Introduction
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We extend the SAN models to allow the modeling and analyses of more complex and realistic scenarios with multiple routes, intersections, and shared routes.
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We provide new data structures to allow the definition of new topologies of tramway networks in a parametric way.
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We defined and included a new metric to analyze the distribution of the traffic towards the whole network, allowing to identify the parts of the tramway networks that are more critical and sensible to the variation of the environment conditions and to the setting of the key architectural parameters.
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Finally, we provide a more detailed explanation of the overall SISTER system functioning, of the interactions among its constituent components, and the new functions and data structures used in the extended model to deal with multiple routes and intersections.
SISTER main architectural components
Location determination system (LDS)
Operational Control Center (OCC)
On-Board Control Unit (OBCU)
Interlocking (IXL)
Focus: interactions between the SISTER architectural components while approaching a junction area
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Detects its virtual position Lv calculated using the Sensor Fusion Algorithm embedded in the LDS component and then:
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It connects at regular intervals to the OCC, sends its virtual position Lv and its own identifier, then disconnects from the OCC, and compares its virtual position Lv with the onboard map for the detection of Virtual Tags.
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The OBCU detects the virtual tag indicating the presence of a junction area. This virtual tag also contains information for connecting to the interlocking that manages the junction area.
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The OBCU of the tram, therefore, detects the virtual route request tag.
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The OBCU sends a connection request to the interlocking along with its own identifier.
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The interlocking receives the connection request, analyzes it, and sends a message to the OBCU to confirm that the connection has been established.
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When OBCU detects the connection request Virtual Tag on the map, it sends to IXL a message with the request and its own identifier. IXL accepts the request.
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The OBCU sends the request for a specific route together with its identifier to the interlocking.
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The interlocking receives the route request and performs the feasibility check of the requested route based on the status of the monitored virtual track circuits, using as input the position of all the trams it is connected to. If the requested route is free from other trams it creates the route, commands all exchanging in the correct position, sets the tram signal to GO, and sends a route created confirmation message to OBCU.
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The tram enters the junction area overcoming the tram signal and periodically sends its position Lv and its identifier to the interlocking it is connected to.
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The interlocking periodically calculates the Location Referencing function, which establishes the occupation of the track circuits and verifies that the sequence of occupation of the track circuit by the tram is that foreseen by the assigned route.
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As soon as the interlocking detects the occupation of the first track circuit in the junction area, this tram signal is set as STOP.
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The tram then enters the junction area and sends its position once per second. IXL monitors the progress of the tram on the route with a Location Referencing function and sets the tram signal as STOP.
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The interlocking clears the route assigned to the tram when the tram exits the virtual tag corresponding to the route release condition.
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When the interlocking detects the exit of the tram from the last track circuit of the junction area, it sends a disconnection request to the tram and then it disconnects.
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OBCU receives the request for disconnection from the interlocking and sends a confirmation response.
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Upon receipt of the confirmation response from the OBCU of the tram, the interlocking disconnects the communication with the OBCU of the tram.
Operational scenario and objectives of the analysis
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Route 1. The trams on Route 1 start from terminal A, on the left side of Fig. 2, and share the first part of the track with trams on Route 2 (8 platforms). The trams on Route 1 arrive at terminal B on the right side of Fig. 2.Route 1 is about 15.3 km long and has 11 junction areas. The first junction is located after 500 m from the beginning of the line. Then, the following distances between junctions were considered: 150 m, 1400 m, 250 m, 1500 m, 200 m, 3500 m, 100 m, 1000 m, 2150 m, and 2550 m.
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Route 2. The trams on Route 2 also start from terminal A, but arrive at terminal C, on the bottom of Fig. 2. Trams on Route 2 share the last part of the track with trams that come from Route 4 (3 platforms).Route 2 is about 10 km long, with 11 junction areas. The first junction is located after 500 m from the beginning of the line and then the following distances between junctions were considered: 150 m, 1400 m, 250 m, 1500 m, 200 m, 3500 m, 100 m, 250 m, 50 m, and 50 m.
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Route 3. The trams on Route 3 start from terminal E, right side of Fig. 2, and share the first part of track with the trams on Route 4 (4 platforms). The trams on Route 3 arrive at terminal F on the right side of Fig. 2.Route 3 is about 11.2 km long and has 10 junction areas. The first junction is located after 500 m from the beginning of the line. Then, the following distances between junctions were considered: 200 m, 1900 m, 1300 m, 100 m, 350 m, 3100 m, 100 m, 1600 m, and 150 m.
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Route 4. The trams on Route 4 also start from terminal E, and arrive at terminal C, on the bottom of Fig. 2, where they share this part of the track with trams that come from Route 2 (3 platforms).Route 4 is about 5.6 km long and has 7 junction areas. The first junction is located after 500 m from the beginning of the line. Then, the following distances between junctions were considered: 200 m, 1900 m, 1300 m, 250 m, 50 m, and 50 m.
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Route 5. The trams on Route 5 start from terminal D, on the bottom of Fig. 2, and proceed to the terminal F, on the left side of Fig. 2. The trams on Route 5 share the beginning of the track with trams on Route 6 (3 platforms), and they share the last part of the track with trams on Route 3 (5 platforms).Route 5 is about 7.5 km long and has 8 junction areas. The first junction is located after 500 meters from the beginning of the line. Then, the following distances between junctions were considered: 150 m, 100 m, 350 m, 3100 m, 150 m, 1600 m, and 150 m.
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Route 6. The trams on Route 6 start from terminal D, on the bottom of Fig. 2, and proceed to the terminal E, on the right side of Fig. 2. The trams on Route 6 share the beginning of the track with trams on Route 5 (3 Platforms), and share the last part of the track with trams on Route 1 (2 platforms).Route 6 is about 6.8 km long and has 5 junction areas. The first junction is located after 500 m from the beginning of the line. Then, the following distances between junctions were considered: 150 m, 500 m, 2150 m, and 2550 m.
Objectives of the analysis and metrics of interest
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Average time required by each tram to cross the considered route: calculated as the difference between the time the tram reaches the end of the route and its departure time.
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Average number of activation of the manual procedure: In the event that the driver has to wait in front of a tram signal set to STOP for a time exceeding a predefined time-out, the driver must contact the ground control unit (OCC) to activate the manual procedure and know how to proceed. The activation of the manual procedure by the driver will result in a delay in the entire management of the tram traffic in that area, and this metric intends to estimate the average number of the manual procedure activation (sight guide).
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Average occupancy time of each segment of a route, i.e., the average time a segment of a route is occupied by a tram. This metric allows to check which are the parts of the route where trams spend more time, thus emphasizing the critical parts of the tramway network.
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Accuracy of the onboard positioning system: it is the maximum error, expressed in meters, of the positioning data communicated by the Local Determination System (LDS) to the other elements of the architecture (OnBoard Control Unit- OBCU and Interlocking-IXL). It is intended to analyze whether and under what conditions this parameter can have an impact on the management of tram signals, on route requests from other trams and therefore on the overall tramway traffic.
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Time-out value for the activation of manual procedures (call to the OCC): this is the maximum time that each tram can wait in front of a tram signal set to STOP, and after which it must contact the ground operations center (OCC) to activate the manual procedure and know how to proceed, accumulating a delay in its path. It is intended to evaluate whether and under what conditions this parameter can have an impact on the tramway performance.
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Quality of the OBCU-IXL communication network: the quality of the communication between the architectural components of the system causes delays in the journey through the route. For example, if the response message from IXL for the tram route request had not been delivered to the OBCU, the tram should still contact the OCC even in the event of a tram signal set to go ahead.
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Level of interference between the mobility of the trams and the surrounding environment: the mobility of a tram can be more or less influenced by normal city traffic. For example, a line with a path completely separate from normal car/pedestrian traffic will have less variable travel times compared to a scenario in which the tram line is shared with cars, with pedestrian crossings, etc. This type of analysis is aimed at understanding the impact of the variability of tram movement on the performance of the tram network.
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Temporary malfunction of a tram: the temporary malfunction (outage) of a single tram, for example, due to an accidental failure, can determine the congestion of part of the tramway. We intend to analyze the tramway capability to reabsorb any delays caused by unexpected and external events to the system.
Modeling the operational scenario
Parameter | Description | Value |
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Bound | The percentage of upper and lower bounds of the uniform distribution | variable: 1%, 3%, |
representing the time taken by the tram to travel an ordinary segment of the line: | 5%, 7%, 10%, | |
LowerBound=(ol/AverageVelocity)∗(1−Bound), and | and 15%. | |
UpperBound=(ol/AverageVelocity)∗(1+Bound). | ||
Epsilon | The maximum error on the tram position calculated by the LDS system (Accuracy) | variable: 1, 3, 5, and 10. |
TMax | The maximum time that a tram can wait in front of a tram signal | variable: 4, 8, 12, 16, |
before contacting the OCC | and 20. | |
p | Probability that a message does not arrive at its destination | variable: 0, 0.001, 0.003, |
0.005, and 0.01. | ||
av | The starting time interval between the trams | variable: 20 and 30 s. |
AverageVelocity | Average tram speed | 14.0 m/s |
RateIXL | IXL processing time in response to connection request and route request messages | 0.1 s |
RateNetwork | Time of transmission of a message from OBCU to IXL or from IXL to OBCU | 0.08 s |
Delay | The additional delay accumulated by a tram following the activation of the manual procedure | 120 s |
lentc | The length of Track Circuit | 45 m |
nl | The total number of segments | 569 |
nt | The total number of trams | 36 |
ol | The length of the ordinary segment | 50 m |
rrtotl | The distance between the Route Request Tag and the tram signal | 85 m |
pt | The time at the tram platform | 20 s |
Tram
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Segment with Connection Request Tag (RC), which represents a segment of the route where the tram detects the first Request Connection Virtual Tag on the OBCU and sends the Connection Request to IXL.
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Segment with Route Request Tag (RR), which represents a segment of the route where the tram detects the second Virtual Tag on the OBCU and sends the Route Request to IXL. The distance between the Route Request Tag and the tram signal is defined by the parameter rrtotl.
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Segment with Track Circuit Tag (TC), which represents the segment of the itinerary in which the tram occupies the virtual track circuits placed after the tram signal, which determine the occupation or not of the route. The length of this segment is defined by the LenTotalCircuits parameter.
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An ordinary segment that represents a segment which does not correspond to virtual tags, of length ol.
IXL
Network
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Connection request messages from OBCU to IXL
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Confirmation messages for connection creation from IXL to OBCU
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Route request messages from OBCU to IXL
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Confirmation route creation messages from IXL to OBCU
Basic interactions between the models
Stochastic activity network (SAN) models
Modeling methodology
The tram SAN model
Initialization
Ordinary Movement
Track Circuit Movement
The IXL SAN model
Connection Request
Route Request
The network SAN model
The composed SAN model
Analyzed scenario and analysis results
Definition of the topology of the line and fixed parameters
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The average Trip Time of each tram involved in the scenario has been computed using the C++ instruction LastActionTime available in the Möbius simulator. This instruction has access to the current simulation clock, and returns the simulation time at which the last activity fired. The metric has been computed as difference between the simulation time at which a tram reaches the end of the line, and the simulation time at which the same tram started its trip: return((Tram−>FinishTime−>Index(i)−>Mark()−Tram−>Schedule−>Index(i)−>Mark())/nt);
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The average number of times the driver had to call OCC and activate the manual procedure has been computed through the definition of an instant of time rate reward variable that returns the number of tokens accumulated in place nOCC of the Tram model: return((1.0∗Tram−>nOCC−>Mark())/nt);
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The average occupancy time metric for a given segment in a track has been computed as the average time a segment of a route is occupied by a tram. For each segment of a route, we defined an interval of time rate reward variable that accumulates a reward 1 for every unit of time the specific segment is occupied by a tram, 0 otherwise, e.g., for segment ID = 20 the rate reward is defined as: return(Tram−>Topology−>Index(20)−>Mark());.
Analysis based on positioning accuracy
Analysis by varying the time-out for the activation of the manual procedure
Analysis by varying the quality of the communication network
Analysis with different tramway mobility characteristics
Combination of previous analyses
Parameter | Best value | Worst value |
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TMax | 20 s | 4 s |
p | 0 | 0.01 |
Bound | 1% | 15% |
Epsilon | 1 m | 10 m |