Calculating the Maximum Assembling on Nested Routing Platforms of Urban Rail Transit Line

Yongliang Wang; Xingchen Zhang

doi:10.1515/JSSI-2014-0372

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Calculating the Maximum Assembling on Nested Routing Platforms of Urban Rail Transit Line

Yongliang Wang and Xingchen Zhang

Published/Copyright: August 25, 2014

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From the journal Journal of Systems Science and Information Volume 2 Issue 4

Abstract

The maximum assembling for some period on nested routing platforms of urban rail transit line were calculated by trend analysis method. Based on influencing factors of maximum assembling on platform, relative hypotheses were given. Platforms were divided to eight types by relations between platform and routing train. Interaction of passenger, train and platform, assembling change process, and calculation frames of maximum assembling on different type platforms carried out to be maximum assembling were concluded by trend analysis method. The numerical example application revealed that trend analysis method to calculate maximum assembling on nested routing platforms is feasible, and the final results by trend analysis method are more accurate than by one of codes for design of metro.

Keywords: urban traffic; maximum assembling on platform; trend analysis method; nested routing

1 Introduction

Nested routing is mixed operation of long and short routing trains on some sections of line, long routing train turns back when it reaches the terminal station and short routing train turns back when it reaches the middle station designated (see [1]). Nested routing is divided to two types (a) and (b) shown in Figure 1 and Figure 2 separately.

How to accurately calculate maximum assembling on nested routing platforms will directly influence evaluation reliability of platform service level. The maximum assembling on nested routing platforms could also provide reference to plan and design station facilities, and decide train capacity. Calculating assembling on platform is mostly carried out on planning and design stages, ignoring influence of operation organization. So, this paper will consider inputting timetable, in according with involving operation mechanism beforehand on planning and design stages.

At present, research on maximum assembling on platform of urban rail transit line is in its infancy. Reference [2] analyzes change of passenger waiting for train on platform under different relations between capacity and demand. Under constant headway, reference [3] puts forward maximum assembling calculation method on platforms belonging to single routing middle stations of urban rail transit line. Based on proportionate running trains of different routings, reference [4] analyzes assembling change on part nested routing platforms. When all the trains owning the same transportation attribute, reference [5] provides calculation method of maximum assembling on platform. According to passengers’ dynamic process on the platform of within a train arrival time, reference [6] designs a way to calculate the number of the assembling passengers in various stages. With full consideration of the timetable coordination, reference [7] calculates the assembling passengers at a one-platform-transfer metro station with varied intervals of trains’ arrivals. Reference [8] gives trend analysis method to calculate maximum assembling on transfer side platform of urban rail transit line.

Based on nested routing timetable given and stopping schedule being stopping at each station, maximum assembling for some period on nested routing platforms of urban rail transit straight line its up or down trains stopping the same platform for each station are calculated by trend analysis method. The numerical example reveals that trend analysis method to calculate maximum assembling on nested routing platforms is feasible, and the final results by trend analysis method are more accurate than by one of code for design of metro.

2 Research hypotheses

Considering influencing factors of assembling on platform, relative hypotheses are as follows.

1) assembling on up and down platform of each station do not affect each other.

2) passenger strictly follow the principle of first under after on.

3) passenger prior ride through train.

4) passenger entering platform for train obey uniform distribution.

5) passenger for some train on platform board it during its dwelling time.

6) departing moment of passenger riding previous train to reach platform is earlier than arriving moment of current train to reach the platform.

7) passenger boarding rate exceeds passenger entering platform rate for train.

8) up or down trains dwelling time and passenger getting-off time are constant for the same station.

9) up or down trains running time are constant for the same section.

3 Platform types

Nested routing platforms of urban rail transit straight line its up or down trains stopping the same platform for each station are divided to eight types by relations between platform and routing train, as shown in Table 1. According to hypothesis 3), platforms distribution of nested routing (a) and (b) are shown in Figure 1 and Figure 2 separately, in which “+” indicates up direction, “–” indicates down direction, Q and Q̅ indicate nested routing (a) and (b) separately, and number indicates platform type.

4 Calculating maximum assembling on nested routing platforms

In order to discuss assembling change process on nested routing platform p, research time interval T_p is divided into Nsp,Tp+1 time elements by departing train number Nsp,Tp from station S_p. The first time element starts at initial moment of research time interval and ends at departing moment of the first train. Each of the second to Nsp,Tp-th time elements starts at departing moment of previous train and ends at departing moment of current train. The (Nsp,Tp+1)-th time element starts at departing moment of the Nsp,Tp-th train and ends at final moment of research time interval. Train departing moment of end station is train departing moment from platform. It could be concluded that the (Nsp,Tp+1)-th time element disappears when departing moment of the Nsp,Tp-th train is the same as final moment of research time interval.

Table 1

Nested routing platform types

Platform type	Relation between platform and routing train	Remark
1p	Platform being start platform of some routing train
2p	Platform being middle platform of some routing train	One routing
3p	Platform being end platform of some routing train

4p	Platform being start platform of one routing train and start platform of the other routing train
5p	Platform being middle platform of one routing train and middle platform of the other routing train
6p	Platform being end platform of one routing train and end platform of the other routing train	Two routing
7p	Platform being start platform of one routing train and middle platform of the other routing train
8p	Platform being middle platform of one routing train and end platform of the other routing train

Figure 1

Platforms distribution of nested routing (a)

Figure 2

Platforms distribution of nested routing (b)

When assembling on platform is 0 at initial moment of research time interval, the first time element could merges with the second to Nsp,Tp-th time elements according to hypothesis 5). This paper supposes that assembling on platform is 0 at initial moment of research time interval to simplify calculation. Consequently, assembling change process on platform comprises former Nsp,Tp time elements and the (Nsp,Tp+1)-th time element, and maximum assembling on nested routing platform p is peak of Nsp,Tp+1 maximum assembling corresponding to respective time element.

4.1 4.1 Trend analysis method

Research approach of trend analysis method is as follows: interaction of passenger, train and platform is concluded by analyzing activity time and change trend of passenger boarding, passenger getting off, passenger entering platform and passenger departing from platform, to grasp assembling change process on nested routing platforms, find maximum assembling appearing moment on platforms, and confirm calculation frames of maximum assembling on different type nested routing platforms carried out to be maximum assembling.

Because some one of 4-8 type platforms is essential some one of 1-3 type platforms in different time, nested routing platforms are divided into 1-3 type platforms and 4-8 type platforms to calculate maximum assembling on them. j_p is routing when platform p is one of 1-3 type platforms. j_p_,1, j_p_,2 are routings when platform p is one of 4-8 type platforms. tSp,S is train dwelling time on station S_p. tSp,S is passenger getting-off time on station S_p. v_p_,o is average departing rate from platform p for passenger riding train to reach platform p. t_p_,o is time interval from train dwelling moment on platform p to disappearing moment for passenger riding the train to reach platform p. vjp,i,vjp,1,i,vjp,2,iare separately average entering platform rate of passenger for j_p, j_p_,1, j_p_,2 train to leave platform p. vjp,d,vjp,1,d,vjp,2,dare separately average boarding rate of passenger for j_p, j_p_,1, j_p_,2 train to leave platform p. vjp,a,vjp,1,a,vjp,2,aare separately average getting-off rate of passenger riding j_p, j_p_,1, j_p_,2 train to reach platform p.

4.2 1-3 type platforms

There are the following relations, according to reference [3–4] and hypothesis 7).

vjp,d>vjp,i(1)

vp,o>vjp,i(2)

vjp,a>vp,o(3)

1) former Nsp,Tp time elements

Assembling change process and maximum assembling appearing moment analysis for some time element of 1-3 type platforms are shown in Figure 3 and Table 2 separately, considering relations between relative parameters. t₁ is tp,o−tSp,S,t2ish−tSp,S,t3ish−tSp,S+tSp,a and h is time length of current time element.

I. 1 type platform 1p

Because station S_1p is start station of routing j_1p train, there are not passenger getting off on platform 1p. t₁ moment does not exist and t₂ moment is the same as t₃ moment.

As can be seen from Figure 3(a) and Table 2, maximum assembling on platform 1p for each time element are passenger already entering platform to depart at t₂/t₃ moment, whose assembling time interval is 0 – t₂/t₃ of current time element according to hypothesis 5).

II. 2 type platform 2p

Station S_2p is middle station of routing j_2p train. As can be seen from Figure 3(b) and Table 2, maximum assembling on platform 2p for each time element are sum of passenger already entering platform to depart and passenger getting off and still not leaving platform at t₃ moment.

Figure 3

Assembling change process for some time element of 1-3 type platforms

Table 2

Maximum assembling appearing moment analysis for some time element of 1-3 type platforms

Platform type	Routing	Time interval	Assembling change trend	Maximum assembling appearing moment
1p	j_1p	0 – t₂/t₃	vj1p,i>0, assembling increases	t₂/t₃
1p	j_1p	t₂/t₃– h	vj1p,i−vj1p,d<0, assembling decreases	t₂/t₃

		0 – t₁ (the first time element)	vj2p,i>0, assembling increases
		0 – t₁ (the first time element)	vj2p,i>0, assembling increases
2p	j_2p	0 – t₁ (not the first time element)	vj2p,i−v2p,o<0, assembling decreases	t₃
		0 – t₁ (not the first time element)	vj2p,i−v2p,o<0, assembling decreases
		t₁ – t₂	vj2p,i>0, assembling increases
		t₂ – t₃	vj2p,i+vj2p,a−v2p,o>0,assembling increases
		t₃ – h	vj2p,i−vj2p,d−v2p,o<0, assembling decreases

		0 – t₁ (the first time element)	assembling is 0
3p	j_3p	0 – t₁ (the first time element)		h
3p	j_3p	0 – t₁ (not the first time element)	−v3p,o<0,assembling decreases	h
		0 – t₁ (not the first time element)	−v3p,o<0,assembling decreases
		t₁ – t₂	assembling is 0
		t₂ – h	vj3p,a−v3p,o>0, assembling increases

Assembling time interval for passenger already entering platform to depart is 0 - t₃ of current time element according to hypothesis 5). Passenger getting off are sum of passenger riding current train to reach platform 2p on previous already dwelling platforms, whose assembling time intervals are time elements current train corresponding to on previous already dwelling platforms separately. According to hypotheses 4), 8) and 9), time elements current train corresponding to on platform 2p is the same as ones current train corresponding to on previous already dwelling platforms. Consequently, assembling time interval for passenger riding current train and getting off is current time element. Up to t₃ moment, departing time interval for passenger getting off and leaving platform is t₂ – t₃ of current time element.

III. 3 type platform 3p

Because station S_3p is end station of routing j_3p train, there are not passenger boarding on platform 3p, and t₃ moment does not exist.

As can be seen from Figure 3(c) and Table 2, maximum assembling on platform 3p for each time element are passenger getting off and still not leaving platform at h moment. Be similar to platform 2p, assembling time interval for passenger getting off is current time element. Up to h moment, departing time interval for passenger getting off and leaving platform is t₂ – h of current time element.

2) the (Nsp,Tp+1) – th time element

I. 1 type platform 1p

As can be seen from Figure 3(a) and Table 2, assembling on platform 1p is 0 at start moment of current time element according to hypothesis 5), and assembling on platform 1p gradually increases when time goes on. Maximum assembling on platform 1p for current time element are passenger already entering platform to depart at tS1p,T1pmoment, whose assembling time interval is current time element.

II. 2 type platform 2p

As can be seen from Figure 3(b) and Table 2, when final moment tS2p,T2p of research time interval is late to t₁ moment, assembling on platform 2p gradually increases. Maximum assembling on platform 2p for current time element are passenger already entering platform to depart at tS2p,T2p moment, whose assembling time interval is current time element.

When final moment tS2p,T2p of research time interval is early to t₁ moment, on the one hand, assembling on platform 2p at tS2p,T2p moment are less than assembling on platform 2p at t₃ moment of the Nsp,Tp-th time element; on the other hand, passenger already entering platform to depart for current time element ignoring passenger getting off and still not leaving platform at tS2p,T2p moment are less than assembling on platform 2p at tS2p,T2p moment. Consequently, passenger already entering platform to depart for current time element could replace assembling on platform 2p at tS2p,T2p moment to compare with maximum assembling on platform 2p for other time elements and not to affect final maximum assembling on platform 2p for research time interval.

In short, we merely calculate passenger already entering platform to depart for current time element to avoid judging order of tS2p,T2p moment and t₁ moment.

III. 3 type platform 3p

As can be seen from Figure 3(c) and Table 2, when final moment tS3p,T3p of research time interval time late to t₁ moment, assembling on platform 3p is 0.

Be similar to platform 2p, when final moment tS3p,T3pof research time interval time early to t₁ moment, assembling on platform 3p being 0 for current time element could replace assembling on platform 3p at tS3p,T3pmoment to compare with maximum assembling on platform 3p for other time elements and not to affect final maximum assembling on platform 3p for research time interval.

In short, we merely let passenger already entering platform to depart for current time element be 0 to avoid judging order of tS3p,T3pmoment and t₁moment.

4.3 4-8 type platforms

1) former Nsp,Tptime elements

I. different routing headways analysis

Along train running direction on stations 4-8 type platforms belonging to, there are sections of routing j_p_,I ∈ {j_p,1, j_p,2} including ones of routing j_p,II ∈ j_p,1,j_p,2}, and passenger entering platform to depart are divided into passenger riding routing j_p_,I or j_p_,II train and passenger only riding routing j_p_,I train. We think that there is only routing j_p_,II train whose headway is comprehensive one of routing j_p_,I headway and j_p_,II headway for passenger riding routing j_p_,I or j_p,II train, and routing j_p_,I headway is unchanged for passenger riding routing j_p_,I train. Routing j_p_,II is only held when routings j_p_,I and j_p_,II are same.

Similarly, along train running opposite direction on stations 4-8 type platforms belonging to, there are sections of routing j_p,I′ ∈ {j_p_,1,j_p,2} including ones of routing j_p,II′ ∈ {j_p_,1,j_p,2}, and passenger reaching platform are divided into passenger riding routing j_p_,I′ or j_p_,II′ train and passenger only riding routing j_p_,I′ train. We think that there is only routing j_p_,II′ train whose headway is comprehensive one of routing j_p_,I′ headway and j_p_,II headway for passenger riding routing j_p_,I′ or j_p_,II′ train, and routing j_p_,I′ headway is unchanged for passenger riding routing j_p_,I′ train. Routing j_p_,II′ is only held when routings j_p_,I and j_p_,II are the same.

II. maximum assembling appearing moment analysis

There are the following relations, according to reference [3-4] and hypothesis 7).

min(vjp,1,d,vjp,2,d)>vjp,1,i+vjp,2,i(4)

vp,o>vjp,1,i+vjp,2,i(5)

min(vjp,1,a,vjp,2,a)>vp,o(6)

Maximum assembling appearing moment analysis for some time element of 4-8 type platforms being 1-3 type in different time are shown in Table 3, considering relations between relative parameters and Figure 3.

Table 3

Maximum assembling appearing moment analysis for some time element of 4-8 type platforms

Platform type	Being platform type in different time	Time interval	Assembling change trend	Maximum assembling appearing moment
4p	1p of j_4p,1, j_4p,2 separately	0 – t₂/t₃ t₂/t₃ – h	vj4p,1,i+vj4p,2,i>0, assembling increases vj4p,1,i+vj4p,2,i−min(vj4p,1,d,vj4p,2,d)<0, assembling decreases	t₂/t₃

	2p of j₅_p_,1,j₅_p_,2 separately	0 – t₁ (the first time element)	vj5p,1,i+vj5p,2,i>0, assembling increases
5p		0-t₁ (not the first time element)	vj5p,1,i+vj5p,2,i−v5p,o<0, assembling decreases	t₃
		t₁ – t₂	vj5p,1,i+vj5p,2,i>0, assembling increases
		t₂ – t₃	vj5p,1,i+vj5p,2,i+min(vj5p,1,a,vj5p,2,a)−v5p,o>0, assembling increases
		t₃-h	vj5p,1,i+vj5p,2,i−min(vj5p,1,d,vj5p,2,d)−v5p,o<0, assembling decreases

	3p of j₆_p_,1,j₆_p_,2 separately	0 – t₁ (the first time element)	assembling is 0
6p		0 – t₁ (not the first time element)	–v₆_p_,o < 0, assembling decreases	h
		t₁-t₂	assembling is 0
		t₂-h	min(vj6p,1,a,vj6p,2,a)−v6p,o>0, assembling increases

	1p of j_7p_,1	0-t₁ (the first time element or former being 1p train)	vj7p,1,i+vj7p,2,i>0, assembling increases	t₂/t₃
7p		0-t₁ (former being 2p train)	vj7p,1,i+vj7p,2,i−vj7p,2,o<0, assembling decreases
		t₁- t₂/t₃	vj7p,1,i+vj7p,2,i>0, assembling increases
		t₂/t₃- h	vj7p,1,i+vj7p,2,i−vj7p,1,d<0, assembling decreases

	2p of j_7p,2	0-t₁ (the first time element or former being 1p train)	vj7p,1,i+vj7p,2,i>0, assembling increases	t₃
		0-t₁ (former being 2p train	vj7p,1,i+vj7p,2,i−v7p,o<0, assembling decreases)

		t₁-t₂	vj7p,1,i+vj7p,2,i>0, assembling increases
		t₂-t₃	vj7p,1,i+vj7p,2,i+vj7p,2,a−v7p,o>0, assembling increases
		t₃-h	vj7p,1,i+vj7p,2,i−vj7p,2,d−v7p,o<0, assembling decreases

		0-t₁ (the first time element)	vj8p,1,i>0, assembling increases
	2p of j_8p,1	0-t₁ (not the first time element)	vj8p,1,i−v8p,o<0, assembling decreases	t₃
8p		t₁-t₂	vj8p,1,i>0, assembling increases
		t₂-t₃	vj8p,1,i+vj8p,1,a−v8p,o>0, assembling increases
		t₃-h	vj8p,1,i−vj8p,1,d−v8p,o<0, assembling decreases

		0-t₁ (the first time element)	vj8p,1,i>0, assembling increases
	3p of j_8p,2	0-t₁ (not the first time element)	vj8p,1,i−v8p,o<0, assembling decreases	h
		t₁-t₂	vj8p,1,i>0, assembling increases	h
		t₂-h	vj8p,1,i+vj8p,2,a−v8p,o>0, assembling increases

III. calculation frame

As can be seen from Table 3, maximum assembling on platform 1p 4 or 7 type platform being in different time for some time element are passenger already entering platform and waiting for routings j_p_,I and j_p_,II trains to depart at t₂/t₃ moment. After analyzing, we could conclude that assembling time interval of passenger waiting for routing j_p_,I train to depart starts at departing moment of former routing j_p_,I train and ends at t₂/t₃ moment of current time element, and assembling time interval of passenger waiting for routing j_p_,II train to depart is 0 – t₂/t₃ of current time element according to different routing headways analysis and hypothesis 5).

As can be seen from Table 3, maximum assembling on platform 2p 5, 7 or 8 type platform being in different time for some time element are sum of passenger already entering platform and waiting for routings j_p_,I and j_p_,II trains to depart at t₃ moment, and passenger riding current train to reach platform 2p and still not leaving platform. After analyzing, we could conclude that assembling time interval of passenger waiting for routing j_p_,I train to depart starts at departing moment of former routing j_p_,I train and ends at t₃ moment of current time element, and assembling time interval of passenger waiting for routing j_p_,II train to depart is 0 – t₃ of current time element according to different routing headways analysis and hypothesis 5).

Passenger riding routing j_p_,I′ train to reach platform 2p are sum of passenger riding current train to reach platform 2p on previous already dwelling platforms, whose assembling time intervals are headways between current routing j_p_,I′ train and former routing j_p_,I′ train on previous already dwelling platforms separately. According to hypotheses 4), 8) and 9), headway between current routing j_p_,I′ train and former routing j_p_,I′ train on platform 2p is the same as one on previous already dwelling platforms. Consequently, assembling time interval for passenger riding routing j_p_,I′ train to reach platform 2p starts at departing moment of former routing j_p_,I′ train and ends at departing moment of current routing j_p_,I′ train. Assembling time interval for passenger riding routing j_p_,II′ train to reach platform 2p is current time element based on different routing j_p_,I′ and j_p_,II′ headways analysis. Up to t₃ moment, departing time interval for passenger getting off and leaving platform is t₂ – t₃ of current time element.

As can be seen from Table 3, maximum assembling on platform 3p 6 or 8 type platform being in different time for some time element are sum of passenger already entering platform and waiting for routing j_p_,I or j_p_,II train to depart at h moment, and passenger riding routings j_p_,I′ and j_p_,II′ trains to reach platform 3p and still not leaving platform. After analyzing, we could conclude that assembling time interval of passenger waiting for routing j_p_,I train to depart starts at departing moment of former routing j_p_,I train and ends at departing moment of current train, and assembling time interval of passenger waiting for routing j_p_,II train to depart is current time element according to hypothesis 5).

Be similar to platform 2p 5, 7 or 8 type platform being in different time, assembling time interval for passenger riding routing j_p_,I′ train to reach platform 2p starts at departing moment of former routing j_p_,I′ train and ends at departing moment of current routing j_p_,I′ train. Assembling time interval for passenger riding routing j_p_,II′ train to reach platform 2p is current time element. Up to h moment, departing time interval for passenger getting off and leaving platform is t₂ – h of current time element.

2) the (Nsp,Tp+1)-th time element

As can be seen from Table 3, assembling change process of 4-8 type platforms for the (Nsp,Tp+1)-th time element are divided into 3 types: assembling gradually increase, assembling first decrease and last increase, assembling gradually decrease to 0.

I. assembling gradually increase

Maximum assembling on platform for current time element are passenger already entering platform and waiting for routings j_p,I and j_p,II trains to depart at tSp,Tp moment when assembling on platform gradually increase. Assembling time interval of passenger waiting for routing j_p,I train to depart starts at departing moment of former routing j_p,I train and ends at departing moment of current train, and assembling time interval of passenger waiting for routing j_p,II train to depart is current time element according to different routing headways analysis and hypothesis 5).

II. assembling first decrease and last increase

When final moment tSp,Tp of research time interval is late to t₁ moment, assembling on platform gradually increase. Maximum assembling on platform for current time element are passenger already entering platform and waiting for routings j_p,I and j_p,II trains to depart at tSp,Tp moment.

When final moment tSp,Tpof research time interval is early to t₁ moment, on the one hand, assembling on platform at tSp,Tpmoment are less than maximum assembling on platform of the Nsp,Tp-th time element; on the other hand, passenger already entering platform to depart for current time element ignoring passenger getting off and still not leaving platform at tSp,Tp moment are less than assembling on platform at tSp,Tp moment. Consequently, passenger already entering platform and waiting for routings j_p,I and j_p,II trains to depart at tSp,Tp moment could replace assembling on platform at tSp,Tp moment to compare with maximum assembling on platform for other time elements and not to affect final maximum assembling on platform for research time interval.

In short, we merely calculate passenger waiting for routings j_p,I and j_p,II trains at tSp,Tp moment to avoid judging order of tSp,Tp moment and t₁ moment.

III. assembling gradually decrease to 0

when assembling on platform gradually decrease to 0, assembling on platform at each moment for current time element are less than maximum assembling on platform of the Nsp,Tp-th time element. Consequently, let maximum assembling on platform for current time element be 0 simply not to affect final maximum assembling on platform for research time interval.

5 Numerical example application

Urban rail transit straight line its up or down trains using the same platform for each station contains 7 stations. Train running time on each section is 360s, train dwelling time on each station is 30s, passenger getting-off time on each station is 30s, and passenger departure rate from each station is 150p/m. Line OD passenger flow for some peak hour and candidate routings are shown in Table 4 and Table 5 separately.

Table 4

Line OD passenger flow for some peak hour

Station	1	2	3	4	5	6	7
1	0	550	580	905	1250	1345	1430
2	550	0	520	575	950	1160	1370
3	580	520	0	1745	1825	1935	2015
4	905	575	1745	0	2045	2355	2765
5	1250	950	1825	2045	0	2450	2835
6	1345	1160	1935	2355	2450	0	3995
7	1430	1370	2015	2765	2835	3995	0

Table 5

Candidate routings

Routing number	Routing composition
1	1-2-3-4-5-6-7
2	1-2-3-4
3	3-4-5-6

Timetable scheme of nested routing (a) is formed by routing 2 and 1 train running alternately for 26 times, and timetable scheme of nested routing (b) is formed by routing 3 and 1 train running alternately for 26 times.

Platforms distribution, maximum assembling on up and down platforms of nested routing (a) scheme are shown in Figure 4, Figure 5 and Figure 6. Platforms distribution, maximum assembling on up and down platforms of nested routing (b) scheme are shown in Figure 7, Figure 8 and Figure 9.

Figure 4

Platforms distribution of nested routing (a) scheme

Figure 5

Maximum assembling on up platforms of nested routing (a) scheme

Figure 6

Maximum assembling on down platforms of nested routing (a) scheme

Figure 7

Platforms distribution of nested routing (b) scheme

Figure 8

Maximum assembling on up platforms of nested routing (b) scheme

Figure 9

Maximum assembling on down platforms of nested routing (b) scheme

We can find the following conclusions by analyzing Figure 4∼9.

1) Maximum assembling on up and down platforms of nested routing (a) or (b) scheme for each station, and ones on up and down platforms for station 3, 4 and 7 separately owning same routing number 2, 2 and 1 for nested routing (a) or (b) scheme, are same by the one of code for design of metro, considering line OD passenger flow for some peak hour shown in Table 4 being symmetrical, but maximum assembling on up and down platforms of nested routing (a) or (b) scheme for each station are different by trend analysis method.

2) Maximum assembling on some one of 1-3 type platforms by trend analysis method are less than ones by code for design of metro. Investigate its reason, on the one hand, maximum assembling appearing moment is early to final moment of current time element; on the other hand, some passengers have left platform.

3) Maximum assembling on some one of 4-8 type platforms by trend analysis method are more than ones by code for design of metro. Investigate its reason, different routings trains transportation attribute on platform and actual headway of different routings trains being more than comprehensive headway of code for design of metro lead to calculation result by trend analysis method overwhelmingly larger.

In short, trend analysis method considers assembling actual change process on nested routing platforms and its calculation results are more accurate.

6 Conclusions

1) Calculating maximum assembling on platforms under nested routing timetable given are solved by trend analysis method, for urban rail transit straight line its up or down trains using the same platform for each station.

2) The numerical example application indicates that trend analysis method is feasible and effective, and the final results by this method are more accurate than by the one of codes for design of metro.

3) Some hypotheses are used to calculate maximum assembling on nested routing platforms. Consequently, revising these hypotheses to correspond to reality needs further research.

Acknowledgements

We thank the referees for their time and comments. References

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Received: 2014-1-2

Accepted: 2014-4-1

Published Online: 2014-8-25

Articles in the same Issue

https://doi.org/10.1515/JSSI-2014-0372

Keywords for this article

urban traffic; maximum assembling on platform; trend analysis method; nested routing