The blocking time diagram is a time–space diagram that includes information on time and train position as a line with different slopes. The time duration of a block section allocated to a specific train is called blocking time. This concept is similar to occupancy time defined by UIC 406 (2012) as shown in Figure 3.1.
Figure 3.1 Physical Definition of an Occupancy Time
Reference: UIC CODE 406 Leaflet (2012) The block section is blocked for other trains during blocking time to avoid train collision in this separation of space. The blocking time of a block for an operating train consists of the following parts (Goverde et al., 2013):
I. Setup time to set and lock the route in the block II. Sight and reaction time before the approach signal
III. Approach time from the approach signal to the signal in the rear of the block IV. Running time on the block
V. Clearing time (running time over the train length to clear the block)
VI. Release time to release the route in the block
The part of the time duration varies with different infrastructures and signal conditions. Each blocking time diagram in this model contains four parts, namely, setup and locking time, approaching time, running time, and release and clearing time, and comprises a blocking time stairway that represents the operation of a train from the initial station to the destination. Examples of a blocking time stairway and the parts of a blocking time diagram are shown in Figure 3.2.
Figure 3.2 Example of a Blocking Stairway
When many trains operate through a route during a certain period, the movements of the trains can be transferred to several blocking time stairways, which represent independent train paths for each train. The time interval between two adjacent trains can be seen as the headway of these trains. For example, the time interval of two trains that depart from a station can be used to compute the departure headway as shown in Figure 3.3.
Figure 3.3 Example of Departure Headway by Blocking Time Diagram
Furthermore, this study determines an important key point. Two trains will not cause conflict in a section if the blocking time diagram and the whole blocking time stairway of the two trains do not overlap with each other. This study uses this concept to develop a capacity model to solve single-, double-, and mixed-track sections. Moreover, this model provides an efficient deadlock avoidance function in the simulation process that prevents a deadlock situation, which causes interruption and failure, from occurring in the simulation. If the simulation process cannot keep the deadlock situation from happening, the judgment standard of whether or not any deadlock situation will occur becomes important but difficult to determine as shown in Figure 3.4.
Figure 3.4 A Popular Deadlock Situation after the Departure of Train 4
This study presents a previous deadlock situation through a blocking time diagram as shown in Figure 3.5. The following train blocking time stairway can be drawn to determine whether or not the departure of Train 4 from Station A will cause a deadlock problem.
Figure 3.5 Blocking diagram of a deadlock problem
Figure 3.6 shows that Train 4 overlaps the blocking time diagrams of Trains 2 and 3 when they depart from Station B. Trains 1, 2, and 3 cannot remain at Station B at the same time because of the lack of station tracks. A deadlock can occur if Train 4 departs from Station A as observed in the blocking time diagram, and this deadlock situation is what the simulation process wants to avoid. Past studies always required complicated algorithm steps to prevent a deadlock condition from happening. This research cannot detect a deadlock situation but achieves deadlock avoidance in the simulation process using the proposed capacity model in an intuitive and efficient way.
Figure 3.6 Result of the Blocking Diagram of a Deadlock Problem 3.2 Development of the Simulation Model Flowchart and Procedures
Figure 3.7 shows the flowchart for the simulation capacity model. The input data of this model only require the standard operation time, infrastructure condition, and operation margins rather than a number of input data requirements. The standard operation time should collect the running time of each block section to produce the blocking time stairway for every train class. The infrastructure condition includes the number of main tracks between adjacent stations and the number of station tracks for train crossing and overtaking. This model needs the operating margin set by railway operators to keep some flexibility of the result close to the actual condition given the external influence.
Standard blocking time Figure 3.7 Simulation Capacity Model Flowchart
Several key procedures in the simulation capacity model and a brief overview of each procedure are presented as follows.
Step 1: Production of the standard blocking time stairway diagram
The train types and train composition in Step 1 of the simulation are two inputs set by the user. The model then randomly chooses a southbound or northbound train class and takes the standard operation time of the chosen train as input data to draw a blocking time diagram of each block section. Every final time interval of the blocking time diagram in the blocking time stairway of Step 1 should be the running time through a certain section.
Step 2: Implementation of the train insertion module
The blocking time stairway diagram of the chosen train is placed into a train conflict matrix using the train insertion module (TIM). The time conflict matrix records the inserted and non-conflicting train blocking time stairway diagram in the text file form to reduce the computing time. It does not memorize and judge every pixel of the diagram
in .bmp or other image file forms. The TIM formulates two main regulations to keep the analyzed capacity result reasonable.
I. The departure time of the newly inserted train at the first station should be after the departure time of the last train in the same direction.
II. The arrival time of the newly inserted train at the last station should be after the arrival time of the last train in the same direction.
If a violation of one of the regulations occurs, the module readjusts the departure time of the newly inserted train at the first station to move the whole train blocking time stairway downward without changing the standard section operation time. Except for these two rules, the TIM cannot resolve other blocking time stairway overlapping situations or call train conflict events that are caused by the newly inserted train.
Step 3: Implementation of the conflict detection module
This step implements the conflict detection module (CDM) to detect whether or not a newly inserted train causes any conflict events with existing trains. The CDM considers the infrastructure condition of the main track number to detect the lack of station tracks for train crossing and overtaking or if a train conflict has occurred between the stations.
If no conflict has happened after the new train is inserted, then the procedure continues to Step 5. Otherwise, CDM focuses on the earliest conflict event to output two sets of data, the conflict-causing train and the conflict-affected train, and follow the conflict resolution module (CRM) to solve the conflict. Given the complicated logic caused by chain reactions of other trains that are close to the conflict-affected train, this study explains the CDM in detail in Section 3.4.
Step 4: Implementation of the conflict resolution module
The CRM is used to solve a train conflict by shifting the departure time of the conflict-causing train or the conflict-affected train backward. The CRM identifies the type of conflict decided by the class and direction of the causing train and the conflict-affected train. Each train conflict event requires different standards of judgment to decide the measure of conflict resolution. The location and time of conflict and the basic train operation rule must be considered to shift the causing train or the conflict-affected train backward and address the conflict event. The CRM is described in Section 3.3.
Step 5: Calculation of the analyzed capacity
After the conflict resolution procedure has been completed, the capacity of existing and non-conflict trains can be estimated by Equation 10.
) 3600
This concept of capacity estimation equation is similar to the capacity model of UIC 406, in which the total train number is divided into the time window of the effective capacity consumption value. For the time window
t
Lt
S, the value oft
Lindicates the lastinserted train even if it is limited by the rules of TIM. A train in the opposite direction is sometimes affected by previous trains, which cause a later departure time. Figure 3.8 shows that five trains are found when the non-conflict occurs in the block section. The departure time at the first station (Station A) of the latest train (the fifth train) is
t
5,L, and the departure time of the fourth train at the first station (Station D) ist
4,L.t
4, is much larger thant
5,L. Thus,t
L should be equal tot
4,L instead oft
5,L, and the defined time window is equal tot
Lt
S. The ratio of the operating margin is set to add extra time to the definedoperating time window
t
Lt
S to give some buffer time for the operation system to improve the stability and reliability of the driving system.Figure 3.8 Example of the Judgment of
t
L ValueThe capacity is calculated, and the model verifies whether or not the simulated train number n reaches the input number of N. If the simulated train number n is equal to the set train number target N, the model ends the simulation procedure; otherwise, the model needs to run another loop start from Step 1 to insert another random train blocking time stairway into the analysis procedure until the result fits the ending condition. The number of analyzed trains increases, the influence of capacity decreases by adding a blocking time stairway diagram of trains, and the value becomes stable and convergent. The model applies the standard deviation concept to help users determine if the capacity value is convergent. The earlier value is usually more unstable than the latter value. This study calculates the standard deviation of the last 30 capacity values to check the convergence condition and suggests 0.1 as the threshold.
3.3 Conflict Resolution Module
Figure 3.9 illustrates the flowchart of the CRM and its relationships with nearby procedures in the simulation process. This study describes the conflict resolution mechanism in Section 3.3.1 and introduces the basic train operation rules in Section 3.3.2.
Conflict Detection
The CRM is used to solve train conflicts in the simulation process by shifting the train departure time backward. While the CDM is being conducted, the simulation procedure detects whether or not conflict has occurred at the main track between two adjacent stations by overtaking or crossing behavior. If conflict occurs, the CDM places the related trains, including the conflict-causing train and the conflict-affected train, as the input data of CRM to determine a resolution measure that can address the conflict.
Multiple conflict events always occur when a new train blocking time stairway is inserted to the existing diagram. Nonetheless, the CRM only deals with one of the events at every turn regardless of the number of conflict events happening at the same time. That is, the resolution order of the multiple conflict events is decided by the CDM instead of the CRM,
The input of the CRM is the two trains, the causing train and the conflict-affected train, and the basic train operation rules. The CRM can judge the time and location of this conflict while obtaining the data of the two trains. The location in the main track where the conflict has occurred can transfer to the previous and following blocking sections, such as a passenger station, signal station, passing loop, or siding, to allow one train to cross or overtake the other train. This railway infrastructure is referred to as “station.” The basic train operation rules set for the train overtaking and crossing indicate that the CDM decides to move one of these two train’s departure time backward at which the blocking section allows the train to cross or overtake the other train. Other conflict events can be solved if the CRM completes this conflict resolution process.
3.3.2 Basic Train Operation Rules
When a train conflict occurs, this study requires standards to decide how to address a conflict and obtain a result that is not far from the actual operation. Therefore, the basic train operation rules are developed to serve as reference for conducting the CRM process.
Train crossing and overtaking have different situations in single- and double-track sections. Thus, this study proposes separate basic train operation rules for crossing and overtaking train interactions. In a double-track section, the operator uses each main track for a certain direction train rather than allowing trains to use both tracks in bi-directional running. Under this operating condition, the train can only address overtaking conflict using different sectional running times in a double-track route. A single-track section is when trains travel in both directions and share the same track. Therefore, overtaking and crossing conflicts can cause many types of conflict in the section.
Train Overtaking Situation
The train overtaking situation can occur on single and double tracks. The same direction train always uses the same main track. The basic train operation rules for solving train overtaking conflict are as follows:
Rule 1: The section that conducts train overtaking should be equipped with additional infrastructure to enable a train to overtake another train.
When two trains have different sectional running time, the following train may catch up with the previous train and cause a train overtaking conflict. Thus, an additional special infrastructure, such as a passenger station, signal station, passing loop, or siding, should be available where the previous train can wait, release route authority, allow the following train to overtake.
Rule 2: The waiting train should limit single and total waiting time.
Given that this study resolves train conflict, the train departure time of one station can be shifted backward, a situation that leads to more waiting time compared with the standard dwelling time. This study limits the single and total waiting time while waiting for another overtaking train to maintain a reasonable result as the actual operating situation. This role is proposed in Equations 11 and 12.
I
s
= Station that can provide train crossing or overtakingS = Set of all stations that can provide train crossing or overtaking
W
is = Waiting time of train i at station s SWT = Limit of single waiting time TWT = Limit of total waiting timeRule 3: The faster train moves and overtakes the slower train at the following station.
If a conflict is caused by the faster train as it catches up with the slower train and the CRM decides to move the departure time of the faster train backward, the faster train should overtake the slower train at the station following the station where the conflict happened. The reason is that the departure time of the faster train at the previous station is later than that of the slower train. The faster train can only overtake the slower train at the following station.
Rule 4: The slower train moves as it waits for the faster train at the previous station.
The CRM decides to move the departure time of the slower train backward to solve the conflict caused by the faster train reaching the slower train. The slower train should wait for the faster train to overtake at the previous station of the conflict location. The arrival time of the slower train at the following station is later than that of the faster train.
Thus, moving the slower train backward to resolve this conflict is impossible.
Rule 5: If the total waiting time of the slower train is more than the limitation, the slower train can no longer be overtaken by other trains.
Rule 2 indicates that the total waiting time, which is the sum of the dwelling time and the delay caused by the CRM process, should be determined whether or not it exceeds
will continue to shift the departure time of a certain train at this station. Otherwise, the train cannot be overtaken by other slow or fast trains. Thus, the departure time of the faster train at the first station should be readjusted to fit this rule.
Rule 6: If the single waiting time of the slower train is more than the limitation, the faster train should overtake the slower train at the next station.
Rule 2 indicates that the single waiting time, which includes the dwelling time and delay caused by the CRM process, should not surpass the single waiting time limitation.
If the single waiting time is excessively large to break this rule, the faster train should attempt to overtake the slower train at the next station. This can be conducted by shifting the departure time of the faster train at the previous station backward or by readjusting the departure time of the faster train at the first station.
Rule 7: The number of waiting trains can be overtaken at one time by a faster train at a certain station depending on the number of station tracks.
This study does not limit the total number of trains waiting at a station to be overtaken by a certain train. Therefore, multiple trains may be waiting at the same station for a faster train to overtake at one time. However, this number should be limited by the number of available station tracks that could accommodate train waiting. If the number of station tracks is not enough to complete the overtaking event at the station, the faster train should attempt to overtake the slower train at the following station. Equation 13 shows that the number of station tracks at station s can limit the total number of waiting trains for overtaking or crossing.
t
= Unit of time periodT = Set of the unit of time period (15 sec.)
WT
st = Total number of waiting trains at station s in time period tT
s = Number of tracks at station s Train Crossing Situation
The train crossing situation occurs on a single track only, while the different direction train meets at the same main track. The following are the basic train operation rules for solving the train crossing conflict.
Rule 1: The section that conducts train crossing should be equipped with additional infrastructure that enables a train to cross another train.
This rule is similar to Rule 1 in the train overtaking situation. Two trains with different directions cause crossing or overtaking conflict. Thus, additional infrastructures, such as a passenger station, signal station, passing loop, or siding, should be provided where the previous train can wait, release route authority, and enable the following train to cross the previous train.
Rule 2: The waiting train should limit the single and total additional waiting time.
This rule is the same as Rule 2 in the train overtaking situation. The waiting train
This rule is the same as Rule 2 in the train overtaking situation. The waiting train