International Journal of Scientific & Engineering Research, Volume 5, Issue 6, June-2014 1162
ISSN 2229-5518
Impact of Moving Block System on Railway Timetable Planning: a qualitative study on existing timetables
CHENGHAO YING
Abstract— This paper proposes a quick way to examine the impact of moving block system on railway timetable planning from minimal amount of data. In general, this method is developed to quickly determine the possible capacity improvement for lines operated in fixed block system if they were upgraded into more sophisticated moving block system. In this paper, railway timetables are characterized by four parameters, the train number, the average speed, the stability and the heterogeneity. Particularly, through examining the interdependency between the capacity improvement and these four parameters, qualitative conclusions are drawn for moving block system upgrade from fixed block system.
Index Terms— Capacity, Moving block system, Railway, Timetable, Block System
—————————— ——————————
apacity on Railways has long been a hot issue and enor- mous amount of efforts have successfully turned into reality. Among all the new technological achievements in railway domain, moving block system shall be one of the most promising. It is because it can greatly reduce the headway be- tween successive trains and thereby improve the capacity sig-
nificantly.
This paper intends to study the capacity improvement
when existing fixed block system is substituted by moving
block system. For a given open time window, if any improve-
ment is achieved, it should be reflected as an increasing un-
used time proportion, meaning more vacancy is available to
load more vehicles on the line. Therefore, in this paper, the
increased unused time ratio, or reduced used time ratio is the focus and the impact of moving block system is evaluated by the time proportion it can reduce from existing timetables.
Matlab and Adobe Illustrator are used in this paper to cal- culate as well as visualize the unused capacity. To start, re- duced headway in moving block system compared to fixed block system is studied, after which the compression method is used to illustrate the amount of time which can be saved from the already consumed in order to demonstrate the extra capacity attained.
Also, in this paper, rail line timetables will be characterized by four parameters as the train number, the average speed, the stability and the heterogeneity. A qualitative approach to moving block system’s impact on timetables with respect to these parameters is conducted. In order to do so, control vari- ate method is applied. For each time, only one of the four pa- rameters changes and the outcome for each is examined.
This paper is outlined as follows: Section 2 formulates a
————————————————
mathematical module for fixed block system as well as puts forward the variables under consideration. Section 3 discusses the main differences between moving block system and fixed block system, and particularly the improvement in capacity. Section 4 discusses the qualitative interdependency between increased capacity produced by moving block system and four major parameters. Section 5 briefly concludes the study and future direction of this work.
For the purposes of this paper, the existing timetable including the trains’ dynamic running diagram and blocking diagram are deemed as already known. Whereas during the study, some of other parameters may change, running diagram and blocking diagram of each train should be considered as un- changeable. Meanwhile, trains with similar dynamic charac- teristics are categorized as a reference train set. In other words, the impact of moving block system studied here is not only on any specific infrastructure but also on particular timetables.
This section defines the variables and the restrains of this module.
The set of the reference trains is given by R = {r1,r2,…,rn} wherein all the trains are moving towards the same direction. Since moving block system does not improve the flow of the trains in stations, the rail route studied is solely a double track line between two stations without joints. Assume that the ini- tial station is A and destination station is B, between which p block sections exist and are indicated as S= {1,2,…,p}. Other definitions are as follows.
Tbbr s : time train r claims s block. It is when the exclusive occupation begins;
Tsigrs : time train r enters s block and is kept 0 for all r ∈ R
and s=1. It is when the train enters the block.
Tber s : time train r clears s block. It is when the exclusive oc- cupation ends;
For all, r ∈ R and s ∈ S.
All other information such as speed curve, block section
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International Journal of Scientific & Engineering Research, Volume 5, Issue 6, June-2014 1163
ISSN 2229-5518
length and train length are not necessary as the information is already encompassed once the aforementioned data is given.
ority.
3 Middle buffer time when both trains have the same
priority.
Suppose there is a train dispatch order L= [l1 , l2 ,…,lm ], where li ∈ R for any i ∈ [1,m], the buffer time needed should
be a function with respect to L as BU(L). BU(L) will not change once L is fixed.
With this module, all kinds of different capacity consumptions like infrastructure occupation (meaning resources are used for exclusive operation) and buffer time can be theoretically com- puted. Infrastructure occupation time is a period of time when the relating resources are used because of the operation and it can be derived from solely the train dispatch order.
For any train dispatch order in the form of L= [l1 , l2 ,…,lm ], where li ∈ R for any i ∈ [1,m].
Then the total infrastructure occupation time should be
Fig. 1. to demonstrate the defined Tbb, Tsig and Tbe. As can be seen, one train claims its occupation before it enters a block section and clear the occupation after it leaves the blocking section.
𝑂𝑇(𝐿) = −𝑇𝑇𝑇𝑙1
𝑚−1
𝑖=1
𝑀𝑀𝑙𝑖+1
𝑖
+ 𝑇𝑇𝑇𝑙𝑚
+ 𝐵𝐵(𝐿) (2)
As a massive transportation making up more than 50% of the total freight share in some countries [1], railway transportation is at any time and at any place carefully planned and moni- tored. The capability of drivers, or locomotive engineers, is heavily dependent on a sophisticated central control system. This is also the reason that one train claims one block section long before it enters it to ensure enough time for visual con- firmation, path establishment and pre-signal confirmation [2] and the block section will not be released until the train com- pletely clears the signal. In order to avoid train crashes, head- ways are kept strictly by CTC (Centralized Train Control).
Meanwhile, headways differ from one case to another, de- pending on the trains and the features of the lines. Nonethe- less, in this case, where all the significant time points are clear, the minimum headway in the form of time can be presented as follow:
Fig. 2. to demonstrate the components of occupation time. Given a train dispatch order L=(ri, rj, rk), occupation time can be calculate as is in equation (2).
In (2), OT, standing for occupation time, is the minimal time needed to operate a train dispatch L provided no delay bigger than buffer time occurs. The reduction of which is also
𝑟𝑖
𝑟𝑖
𝑟𝑗
the main target in this paper, namely, to what extent can mov-
𝑀𝑀𝑟𝑗 = max�𝑇𝑇𝑇𝑠
− 𝑇𝑇𝑇𝑠 � (1)
ing block system reduce OT(L) is discussed in this paper.
For any ri, rj ∈ R while ri departs first and for every s in S.
𝑀𝑀𝑟𝑖 stands for the minimum time interval rj train has to
keep to depart after the departure of ri train, otherwise train
collisions may occur. As can be seen from (1), in timetable
planning, the headway in between depends on both of the
leading train and the following train.
Buffer time is a matter of stability. Buffer time reduce the risk of transmitting delays between trains or they reduce the size of the knock on delay transferred from one train to the follow- ing trains. [3]. Usually, more stable the timetable is, the less dependent it is on buffer time. Most railways use the follow- ing basic rules [2].
1 Great buffer time when the second train has a higher priority.
2 Low buffer time when the first train has a higher pri-
Moving block system is designed to reduce the minimum headway between consecutive trains in order to further im- prove the line capacity. As the name itself indicates, unlike fixed block system where the block sections are fixed, the block sections can be seen as moving along together with the leading train.
Unlike fixed block system, where the safety of trains is guaranteed by the principle that in one physical block section only one train can exist, in moving block system, no physical blocking section is needed. Meanwhile, a block section is de- marcated by two main signals in fixed block system while the necessity is replaced in moving block system by more sophis-
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International Journal of Scientific & Engineering Research, Volume 5, Issue 6, June-2014 1164
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ticated cab signals in order to carefully keep a safety distance for the leading train from the following train [4].
With the fast-paced technology development, the techno- logical hurdles which used to hamper the utilization of the moving block system have now been removed. Real-time and anti-hacking communication technology has been developed to a high level that it is possible now to transit the identity, location, direction and speed of each vehicle to the Centralized Train Control to conduct important calculations in real time.
With reduced headways, the occupation time which com- prises headway and butter time, will decrease.
Fig. 4. to demonstrate the blocking time reduction moving block sys- tem can generate on a fixed block system based timetable. The lighter part in this illustration stands for the extra time or distance that can be gained by moving block system upgrade.
Fig. 3. to demonstrate the difference between fixed block system and moving block system. In fixed block system, following train is strictly kept out of occupied section by red signal while in moving block sys- tem the following train is kept a safety distance from the leading train.
As is clearly depicted in Fig. 3, the imaginary block sec- tion’s moving generates a constant movement authority for the following train to nearly the rear of the leading train [5].
In this paper where capacity is mainly discussed, the most significant improvement of moving block system compared to fixed block system is that it can considerably reduce the headways. In order to create an analogy with fixed block sys- tem, the improved part of moving block system is equivalent to enabling the train to claim the ending point of a block sec- tion later and release the occupation of the beginning point of the block section earlier.
In Fig. 4, through cutting one triangle from each rectangle, the diagram is more space-effective compared to Fig. 2 just as how an oblique parking would save space in a parking lot.
While in real moving block diagram, the outline shall be smoother which can be achieved by high degree polynomial curve fitting in simulation visualization, for the purpose of capacity study however, this complexity can be avoided. Re- sults derived from this method shall be enough to offer a qual- itative conclusion.
Using this linear approximation obtained, it is possible to calculate all the new minimum headways needed for the mov- ing block system.
Following the assumption that no further variables will change during the upgrading from fixed block system to mov- ing block system, reduced headways can be computed as fol- low.
Fig. 5. to demonstrate the occupation time reduction. In this case, with L being [ri, rj, rk], the proportion of occupation time reduced is indicated in the right-down area.
Noteworthy is that so far no additional information or data is needed. Nevertheless, a straightforward way is presented to demonstrate how moving block system can improve railway capacity and the fact that capacity improvement is heavily dependent on the headway reduction is made clear.
However, conclusions are never robust on one specific case. Symbolic calculation and deduction must be conducted to fur- ther evaluate the moving block system in regard to railway capacity.
Railway capacity is a hot issue and there exists no universal definition. Enormous work has been conducted in order to define railway capacity in a way so that it can be accepted eve- rywhere. Among which the UIC 406 leaflet [6] from 2004 of-
𝑟𝑖
𝑟𝑖
𝑟𝑗
𝑀𝑀𝑟𝑗 = max�𝑇𝑇𝑇𝑠−1 − 𝑇𝑇𝑇𝑠 � (1)
For any ri, rj ∈ R while ri departs first and for every s in S
while the edge effect is ignored.
fers a way which is both simple and effective.
Oddly enough, the very first point of UIC 406 is capacity as
such does not exist but depends on the way it is utilized.
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However, what is revolutionary is it puts forward a brief in- troduction of parameters underpinning capacity as the num- ber of trains, the average speed, the stability and the heteroge- neity. Meanwhile, all these parameters have a positive correla- tion with capacity as implied in this leaflet.
This leaflet imposes huge impacts on how railway engi- neers understand capacity. Thus it is a wise way to examine all four parameters when evaluating a new system. In the fol- lowing part of this session, these four basic parameters are examined one by one while other three are kept unchanged and they are denoted as N, A, Sa, H respectively.
Additional definitions:
and pre-signal distance. Therefore, provided m is a big
enough integer, ρ(L)∝ 1/Sa. And furthermore,
C(A)<0 (4)
Stability on railway timetable can be reflected as the need for buffer time. On timetables in which unexpected delays are rare, it is relatively more lenient to not assign as much buffer time as it has to do on timetables otherwise. Meanwhile, under the assumption of this paper, moving block system has no positive effects on the buffer policy, meaning that buffer time is independent from the system in use. Therefore, according to
UC(L) = −𝑇𝑇𝑇𝑙1
+ 𝑇𝑇𝑇𝑙𝑚
: fixed part in OT if L is fixed.
the definition of ρ(L) and the fact that BU(L) ∝ 1/Sa(L), the
RE(L): theoretical occupation time reduction benefited from
deduction is not quite strenuous.
moving block system with respect to train dispatch order L.
𝑑ρ(L)
𝑅𝐸(𝐿)
−𝑅𝐸(𝐿)
𝑂𝑇(𝐿)+∆𝐵𝑈(𝐿)
𝑂𝑇(𝐿)
RE(L)=OT(L)-OT(L)M, where OT(L)M represents the theoretical
OT in moving block system.
ρ(L) = 𝑅𝐸 (𝐿): proportion of time a moving block system can
C(Sa) = ∝
𝑑𝑆𝑎(𝐿)
> 0 (5)
−∆𝐵𝑈(𝐿)
𝑂𝑇(𝐿)
save from the existing system.
C(X) = 𝑑ρ(L) : correlation between ρ(L) and X(L), where X
𝑑𝑋(𝐿)
can be N, A, Sa or H, standing four parameter aforesaid. In
addition ρ(L) ∝ X(L) means ρ is positive correlated with X and
vice versa.
Consider a timetable which can be represented as L= [l1 ,
l2 ,…,lm ]. In order to study the correlation between ρ and train
Heterogeneity is a subject hard to define, especially in quanti-
tative perspective [7]. Therefore, study into heterogeneity
stops at whether the existence of heterogeneity makes the
moving block system more effective.
Assume there is one timetable represented as L= [l1 , l2 ,…,lm ] in which ri exists but rj and rk do not. The average
speed of rj and rk equals to the average speed of ri. By adding
two ri trains or one rj and one rk, the heterogeneities are
changed while train number and average speed are remained
the same.
𝑟𝑖 + 𝑇𝑇𝑇𝑟𝑖 − 𝑇𝑇𝑇𝑟𝑖 − 𝑇𝑇𝑇𝑟𝑖
number N while keeping the average speed, stability and het-
∆𝑂𝑇(𝐿𝐿) = 𝑇𝑇𝑇𝑝
� 𝑟𝑘
𝑠1
𝑟𝑗
𝑠1
𝑟𝑘
1
𝑟𝑗
erogeneity unchanged, L can be multiplied by a constant α > 1.
∆𝑂𝑇(𝐿𝐿𝐿) = 𝑇𝑇𝑇𝑝
+ 𝑇𝑇𝑇𝑠2 − 𝑇𝑇𝑇𝑠2 − 𝑇𝑇𝑇1
Following the definition,
∆𝑂𝑇(𝐿𝐿)𝑀 = 𝑇𝑇𝑇𝑝
𝑠1−1
𝑠1 1
𝑟𝑖 + 𝑇𝑇𝑇𝑟𝑖 − 𝑇𝑇𝑇𝑟𝑖 − 𝑇𝑇𝑇𝑟𝑖
RE(αL)−RE(L)
� 𝑟𝑘
𝑟𝑗
𝑟𝑘
𝑟𝑗
C(X) = ρ(αL)−ρ(L) = 𝑂𝑇(αL) 𝑂𝑇(𝐿).
∆𝑂𝑇(𝐿𝐿𝐿)𝑀 = 𝑇𝑇𝑇𝑝
+ 𝑇𝑇𝑇𝑠2−1 − 𝑇𝑇𝑇𝑠2 − 𝑇𝑇𝑇1
(α−1)
(α−1)
𝑅𝑅(𝐿𝐿) = 𝑇𝑇𝑇𝑟𝑖 − 𝑇𝑇𝑇𝑟𝑖
When the edge effect is negligible, the effect on minimum
� 𝑠1
𝑠1−1
𝑟𝑗 − 𝑇𝑇𝑇𝑟𝑗
headways should be proportional increased by a factor α .
𝑅𝑅(𝐿𝐿𝐿) = 𝑇𝑇𝑇𝑠2
𝑠2−1
𝑟𝑖 − 𝑇𝑇𝑇𝑟𝑖
Thus the deduction continues as follow.
𝑇𝑇𝑇𝑠1
∆ρ(Li) =
𝑠1−1
α∗RE(L)
−RE(L)
⎪ 𝑇𝑇𝑇𝑝
𝑟𝑖
𝑟𝑖
𝑟𝑖
C(N) = α∗𝑂𝑇(L)−(α−1)∗𝑈𝐶(𝐿) 𝑂𝑇(𝐿) > 0 (3)
𝑟𝑖 + 𝑇𝑇𝑇𝑠1 − 𝑇𝑇𝑇𝑠1 − 𝑇𝑇𝑇1
𝑟𝑗 − 𝑇𝑇𝑇𝑟𝑗
(α−1)
𝑇𝑇𝑇𝑠2
𝑠2−1
⎪∆ρ(Ljk) =
𝑟𝑘
𝑟𝑗 − 𝑇𝑇𝑇𝑟𝑘 − 𝑇𝑇𝑇𝑟𝑗
⎩ 𝑇𝑇𝑇𝑝
+ 𝑇𝑇𝑇𝑠2
𝑟𝑘
𝑠2
𝑟𝑗
1
𝑟𝑘
𝑟𝑗
Similarly, to keep all other three parameter besides train speed
∆ρ(Li)
𝑙𝑇𝑙𝑙𝑙ℎ(𝑠1)
𝑣𝐿
𝑇𝑇𝑇𝑝
+ 𝑇𝑇𝑇𝑠2 − 𝑇𝑇𝑇𝑠2 − 𝑇𝑇𝑇1
unchanged, two imaginary timetables can be assumed as
∆ρ(Ljk) = 𝑙𝑇𝑙𝑙𝑙ℎ(𝑠2) ∗ 𝑣𝐿 ∗ 𝑇𝑇𝑇𝑟𝑖 + 𝑇𝑇𝑇𝑟𝑖 − 𝑇𝑇𝑇𝑟𝑖 − 𝑇𝑇𝑇𝑟𝑖
𝑝 𝑠1
𝑠1 1
L1=[ri, ri, …, ri] and L2=[rj, rj, …, rj] with the same train num-
ber m and suppose train rj is faster than train ri.
Since there is no heterogeneity in either timetable, every
minimum headway in between is the same. Following the equation to calculate the minimum headways for every two trains, the combined minimum headway for Li in fixed block
In railway design, the length of each block shall not differ
in a significant way and usually, s1, s2 in above expression are much likely to be on the edge when trains are accelerating or decelerating. Furthermore, when the length from beginning to destination is long enough, the edge effect is negligible.
𝑟𝐿
𝑟𝐿
Therefore,
system is m ∗ (𝑇𝑇𝑇𝑠 − 𝑇𝑇𝑇𝑠 ) while in moving block system is
∆ρ(Li)
𝑣𝐿
𝑇𝑇𝑇𝑝
~ > 1
m ∗ (𝑇𝑇𝑇𝑠−1 − 𝑇𝑇𝑇𝑠 ) where s is one specific block section
∆ρ(Ljk) ~ = 𝑣𝐿 ∗ 𝑇𝑇𝑇𝑟𝑖
𝑟𝐿
𝑟𝐿
𝑝
which make these expressions maximal. Therefore,
In this expression, rn is the slower one while j is the first
𝑟𝐿
𝑟𝐿
ρ(Li) = 𝑅𝐸 (𝐿𝑖) = 𝑚∗(𝑇𝑇𝑇𝑠 −𝑇𝑇𝑇𝑠−1) .
departing train which can be the faster one or not.
𝑟𝑖
𝑟𝑖
𝑟𝐿
𝑟𝐿
𝑂𝑇(𝐿𝑖)
−𝑇𝑏𝑏1 +𝑇𝑏𝑒𝑝 +𝐵𝑈(𝐿𝑖)+m∗(𝑇𝑇𝑇𝑠 −𝑇𝑇𝑇𝑠 )
If the assumptions here are plausible in railway industry,
ri ri
ri ri
Let Q= Tbes − Tbes−1 and P= Tbes − Tbbs .
Note that Q is positive correlated to the reciprocal of speed
since this is basically the travel time between block sections. However, P is not strongly related to average speed since the majority of P is for visual confirmation, path establishment
C(H) is more likely to be positive, meaning that heterogeneity has negative effects on moving block system upgrade.
C(H)>0 (6)
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International Journal of Scientific & Engineering Research, Volume 5, Issue 6, June-2014 1166
ISSN 2229-5518
In this paper, moving block system’s impact on capacity is studied and in particular its relation between four parameters underpinning is studied.
Moving block system can reduce the headway by signifi- cant amount and thereby further reduce the total occupation time. However, the impact of moving block system differs according to the characteristics of the train and infrastructure.
Specifically, four basic parameters of capacity are studied. Moving block system performs better on lines with large train numbers, relatively low average speed, high stability where buffer time is not largely assigned and low train type hetero- geneity. It then leads to a suggestion: moving block system should be applied on lines preferably with large train number, normal average speed, high stability and low heterogeneity.
However, the future of traffic planning should be done by gathering real-time data from the field [8]. This study is solely based on existing timetables, which means the complexities on real operation including unexpected events and emergency response, are not considered. In future study, such events can be considered so it can offer further suggestions on railway planning.
[1] W.-K. Chen, "EU Transport in Figures; Statistical Pocket- book".European Commission Directorate-General for Energy and Transport; Eurostat. 2007.
[2] J. Pachl, “Blocking Time and Headway Theory”, Railway Operation and Control, pp. 47-51, 2002
[3] B. Schittenhelm, “Planning With Timetable Supplements in Railway
Timetable", Annual Transport Conference at Aalborg University,
2011.
[4] UIC, Influence of ETCS on line capacity Generic study, 2008
[5] B.M. Ede, "Moving Block in Communication-Based Train Control: Boon or Boondoggle?", Transportation Technology Center Inc. Pueb- lo, USA
[6] UIC, UIC CODE 406, 1st Edition, 2004
[7] M. Dingler, Y.C Lai, Christopher P.L, “Impact of train Type Hetero- geneity on Single Track Railway Capacity”
[8] A.D Ariano, F.Corman, I.A. Hansen, “Railway Traffic Optimization
by Advanced Scheduling and Re-routing Algorithms”
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