
The fifth calculating unit is used for judging whether i is equal to M-1 or not, if so, the sixth calculating unit is started, and if not, the third calculating unit and the fourth calculating unit are repeated;
a sixth calculation unit for calculating the train group L1～LMTime spent in train diagram
Figure BDA0002317530900000091
And can know the occupied time T of the train stop station in the train operation diagramParking space＝TAccount for-(M-1)I。
Further, the fourth calculation module includes:
a seventh calculation unit for setting a high-grade train LkLower-grade train L next to the preceding train and being crossedjMinimum inter-arrival time at an overrun station is Ij-kThen, Ij-k＝max{I,tStop+IGo toIn which IGo toThe train-to-pass interval;
an eighth calculating unit for the peer-to-peer train L because there is no crossing relation between the peer-to-peer trainsi、LjInter-originating interval time Ii-jThrough the calculation of steps S102 to S104, the high-grade train L is obtained under the condition of tight departurekWith low-grade train LiMinimum departure interval I betweeni-k＝∑Ii-j+Ij-k；
A ninth calculating unit for counting the low-grade train LiIs covered by a high-grade train LkWhen the station is overtaking, the sum of the station stop time difference value of the two stations before the overtaking station and the minimum arrival interval time of the two stations at the overtaking station is more than LiAnd LkThe starting interval time between the two trains is obtained by the formula (2-1)iStation when crossed:
Figure BDA0002317530900000092
in the formula (2-1), YLiIs a low-grade train LiStation, Δ t, when being crossedizIs a train LiAt YLiA stop time before the station.
Further, the fifth calculation module includes:
a tenth calculating unit, configured to rank the passing stations Y according to a station reverse order, where Y is {1,2, ·.,. Y }, where the station order corresponds to a front-back order of the crossed trains, that is, according to a time order, the passing stations of the first rank of lower-level trains crossed in the train group are ranked as 1, and the passing stations of the last rank of lower-level trains crossed are ranked as Y, so that the crossed lower-level trains share Y columns;
an eleventh calculating unit for calculating a lower-grade train L whose first train is crossed in the train group by the following formula1To high-grade train LkTime T occupied in train operation diagramAccount for：
Figure BDA0002317530900000101
In the formula (2-2), the first two terms are the first train L of the train group1To high-grade train LkInter-originating interval time of, wherein the first item
Figure BDA0002317530900000102
Is a train of the same class L1And LYInter-originating interval time, second item Ij-kFor the last lower-grade train L to be crossedYAnd high grade LkThe originating interval of (a) can be calculated as shown in the formula (2-3), where tGo toThe minimum time interval from the arrival of a train at a station in one direction to the stop of the train passing another train in the same direction from the station is called the arrival time interval of the train in the same direction, and the third term
Figure BDA0002317530900000103
Is LYAt an overrun station and LkDeparture Interval of, item four
Figure BDA0002317530900000104
Is LYFrom the passing station YLYThe sum of the stop time from the next station to the end station to the station, and a fifth term tGet upAnd adding time for train departure.
IY-k＝max(I,tStop+tGo to) (2-3)
A twelfth calculation unit for setting the low-grade train LiIs covered by a high-grade train LkThe station of the cross is y, and L is at the y stationiDeparture time and LkThe departure time interval is
Figure BDA0002317530900000105
The first train is crossed the low-grade train L1At the passing station YL11 and high-grade train LkThe time interval of departure time is
Figure BDA0002317530900000106
Wherein t isHair smoothing deviceThe minimum interval time from the time when a train in a certain direction passes through a station to the time when the train is sent from the station to another train in the same direction is recorded as the train sending time interval in the same direction;
Figure BDA0002317530900000107
is a train LkAnd L1Departure interval at an overrun station due to train L1By train LkAfter the two trains are overtravel, the two trains do not have an overtravel relationship, and L1Starting after the vehicle stops at the overpass station 1, then
Figure BDA0002317530900000108
Wherein
Figure BDA0002317530900000109
Is a train LiAnd a train LkDeparture intervals when the overtaking stations 1 are all originated;
a thirteenth calculating unit for setting the second row of the crossed low-grade train L2At the passing station YL 22 and high-grade train LkThe time interval of departure time is Iy-kIn which Iy-kIs a train L1And L2Departure interval at the passing station 1, L1At the passing station YL11 Biba, L2At the passing station YL1When 1 is stopped or passed, then
Figure BDA0002317530900000111
As shown in the formula (2-4),
Figure BDA0002317530900000112
is as a train L2Train L when stopping at an overrun station1And L2At the passing station YL11, the same reason is L2At the passing station YL11 parking orThrough, then
Figure BDA0002317530900000113
As shown in formula (2-5);
Figure BDA0002317530900000114
Figure BDA0002317530900000115
a fourteenth calculating unit for calculating the train L in sequencekAnd LYAt the passing station YLYDeparture interval of Y
Figure BDA0002317530900000116
As shown in formula (2-6);
Figure BDA0002317530900000117
L(Y-1)at the passing station YL(Y-1)Y-1 Bi che, LYAt the passing station YL(Y-1)When Y-1 stops or passes, then
Figure BDA0002317530900000118
As shown in formulas (2-7), wherein
Figure BDA0002317530900000119
Is a train LYTrain L when stopping at an overrun station(Y-1)And LYAt the passing station YL(Y-1)Departure interval of Y-1, also due to LYAt the passing station YL(Y-1)When Y-1 stops or passes, then
Figure BDA00023175309000001110
As shown in formulas (2-8):
Figure BDA00023175309000001111
Figure BDA00023175309000001112
the fifteenth calculating unit is used for calculating the occupation time of the train in the operation diagram due to the influence of the stop station through the following formula;
Tparking space＝TAccount for-YI (2-9)。
The invention has the beneficial effects that:
the invention provides a method for calculating the passing capacity of a high-speed railway line based on a train stop matrix, which can directly calculate the extra occupied time of a train stop in a train operation diagram under the non-passing condition and the passing condition, visually reflect the influence of the train stop on the passing capacity, ensure the accuracy and the reasonability of a calculation result and avoid selecting and optimizing a plurality of feasible schemes.
Drawings
Fig. 1 is a schematic flow chart of a train passing capacity calculation method according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a method for calculating train passing capacity according to an embodiment of the present invention when there is no crossing relationship between trains;
FIG. 3 is a schematic flow chart of a method for calculating train passing capacity according to an embodiment of the present invention when an overrun relationship exists between trains;
fig. 4 is a schematic structural diagram of a train passing capacity calculation system according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures. Meanwhile, in the description of the present invention, the terms "first", "second", and the like are used only for distinguishing the description, and are not to be construed as indicating or implying relative importance. In the description of the present invention, the terms "S1", "S2", etc. before each step are further used to label the steps, and are not to be construed as indicating or implying a sequential relationship between each step.
As shown in fig. 1, the embodiment provides a method for calculating the passing capacity of a train, and the method can be divided into two different steps according to whether there is an overrun relationship between trains
When no crossing relationship exists between trains as shown in FIG. 2, the method comprises the following steps:
s1, acquiring train stop time in a train operation diagram, listing a train stop time difference matrix at each station according to a train departure sequence, wherein rows and columns of the matrix s represent trains L at the stationsiWith adjacent train LjDifference of station stop;
s2, judging whether the train workshops have an overtravel relationship, and if the train workshops do not have the overtravel relationship, entering the step S3;
s3, calculating the time of the train group occupying the running chart under the condition that the train workshop does not have the crossing relation and the time of the train running chart additionally occupied by the train stopping station;
s6, judging the influence of the train stop scheme on the passing capacity according to the train operation diagram time additionally occupied by the train stop; the shorter the train diagram time that is additionally occupied for train stopping, the less the capacity of the train to be deducted by the train stopping.
As shown in fig. 3, when there is an overrun relationship between trains, the method includes the steps of:
s1, acquiring a train running chartThe stop time of the train in the (1) is listed as a time difference matrix of the stop time of the train at each station according to the train departure sequence, and the rows and the columns of the matrix s represent the train L at the stations siWith adjacent train LjDifference of station stop;
s2, judging whether the train workshops have an overrun relationship, and if the train workshops have the overrun relationship, entering the step S4;
s4, calculating a train crossing station;
s5, calculating the time of the train group occupying the running chart under the condition that the train workshop has an overrun relation and the time of the train running chart additionally occupied by the train stopping station;
s6, judging the influence of the train stop scheme on the passing capacity according to the train operation diagram time additionally occupied by the train stop; the shorter the train diagram time that is additionally occupied for train stopping, the less the capacity of the train to be deducted by the train stopping.
Train group L1～LMThe occupied time in the train operation diagram is the train group L1～LMTime interval of origination of and train LMThe sum of the stop time, the occupied operation diagram time due to the influence of the stop of the train is the train group L1～LMThe total time occupied minus (M-1) train tracking interval times I. For train LMThe stop time of (1) is a known quantity, train group L1～LMBy train LiWith adjacent train LjThe interval between them is accumulated to form a composition, and thus, the train group L is calculated1～LMThe key to the occupied passing capacity is to solve the train LiWith adjacent train LjThe interval time therebetween. First, a train L can be constructediWith adjacent train LjA difference matrix of whether each station is stopped, wherein i ═ 1, 2.. and M-1}, j ═ 2.. and M }, and rows and columns of the matrix s represent trains L at s stationsiWith adjacent train LjThe difference value of the stop stations indicates that the rear row-column vehicle L is judged when the longitudinal accumulated value of the i columns is less than 1jThe station-stopping can fully utilize the front train LiTime of stopping, train LiWith adjacent train LjInter-originating interval time Ii-jTo track the interval, the lead train LiThe station does not need to be stoppedThe extra time is taken in the figure, when the accumulated value in the i-column longitudinal direction is equal to 1, the preceding train LiStopping the train and needing to occupy delta t additionally in the train operation diagram, and I for ensuring the tracking time interval of the adjacent trains at the station with the accumulated value of 1i-jTo track interval I plus Δ t, if the next vertical accumulation value of I is 1, then Ii-jSequentially accumulating the tracking interval I plus 2 delta t, if the accumulated value is less than 1, then Ii-jThe train L can be calculated without additional increaseiWith adjacent train LjInterval time I betweeni-j。
In the step S3, the method for calculating the train diagram time occupied by the train group and the train diagram time additionally occupied by the train stop without the train crossing relationship includes the following steps:
s101, arranging a train LiAt ZsHas a stop time of Δ tisAccording to the train LiWith adjacent train LjAnd constructing a train stop time difference matrix at the stop time of each station, wherein i is {1, 2., M-1} and j is { 2., M } and rows and columns of the matrix represent the train L at the station siWith adjacent train LjDifference in station stopping time;
s102, setting a train group train LiAnd adjacent rear ranks vehicle LjDeparture interval I at the departure stationi-j＝ΔTi-j+ I, wherein Δ Ti-jDue to the train stop scheme, the train LiExtra time is needed in the operation diagram, the initial value of i is 1, and the initial value of j is i + 1;
s103, setting delta T from the train stop difference matrix i columni-j0, accumulated value βi-j0, according to train LiAnd a train LjThe station stop difference value matrix of each station is accumulated from the first row of the i columns of the matrix to the back, if the accumulated value is up to the s rows of the i columns of the matrix
Figure BDA0002317530900000151
Record Δ Ti-j＝βi-jand is provided with βi-jif it is 0, the process proceeds to step S104, where the accumulated value β is addedi-jIs always negative or zero, then Δ Ti-jKept unchanged, in turnAccumulating backwards until the last row of the matrix is N rows, and calculating Ii-jI +1, the process proceeds to step S105;
s104, accumulating from the i column s +1 row of the matrix backwards in sequence, if meeting beta againi-jIf > 0, update the delta Ti-j＝β+ΔTi-jSequentially accumulating the signals backwards according to the method in the step S103 until the last row of the matrix I is N, and calculating Ii-j，i＝i+1；
S105, judging whether i is equal to M-1, if so, entering a step S106, otherwise, repeating the step S103 and the step S104;
s106, calculating a train group L1～LMTime spent in train diagram
Figure BDA0002317530900000152
And can know the occupied time T of the train stop station in the train operation diagramParking space＝TAccount for-(M-1)I。
In step S4, the method for determining an overrun station includes the steps of:
s201, setting a high-grade train LkLower-grade train L next to the preceding train and being crossedjMinimum inter-arrival time at an overrun station is Ij-kThen, Ij-k＝max{I,tStop+IGo toIn which IGo toThe train-to-pass interval;
s202, as the cross-over relationship does not exist between the equal-level trains, the equal-level train Li、LjInter-originating interval time Ii-jThrough the calculation of steps S102 to S104, the high-grade train L is obtained under the condition of tight departurekWith low-grade train LiMinimum departure interval I betweeni-k＝∑Ii-j+Ij-k；
S203, when the low-grade train LiIs covered by a high-grade train LkWhen the station is overtaking, the sum of the station stop time difference value of the two stations before the overtaking station and the minimum arrival interval time of the two stations at the overtaking station is more than LiAnd LkThe starting interval time between the two trains is obtained by the formula (2-1)iStation when crossed:
Figure BDA0002317530900000161
in the formula (2-1), YLiIs a low-grade train LiStation, Δ t, when being crossedizIs a train LiAt YLiA stop time before the station.
In step S5, the method for calculating the time of the train diagram occupied by the train group and the time of the train diagram additionally occupied by the train stopping station in the crossing relationship between the trains includes the following steps:
in order to fully utilize the passing capacity of a high-speed railway line, a high-grade train with few stops needs to cross a low-grade train with more stops, under the condition that the trains are closely dispatched, the high-grade train can firstly determine the stations of the high-grade train crossing the low-grade train, and based on the stations, the dispatching interval between the crossing station and the high-grade train after each low-grade train is crossed can be sequentially calculated, so that the time occupied by a train group in an operation diagram is the sum of the starting interval time between the trains, the dispatching interval between the last column of the crossed low-grade train and the high-grade train, the dispatching interval between the crossing station and the last column of the crossed low-grade train, the sum of the stopping time between the next station of the crossing station and the end station and the additional train dispatching time and the additional time division of the train. On the basis, the time that the train occupies more time in the train operation diagram due to the influence of train stop can be deduced.
S301, sorting the overtaking stations Y according to the station reverse sequence, wherein Y is {1,2,. and.. Y }, the station sequence corresponds to the front and back sequence of the overtaken trains, namely according to the time sequence, the overtaking stations of the first lower-level train which is overtaken in the train group are sorted into 1, and the overtaking stations of the last lower-level train which is overtaken in the train group are sorted into Y, so that the overtaken lower-level trains share Y columns;
s302, the first-train crossed low-grade train L in the train group1To high-grade train LkTime T occupied in train operation diagramAccount forCalculated by the following formula:
Figure BDA0002317530900000171
in the formula (2-2), the first two terms are the first train L of the train group1To high-grade train LkInter-originating interval time of, wherein the first item
Figure BDA0002317530900000172
Is a train of the same class L1And LYInter-originating interval time, second item Ij-kFor the last lower-grade train L to be crossedYAnd high grade LkThe originating interval of (a) can be calculated as shown in the formula (2-3), where tGo toThe minimum time interval from the arrival of a train at a station in one direction to the stop of the train passing another train in the same direction from the station is called the arrival time interval of the train in the same direction, and the third term
Figure BDA00023175309000001712
Is LYAt an overrun station and LkDeparture Interval of, item four
Figure BDA0002317530900000173
Is LYFrom the passing station YLYThe sum of the stop time from the next station to the end station to the station, and a fifth term tGet upAnd adding time for train departure.
IY-k＝max(I,tStop+tGo to) (2-3)
S303, setting a low-grade train LiIs covered by a high-grade train LkThe station of the cross is y, and L is at the y stationiDeparture time and LkThe departure time interval is
Figure BDA0002317530900000174
The first train is crossed the low-grade train L1At the passing station YL11 and high-grade train LkThe time interval of departure time is
Figure BDA0002317530900000175
Wherein t isHair smoothing deviceFrom the time when a train passes through a station to a certain directionThe minimum interval time for stopping when the train is sent to another train in the same direction from the station is recorded as the train sending time interval in the same direction;
Figure BDA0002317530900000176
is a train LkAnd L1Departure interval at an overrun station due to train L1By train LkAfter the two trains are overtravel, the two trains do not have an overtravel relationship, and L1Starting after the vehicle stops at the overpass station 1, then
Figure BDA0002317530900000177
Wherein
Figure BDA0002317530900000178
Is a train LiAnd a train LkDeparture intervals when the overtaking stations 1 are all originated;
s304. the second row of crossed low-grade trains L2At the passing station YL 22 and high-grade train LkThe time interval of departure time is Iy-kIn which Iy-kIs a train L1And L2Departure interval at the passing station 1, L1At the passing station YL11 Biba, L2At the passing station YL1When 1 is stopped or passed, then
Figure BDA0002317530900000179
As shown in the formula (2-4),
Figure BDA00023175309000001710
is as a train L2Train L when stopping at an overrun station1And L2At the passing station YL11, the same reason is L2At the passing station YL1When 1 is stopped or passed, then
Figure BDA00023175309000001711
As shown in formula (2-5);
Figure BDA0002317530900000181
Figure BDA0002317530900000182
s305. sequentially calculating train LkAnd LYAt the passing station YLYDeparture interval of Y
Figure BDA0002317530900000189
As shown in formula (2-6);
Figure BDA0002317530900000183
L(Y-1)at the passing station YL(Y-1)Y-1 Bi che, LYAt the passing station YL(Y-1)When Y-1 stops or passes, then
Figure BDA0002317530900000184
As shown in formulas (2-7), wherein
Figure BDA0002317530900000185
Is a train LYTrain L when stopping at an overrun station(Y-1)And LYAt the passing station YL(Y-1)Departure interval of Y-1, also due to LYAt the passing station YL(Y-1)When Y-1 stops or passes, then
Figure BDA0002317530900000186
As shown in formulas (2-8):
Figure BDA0002317530900000187
Figure BDA0002317530900000188
s306, calculating the occupied time of the train in the operation diagram due to the influence of the stop of the train through the following formula;
Tparking space＝TAccount for-YI (2-9)。
As shown in fig. 4, the present embodiment provides a train passing capacity calculating system, which is configured to implement the train passing capacity calculating method described above, and the system includes:
the first calculation module 10 is used for acquiring train stop time in a train operation diagram and listing a train stop time difference matrix according to a train departure sequence;
the second calculation module 20 is used for judging whether the train workshops have an overrun relationship, and if the train workshops do not have the overrun relationship, the third calculation module 30 is started; otherwise, entering a fourth calculation module 40;
the third calculation module 30 is used for calculating the time of the train operation diagram occupied by the train group under the train-to-train non-crossing relationship and the time of the train operation diagram additionally occupied by the train stop, and the sixth calculation module 60 is advanced;
the fourth calculation module 40 is used for calculating the train overtaking station;
the fifth calculation module 50 is used for calculating the time of the train operation diagram occupied by the train group and the time of the train operation diagram additionally occupied by the train stop station under the crossing relationship of the train workshops;
the sixth calculation module 60 is configured to determine, according to the train working diagram time additionally occupied by the train stop, an influence of the train stop scheme on the passing capacity; the shorter the train diagram time that is additionally occupied for train stopping, the less the capacity of the train to be deducted by the train stopping.
The third calculation module 30 includes:
a first calculation unit 301 for setting a train LiAt ZsHas a stop time of Δ tisAccording to the train LiWith adjacent train LjAnd constructing a train stop time difference matrix at the stop time of each station, wherein i is {1, 2., M-1} and j is { 2., M } and rows and columns of the matrix represent the train L at the station siWith adjacent train LjDifference in station stopping time;
a second calculating unit 302 for setting a train group train LiAnd adjacent rear ranks vehicle LjDeparture interval I at the departure stationi-j＝ΔTi-j+ I, wherein Δ Ti-jDue to the train stop scheme, the train LiExtra time is required in the operation chartThe initial value of i is 1, and the initial value of j is i + 1;
a third calculating unit 303 for setting Δ T from the train stop difference matrix i columni-j0, accumulated value βi-j0, according to train LiAnd a train LjThe station stop difference value matrix of each station is accumulated from the first row of the i columns of the matrix to the back, if the accumulated value is up to the s rows of the i columns of the matrix
Figure BDA0002317530900000191
Record Δ Ti-j＝βi-jand is provided with βi-jif the accumulated value is equal to 0, the fourth calculation unit is entered, if the accumulated value is equal to betai-jIs always negative or zero, then Δ Ti-jKeeping the matrix unchanged, sequentially accumulating backwards until the last row of the matrix is N rows, and calculating Ii-jEntering a fifth calculation unit if i is i + 1;
a fourth calculation unit 304 for accumulating backward in sequence starting from the i column s +1 row of the matrix, if β is encountered againi-jIf > 0, update the delta Ti-j＝β+ΔTi-jSequentially accumulating backwards according to the method of the third calculation unit until the last row of the matrix I and the last N rows, and calculating Ii-j，i＝i+1；
A fifth calculating unit 305, configured to determine whether i is equal to M-1, if yes, enter a sixth calculating unit, and otherwise, repeat the third calculating unit and the fourth calculating unit;
a sixth calculating unit 306 for calculating the train group L1～LMTime spent in train diagram
Figure BDA0002317530900000201
And can know the occupied time T of the train stop station in the train operation diagramParking space＝TAccount for-(M-1)I。
The fourth calculation module 40 includes:
a seventh calculation unit 401 for setting a high-grade train LkLower-grade train L next to the preceding train and being crossedjMinimum inter-arrival time at an overrun station is Ij-kThen, Ij-k＝max{I,tStop+IGo to}，Wherein IGo toThe train-to-pass interval;
an eighth calculating unit 402 for the peer-to-peer train L because there is no crossing relationship between the peer-to-peer trainsi、LjInter-originating interval time Ii-jThrough the calculation of steps S102 to S104, the high-grade train L is obtained under the condition of tight departurekWith low-grade train LiMinimum departure interval I betweeni-k＝∑Ii-j+Ij-k；
A ninth calculating unit 403 for counting the low-grade train LiIs covered by a high-grade train LkWhen the station is overtaking, the sum of the station stop time difference value of the two stations before the overtaking station and the minimum arrival interval time of the two stations at the overtaking station is more than LiAnd LkThe starting interval time between the two trains is obtained by the formula (2-1)iStation when crossed:
Figure BDA0002317530900000202
in the formula (2-1), YLiIs a low-grade train LiStation, Δ t, when being crossedizIs a train LiAt YLiA stop time before the station.
The fifth calculation module 50 includes:
a tenth calculating unit 501, configured to rank the passing stations Y according to a station reverse order, where Y is {1, 2.,..,. Y }, where the station order corresponds to a front-back order of the passed trains, that is, according to a time order, the passing stations of the first rank of low-level trains that are passed in the train group are ranked as 1, and the passing stations of the last rank of low-level trains that are passed are ranked as Y, so that the passed low-level trains share Y columns;
an eleventh calculating unit 502 for calculating the lower-grade train L whose first train is crossed in the train group by the following formula1To high-grade train LkTime T occupied in train operation diagramAccount for：
Figure BDA0002317530900000211
In the formula (2-2), the first two terms are the first train L of the train group1To high-grade train LkInter-originating interval time of, wherein the first item
Figure BDA0002317530900000212
Is a train of the same class L1And LYInter-originating interval time, second item Ij-kFor the last lower-grade train L to be crossedYAnd high grade LkThe originating interval of (a) can be calculated as shown in equation 2-3, where tGo toThe minimum time interval from the arrival of a train at a station in one direction to the stop of the train passing another train in the same direction from the station is called the arrival time interval of the train in the same direction, and the third term
Figure BDA0002317530900000213
Is LYAt an overrun station and LkDeparture Interval of, item four
Figure BDA0002317530900000214
Is LYFrom the passing station YLYThe sum of the stop time from the next station to the end station to the station, and a fifth term tGet upAnd adding time for train departure.
IY-k＝max(I,tStop+tGo to) (2-3)
A twelfth calculation unit 503 for setting the low-grade train LiIs covered by a high-grade train LkThe station of the cross is y, and L is at the y stationiDeparture time and LkThe departure time interval is
Figure BDA0002317530900000215
The first train is crossed the low-grade train L1At the passing station YL11 and high-grade train LkThe time interval of departure time is
Figure BDA0002317530900000216
Wherein t isHair smoothing deviceWhen the train passes through the station from a certain directionStarting, recording the minimum interval time from the station to the stop of the train in the same direction as the train on-off time interval in the same direction;
Figure BDA0002317530900000217
is a train LkAnd L1Departure interval at an overrun station due to train L1By train LkAfter the two trains are overtravel, the two trains do not have an overtravel relationship, and L1Starting after the vehicle stops at the overpass station 1, then
Figure BDA0002317530900000218
Wherein
Figure BDA0002317530900000219
Is a train LiAnd a train LkDeparture intervals when the overtaking stations 1 are all originated;
a thirteenth calculating unit 504 for setting the second column of the crossed low-grade train L2At the passing station YL 22 and high-grade train LkThe time interval of departure time is Iy-kIn which Iy-kIs a train L1And L2Departure interval at the passing station 1, L1At the passing station YL11 Biba, L2At the passing station YL1When 1 is stopped or passed, then
Figure BDA0002317530900000221
As shown in the formula (2-4),
Figure BDA0002317530900000222
is as a train L2Train L when stopping at an overrun station1And L2At the passing station YL11, the same reason is L2At the passing station YL1When 1 is stopped or passed, then
Figure BDA0002317530900000223
As shown in formula (2-5);
Figure BDA0002317530900000224
Figure BDA0002317530900000225
a fourteenth calculating unit 505 for sequentially calculating the trains LkAnd LYAt the passing station YLYDeparture interval of Y
Figure BDA0002317530900000226
As shown in formula (2-6);
Figure BDA0002317530900000227
L(Y-1)at the passing station YL(Y-1)Y-1 Bi che, LYAt the passing station YL(Y-1)When Y-1 stops or passes, then
Figure BDA0002317530900000228
As shown in formulas (2-7), wherein
Figure BDA0002317530900000229
Is a train LYTrain L when stopping at an overrun station(Y-1)And LYAt the passing station YL(Y-1)Departure interval of Y-1, also due to LYAt the passing station YL(Y-1)When Y-1 stops or passes, then
Figure BDA00023175309000002210
As shown in formulas (2-8):
Figure BDA00023175309000002211
Figure BDA00023175309000002212
a fifteenth calculating unit 506, configured to calculate a multi-occupancy time of the train in the working diagram due to the influence of the stop of the train by using the following formula;
Tparking space＝TAccount for-YI (2-9)。
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (8)

1. A train passing capacity calculation method, characterized by comprising the steps of:
s1, acquiring train stop time in a train operation diagram, listing a train stop time difference matrix at each station according to a train departure sequence, wherein rows and columns of the matrix s represent trains L at the stationsiWith adjacent train LjDifference of station stop;
s2, judging whether the train workshops have an overtravel relationship, and if the train workshops do not have the overtravel relationship, entering the step S3; if the train has an overrun relationship, the process proceeds to step S4;
s3, calculating the time of the train group occupying the running chart under the condition that the train workshop does not have the crossing relation and the time of the train running chart additionally occupied by the train stopping station;
s4, calculating a train crossing station;
s5, calculating the time of the train group occupying the running chart under the condition that the train workshop has an overrun relation and the time of the train running chart additionally occupied by the train stopping station;
s6, judging the influence of the train stop scheme on the passing capacity according to the train operation diagram time additionally occupied by the train stop; the shorter the train diagram time that is additionally occupied for train stopping, the less the capacity of the train to be deducted by the train stopping.
2. The method for calculating the train passing ability according to claim 1, wherein the method for calculating the train diagram time occupied by the train group and the train diagram time additionally occupied for train stop in the train-to-train non-crossing relationship in step S3 comprises the steps of:
s101, arranging a train LiAt ZsHas a stop time of Δ tisAccording toTrain LiWith adjacent train LjAnd constructing a train stop time difference matrix at the stop time of each station, wherein i is {1, 2., M-1} and j is { 2., M } and rows and columns of the matrix represent the train L at the station siWith adjacent train LjDifference in station stopping time;
s102, setting a train group train LiAnd adjacent rear ranks vehicle LjDeparture interval I at the departure stationi-j＝ΔTi-j+ I, wherein Δ Ti-jDue to the train stop scheme, the train LiExtra time is needed in the operation diagram, the initial value of i is 1, and the initial value of j is i + 1;
s103, setting delta T from the train stop difference matrix i columni-j0, accumulated value βi-j0, according to train LiAnd a train LjThe station stop difference value matrix of each station is accumulated from the first row of the i columns of the matrix to the back, if the accumulated value is up to the s rows of the i columns of the matrix
Figure FDA0002317530890000021
Record Δ Ti-j＝βi-jand is provided with βi-jif it is 0, the process proceeds to step S104, where the accumulated value β is addedi-jIs always negative or zero, then Δ Ti-jKeeping the matrix unchanged, sequentially accumulating backwards until the last row of the matrix is N rows, and calculating Ii-jI +1, the process proceeds to step S105;
s104, accumulating from the i column s +1 row of the matrix backwards in sequence, if meeting beta againi-jIf > 0, update the delta Ti-j＝β+ΔTi-jSequentially accumulating the signals backwards according to the method in the step S103 until the last row of the matrix I is N, and calculating Ii-j，i＝i+1；
S105, judging whether i is equal to M-1, if so, entering a step S106, otherwise, repeating the step S103 and the step S104;
s106, calculating a train group L1～LMTime spent in train diagram
Figure FDA0002317530890000022
And can know that the train stops and occupies more space in the train operation chartTime of use TParking space＝TAccount for-(M-1)I。
3. The method for determining an overrun station as claimed in claim 2, wherein in said step S4, the method for determining an overrun station comprises the steps of:
s201, setting a high-grade train LkLower-grade train L next to the preceding train and being crossedjMinimum inter-arrival time at an overrun station is Ij-kThen, Ij-k＝max{I,tStop+IGo toIn which IGo toThe train-to-pass interval;
s202, as the cross-over relationship does not exist between the equal-level trains, the equal-level train Li、LjInter-originating interval time Ii-jThrough the calculation of steps S102 to S104, the high-grade train L is obtained under the condition of tight departurekWith low-grade train LiMinimum departure interval I betweeni-k＝∑Ii-j+Ij-k；
S203, when the low-grade train LiIs covered by a high-grade train LkWhen the station is overtaking, the sum of the station stop time difference value of the two stations before the overtaking station and the minimum arrival interval time of the two stations at the overtaking station is more than LiAnd LkThe starting interval time between the two trains is obtained by the formula (2-1)iStation when crossed:
Figure FDA0002317530890000031
in the formula (2-1), YLiIs a low-grade train LiStation, Δ t, when being crossedizIs a train LiAt YLiA stop time before the station.
4. The method for calculating the train passing ability according to claim 3, wherein the method for calculating the time of the train diagram occupied by the train group and the time of the train diagram additionally occupied by the train stop in the crossing relationship between the trains in the step S5 comprises the following steps:
s301, sorting the overtaking stations Y according to the station reverse sequence, wherein Y is {1,2,. and.. Y }, the station sequence corresponds to the front and back sequence of the overtaken trains, namely according to the time sequence, the overtaking stations of the first lower-level train which is overtaken in the train group are sorted into 1, and the overtaking stations of the last lower-level train which is overtaken in the train group are sorted into Y, so that the overtaken lower-level trains share Y columns;
s302, the first-train crossed low-grade train L in the train group1To high-grade train LkTime T occupied in train operation diagramAccount forCalculated by the following formula:
Figure FDA0002317530890000032
in the formula (2-2), the first two terms are the first train L of the train group1To high-grade train LkInter-originating interval time of, wherein the first item
Figure FDA0002317530890000033
Is a train of the same class L1And LYInter-originating interval time, second item Ij-kFor the last lower-grade train L to be crossedYAnd high grade LkThe originating interval of (a) can be calculated as shown in the formula (2-3), where tGo toThe minimum time interval from the arrival of a train at a station in one direction to the stop of the train passing another train in the same direction from the station is called the arrival time interval of the train in the same direction, and the third term
Figure FDA0002317530890000034
Is LYAt an overrun station and LkDeparture Interval of, item four
Figure FDA0002317530890000035
Is LYFrom the passing station YLYThe sum of the stop time from the next station to the end station to the station, and a fifth term tGet upAdding time division for train start;
IY-k＝max(I,tstop+tGo to) (2-3)
S303, setting a low-grade train LiIs covered by a high-grade train LkThe station of the cross is y, and L is at the y stationiDeparture time and LkThe departure time interval is
Figure FDA0002317530890000041
The first train is crossed the low-grade train L1At the passing station YL11 and high-grade train LkThe time interval of departure time is
Figure FDA0002317530890000042
Wherein t isHair smoothing deviceThe minimum interval time from the time when a train in a certain direction passes through a station to the time when the train is sent from the station to another train in the same direction is recorded as the train sending time interval in the same direction;
Figure FDA0002317530890000043
is a train LkAnd L1Departure interval at an overrun station due to train L1By train LkAfter the two trains are overtravel, the two trains do not have an overtravel relationship, and L1Starting after the vehicle stops at the overpass station 1, then
Figure FDA0002317530890000044
Wherein
Figure FDA0002317530890000045
Is a train LiAnd a train LkDeparture intervals when the overtaking stations 1 are all originated;
s304. the second row of crossed low-grade trains L2At the passing station YL22 and high-grade train LkThe time interval of departure time is Iy-kIn which Iy-kIs a train L1And L2Departure interval at the passing station 1, L1At the passing station YL11 Biba, L2At the passing station YL1When 1 is stopped or passed, then
Figure FDA0002317530890000046
As shown in the formula (2-4),
Figure FDA0002317530890000047
is as a train L2Train L when stopping at an overrun station1And L2At the passing station YL11, the same reason is L2At the passing station YL1When 1 is stopped or passed, then
Figure FDA0002317530890000048
As shown in formula (2-5);
Figure FDA0002317530890000049
Figure FDA00023175308900000410
s305. sequentially calculating train LkAnd LYAt the passing station YLYDeparture interval of Y
Figure FDA00023175308900000411
As shown in formula (2-6);
Figure FDA00023175308900000412
L(Y-1)at the passing station YL(Y-1)Y-1 Bi che, LYAt the passing station YL(Y-1)When Y-1 stops or passes, then
Figure FDA00023175308900000413
As shown in formulas (2-7), wherein
Figure FDA00023175308900000414
Is a train LYTrain L when stopping at an overrun station(Y-1)And LYAt the passing station YL(Y-1)Departure interval of Y-1, also due to LYAt the passing station YL(Y-1)When Y-1 stops or passes, then
Figure FDA00023175308900000415
As shown in formulas (2-8):
Figure FDA0002317530890000051
Figure FDA0002317530890000052
s306, calculating the occupied time of the train in the operation diagram due to the influence of the stop of the train through the following formula;
Tparking space＝TAccount for-YI (2-9)。
5. A train passing capability calculating system for implementing the train passing capability calculating method according to any one of claims 1 to 4, the system comprising:
the first calculation module is used for acquiring train stop time in a train operation diagram and listing a train stop time difference matrix according to a train departure sequence;
the second calculation module is used for judging whether the train workshops have the crossing relationship, and if the train workshops do not have the crossing relationship, the third calculation module is started; if the train has an overrun relationship, entering a fourth calculation module;
the third calculation module is used for calculating the time of the train operation diagram occupied by the train group under the condition that the train workshop has no crossing relationship and the time of the train operation diagram additionally occupied by the train stop;
the fourth calculation module is used for calculating the train overtaking station;
the fifth calculation module is used for calculating the time of the train operation diagram occupied by the train group under the condition that the crossing relationship exists among the trains and the time of the train operation diagram additionally occupied by the train stop;
and the sixth calculation module is used for judging the influence of the train stop scheme on the passing capacity according to the train working diagram time additionally occupied by the train stop, wherein the shorter the train working diagram time additionally occupied by the train stop is, the smaller the passing capacity deducted by the train stop is.
6. The train passing capability computing system of claim 5, wherein the third computing module comprises:
a first calculating unit for setting a train LiAt ZsHas a stop time of Δ tisAccording to the train LiWith adjacent train LjAnd constructing a train stop time difference matrix at the stop time of each station, wherein i is {1, 2., M-1} and j is { 2., M } and rows and columns of the matrix represent the train L at the station siWith adjacent train LjDifference in station stopping time;
a second calculation unit for setting a train group train LiAnd adjacent rear ranks vehicle LjDeparture interval I at the departure stationi-j＝ΔTi-j+ I, wherein Δ Ti-jDue to the train stop scheme, the train LiExtra time is needed in the operation diagram, the initial value of i is 1, and the initial value of j is i + 1;
a third calculation unit for setting delta T from the train stop difference matrix i columni-j0, accumulated value βi-j0, according to train LiAnd a train LjThe station stop difference value matrix of each station is accumulated from the first row of the i columns of the matrix to the back, if the accumulated value is up to the s rows of the i columns of the matrix
Figure FDA0002317530890000061
Record Δ Ti-j＝βi-jand is provided with βi-jif the accumulated value is equal to 0, the fourth calculation unit is entered, if the accumulated value is equal to betai-jIs always negative or zero, then Δ Ti-jKeeping the matrix unchanged, sequentially accumulating backwards until the last row of the matrix is N rows, and calculating Ii-jEntering a fifth calculation unit if i is i + 1;
a fourth calculation unit for accumulating backward in sequence starting from the i column s +1 row of the matrix, if encountering againβi-jIf > 0, update the delta Ti-j＝β+ΔTi-jSequentially accumulating backwards according to the method of the third calculation unit until the last row of the matrix I and the last N rows, and calculating Ii-j，i＝i+1；
The fifth calculating unit is used for judging whether i is equal to M-1 or not, if so, the sixth calculating unit is started, and if not, the third calculating unit and the fourth calculating unit are repeated;
a sixth calculation unit for calculating the train group L1～LMTime spent in train diagram
Figure FDA0002317530890000062
And can know the occupied time T of the train stop station in the train operation diagramParking space＝TAccount for-(M-1)I。
7. The train passing capability calculation system of claim 6, wherein the fourth calculation module comprises:
a seventh calculation unit for setting a high-grade train LkLower-grade train L next to the preceding train and being crossedjMinimum inter-arrival time at an overrun station is Ij-kThen, Ij-k＝max{I,tStop+IGo toIn which IGo toThe train-to-pass interval;
an eighth calculating unit for the peer-to-peer train L because there is no crossing relation between the peer-to-peer trainsi、LjInter-originating interval time Ii-jThrough the calculation of steps S102 to S104, the high-grade train L is obtained under the condition of tight departurekWith low-grade train LiMinimum departure interval I betweeni-k＝∑Ii-j+Ij-k；
A ninth calculating unit for counting the low-grade train LiIs covered by a high-grade train LkWhen the station is overtaking, the sum of the station stop time difference value of the two stations before the overtaking station and the minimum arrival interval time of the two stations at the overtaking station is more than LiAnd LkThe starting interval time between the two trains is obtained by the formula (2-1)iStation when crossed:
Figure FDA0002317530890000071
in the formula (2-1), YLiIs a low-grade train LiStation, Δ t, when being crossedizIs a train LiAt YLiA stop time before the station.
8. The train passing capability calculation system of claim 7, wherein the fifth calculation module comprises:
a tenth calculating unit, configured to rank the passing stations Y according to a station reverse order, where Y is {1,2, ·.,. Y }, where the station order corresponds to a front-back order of the crossed trains, that is, according to a time order, the passing stations of the first rank of lower-level trains crossed in the train group are ranked as 1, and the passing stations of the last rank of lower-level trains crossed are ranked as Y, so that the crossed lower-level trains share Y columns;
an eleventh calculating unit for calculating a lower-grade train L whose first train is crossed in the train group by the following formula1To high-grade train LkTime T occupied in train operation diagramAccount for：
Figure FDA0002317530890000072
In the formula (2-2), the first two terms are the first train L of the train group1To high-grade train LkInter-originating interval time of, wherein the first item
Figure FDA0002317530890000073
Is a train of the same class L1And LYInter-originating interval time, second item Ij-kFor the last lower-grade train L to be crossedYAnd high grade LkThe originating interval of (a) can be calculated as shown in the formula (2-3), where tGo toFrom when a train arrives at a station in a certain direction to when the train passes another stationThe minimum interval time of the same-direction train time stop is called the same-direction train arrival time interval, and the third item
Figure FDA00023175308900000812
Is LYAt an overrun station and LkDeparture Interval of, item four
Figure FDA0002317530890000081
Is LYFrom the passing station YLYThe sum of the stop time from the next station to the end station to the station, and a fifth term tGet upAdding time division for train start;
IY-k＝max(I,tstop+tGo to) (2-3)
A twelfth calculation unit for setting the low-grade train LiIs covered by a high-grade train LkThe station of the cross is y, and L is at the y stationiDeparture time and LkThe departure time interval is
Figure FDA0002317530890000082
The first train is crossed the low-grade train L1At the passing station YL11 and high-grade train LkThe time interval of departure time is
Figure FDA0002317530890000083
Wherein t isHair smoothing deviceThe minimum interval time from the time when a train in a certain direction passes through a station to the time when the train is sent from the station to another train in the same direction is recorded as the train sending time interval in the same direction;
Figure FDA0002317530890000084
is a train LkAnd L1Departure interval at an overrun station due to train L1By train LkAfter the two trains are overtravel, the two trains do not have an overtravel relationship, and L1Starting after the vehicle stops at the overpass station 1, then
Figure FDA0002317530890000085
Wherein
Figure FDA0002317530890000086
Is a train LiAnd a train LkDeparture intervals when the overtaking stations 1 are all originated;
a thirteenth calculating unit for setting the second row of the crossed low-grade train L2At the passing station YL22 and high-grade train LkThe time interval of departure time is Iy-kIn which Iy-kIs a train L1And L2Departure interval at the passing station 1, L1At the passing station YL11 Biba, L2At the passing station YL1When 1 is stopped or passed, then
Figure FDA0002317530890000087
As shown in the formula (2-4),
Figure FDA0002317530890000088
is as a train L2Train L when stopping at an overrun station1And L2At the passing station YL11, the same reason is L2At the passing station YL1When 1 is stopped or passed, then
Figure FDA0002317530890000089
As shown in formula (2-5);
Figure FDA00023175308900000810
Figure FDA00023175308900000811
a fourteenth calculating unit for calculating the train L in sequencekAnd LYAt the passing station YLYDeparture interval of Y
Figure FDA0002317530890000091
As shown in formula (2-6);
Figure FDA0002317530890000092
L(Y-1)at the passing station YL(Y-1)Y-1 Bi che, LYAt the passing station YL(Y-1)When Y-1 stops or passes, then
Figure FDA0002317530890000093
As shown in formulas (2-7), wherein
Figure FDA0002317530890000094
Is a train LYTrain L when stopping at an overrun station(Y-1)And LYAt the passing station YL(Y-1)Departure interval of Y-1, also due to LYAt the passing station YL(Y-1)When Y-1 stops or passes, then
Figure FDA0002317530890000095
As shown in formulas (2-8):
Figure FDA0002317530890000096
Figure FDA0002317530890000097
the fifteenth calculating unit is used for calculating the occupation time of the train in the operation diagram due to the influence of the stop station through the following formula;
Tparking space＝TAccount for-YI (2-9)。
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