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1
Availability and Performance Analysis of
Train-to-train Data Communication System
Haifeng Song, Eckehard Schnieder
Abstract—Communication-based train control (CBTC) system
is widely applied in the world. The primary functions are
carried out by the wireless communications, which implement
the communication between train and ground. However, this
kind of solution involves too many subsystems and interfaces,
which makes the group equipment complex and expensive to
maintain. What is more, once the ground control center or the
communication channel is out of service, the train must operate
in degraded modes, and more human factors will be involved. As
a result, the efficiency and safety of the train operation will be
affected. In order to significantly increase efficiency and safety,
train-to-train communication is proposed as a new solution for
railway signaling. Hence, the availability and performance analy-
sis of the direct train-to-train (T2T) data communication system
is essential. In this paper, the system structure is described,
and different parameters that can affect the performance of
the communication system are discussed. In order to evaluate
the system availability and performance, the stochastic Petri
nets (SPNs) are applied to formalize the communication system.
Numerical analysis is carried out with different parameters,
which consider both bit error and transmission rates. The results
show that method applied in this paper can be used to evaluate
the performance and availability of the T2T data communication
system.
Index Terms—Train-to-train communication, system availabil-
ity, train control, stochastic Petri nets, evaluation
I. INTRODUCTION
With the development of Communication-based train con-
trol (CBTC) system and moving block theory, the distance
between two trains is shortened. Train protection systems
require a safety distance, which is mainly dependent on the
train’s speed and time required to execute the braking action.
To implement the communication, there are two possible
communication channels: train-to-ground and train-to-train
(T2T). Traditionally, the train reports its location to the ground
and receives commands from the control center. However, T2T
communication is not applied widely in current train control
system solutions. Since there is no specification for T2T data
communication, relevant scientific research is carrying out in
recent years. For example, the Next Generation Train (NGT)
project funded by the German Aerospace Center DLR, which
is our project partner [5]; as well the Shift2Rail joint venture
project, in which we serve as the member of Scientific Com-
mittee. The benefits of applying T2T communication is that
Haifeng Song is with the School of Electronic and Information Engineering,
Beijing Jiaotong University, China; Institute for Traffic Safety and Automation
Engineering, Technische Universit¨
at Braunschweig, Braunschweig 38108,
Germany, email: h.song@tu-braunschweig.de, songhaifeng2011@gmail.com
Eckehard Schnieder is with the Institute for Traffic Safety and Automation
Engineering, Technische Universit¨
at Braunschweig, Braunschweig 38108,
Germany.
a low latency communication can safely reduce the distance
between two consecutive trains [5], and a more flexible train
control system can be proposed based on this new communica-
tion channel [6]. Moreover, a T2T communication can improve
the energy efficiency for the trains by synchronizing coupling
control [7]. In this paper, we define the T2T communication
system as a directly device-to-device without traversing the
Base Station (BS) or core network.
However, the T2T communication system is susceptible to
be disrupted by failures in computational and communication
components. For example, data corruption, untimely packet
delivery, and so on. Substantial research has been done on
the data communication system performance and optimization.
Authors of [8] present the results of the propagation loss of
T2T at 450 MHz in different measurement scenarios. The
measurements are carried out along a regional railway network
in Bavaria, Germany. In [9] propagation characteristics are
studied in the 5G millimeter-wave band in the Chinese High-
Speed Railway.
In engineering implementations, German Aerospace Center
introduces a train collision avoidance system (RCAS) based
on the T2T communication [10]; Alstom puts forward a
train-centric CBTC solution; our previous work [11] designs
and analyzes a train-centric communication-based train dis-
tance measurement system, which can carry out the distance
measurement independently; authors of [12] propose a new
movement authority based on vehicle-centric communication,
which permits the train to detect the condition of switches and
trains within a specific scope.
Given that system availability and performance analysis is
discussed at different stages, a reusable model, which can
easily be parameterized, is essential. Petri nets, which were
invented in August 1939 by Carl Adam Petri, have been used
widely by a lot of works [13], [14]. Generally, system activities
can be described as transitions among different system states.
In order to numerically analyze the reliability of a system,
Stochastic Petri nets (SPNs) have been applied. SPNs have
proven to be a useful formalism for real-time systems [15].
Different from high-level Petri nets, such as colored Petri
nets, SPNs can easily put forward the steady-state analysis; by
parameterizing the corresponding transitions with different fire
rates, numerical analysis of specific system activities can be
carried out. The software Π-Tool, which is developed by our
institute (iVA, Technische Universit¨
at Braunschweig), carries
out the formalization and analysis procedure. It offers the
token game, state space based analysis, steady-state analysis,
and so on.
By using SPNs, performance evaluation and availability
2
analysis are carried in cellular networks [16], dynamic systems
[17], IEEE 802.11 wireless LANs [18], and so on. In [16],
the dynamic packet arrivals performance of a device-to-device
(D2D) communication system is analyzed using SPNs. SPNs
are used to analyze the availability of a movement authority
system in [19] is the further example.
However, the above research mainly studies the propagation
or overall system availability of T2T communication-based
systems. Moreover, none of them carry out the availability and
performance analysis of the T2T data communication system.
The data communication system has significant changes com-
pared with existing solutions in current train control systems.
So far as we know, there are few pieces of research about the
reliability analysis of T2T communication system. The normal
operation of the system is dependent on a reliable, real-time
data communication system. To ensure the data communica-
tion is reliable, the T2T data communication system should
be evaluated before it is put into practical implementation.
In this paper, we provide a direct T2T data communication
system, and a procedure to evaluate the system’s availability
and performance. Based on our previous work, we provide
researcher the system structure of a T2T data communication
system, which can not only implement the data communication
but also provide the train to train distance measurement.
Various engineering related parameters are discussed, such as
message format, detection range, channel capability, and so on.
As a result, the researcher can be more targeted and efficiently
chose the best solution.
For the availability and performance analysis, SPNs models
are built. By modifying the fire rate of transitions, the SPNs
model can easily model error rates in different parts of packets
(i.e., header, command, data, and footer). In the models, the
interrelationship among the system availability, performance,
message format, bit error rate, and transmission rate are
discussed.
The remainder of the paper is organized as follows: after
briefly describe the structure of T2T data communication
system, the parameters that can affect the performance of the
communication system are discussed in Section II. Section III
presents the basic definition of SPNs, and describes how a
T2T data communication system is modeled. Some numerical
results are discussed in Section IV. Based on the results, the
system availability is evaluated. Additionally, the relationship
between transmission rates and date update interval is dis-
cussed. Finally, Section V concludes this paper and presents
future works.
II. T2T DATA COMMUNICATION SYSTEM
A. The structure of T2T data communication system
Based on the IEEE 1474 (Standard for Communications-
Based Train Control (CBTC) Performance and Functional
Requirements), the current CBTC includes automatic train
supervision (ATS) system, zone controller (ZC), computer
interlocking (CI), vehicle on board computer (VOBC), main-
tenance, and data communication system (DCS) network, as
shown in Fig. 1 (1). The ZC receives the route messages
from ATS, and formulates movement authority (MA) based
on the train’s location report and the condition of wayside
equipment. The VOBC calculates the braking profile based on
its own position and the MA transferred from ZC. However,
the existing CBTC system has the following defects:
•there are many interfaces between the various subsys-
tems, correspondingly the complexity of the system is
increased;
•due to more wayside equipment, the maintenance cost of
the system is relatively high;
•the train cannot be directly informed of the preceding
train’s information, which needs to be forwarded through
the ZC. Hence, the reaction time of the system is in-
creased.
ATS ZC CI Maintenance
DCS network
VOBC VOBC
Braking profile
ATS Maintenance
DCS network
VOBC
Braking profile
Wayside
equipment
Wayside
equipment
Station ATS
(1)
(2)
T2T VOBC T2T
Fig. 1: The structure of existing and T2X system
The basic structure of T2T data communication system is
shown in Fig. 1 (2). The functions of ZC and CI integrated
into trains and wayside equipment. ATS communicate directly
with VOBC and sends route information to VOBC. For the
trains, a new architecture T2T data communication system is
installed. Hence, a direct train-to-train communication channel
is available. It permits the following train can obtain the
information of the preceding train, and calculate its own MA
without the assistance of ZC. As a result, the communication
procedure is simplified.
Note that communication with a centralized controller is
needed because of position accuracy, especially when several
railway tracks are side-by-side. When there is an interlocking
mistake, trains shouldnt be surprised to see one train in
front coming from the opposite direction. The idea should be
investigated to be sure that T2T is collision free.
In this paper, we present readers a proposal of the T2T
data communication system structure as shown in Fig. 3.
There is a quite interesting application based on the T2T
data communication system. As an independent train-to-train
communication channel is available, and the transceivers are
installed in trains. Hence, it is possible to rely on the Time
of Arrival (TOA) to calculate the distance between two trains
3
PN Generator
Transmitter
Receiver
Correlation
Judgment
Phase Adjusting
Phase
Comparison
Distance
Calculation
Basic
Information BPSK
Carrier
Wave
Carrier
Wave
Transmitted
Signal
Received
Signal
Appropriate
Avoidance
Algorithm
Digital Map
Speed
Position
Direction
ID#
Length
ATP distance Algorithm Spread spectrum ranging distance Transceiver
Vehicle output
Train-to-Train communication data flow
Fig. 2: Data flow in the T2T communication system
during the data communication process. The system involves
four main sections/functions:
•ATP distance information, which includes speed, po-
sition, direction, train ID, length, can be obtained from
onboard equipment and involved in the T2T communica-
tion message.
•Algorithm is in charge of making reaction based on the
practical operation stage and train information [12].
•Spread spectrum ranging distance is calculated based
on the TOA method, more details can be found in our
previous publications [20].
•Transceiver implements the data communication proce-
dure, which is modeled analyzed by using SPNs in the
following sections.
This application is widely used in different scenarios. For
example, it can serve as a train collision avoidance system.
With T2T data communication system, the following train
can obtain the position and speed of the preceding train. It is
especially beneficial for the close proximity driving movement.
For example, when the tram operates in the visual inspection,
as shown in Fig. 3, and the system can prevent collision caused
by human errors and failure of signaling system [11].
Fig. 3: Tram operates in the visual inspection model
Since the signal is transferring in light speed (3 ×108m/s),
it is unavailable to capture the time delay of two signals
directly by hardware. However, based on the autocorrelation
characteristics of pseudo-random noise (PRN) code, the time
offset of the two sequences s(t) and r(t) can be easily captured
[21]. The autocorrelation of PRN code can be used to capture
the τ, and more details can be found in our former publication
[11]. This paper is focusing on the performance evaluation of
the T2T data communication system.
B. Main parameters of T2T data communication system
The primary task of T2T data communication system is
carrying out the data exchange. Before a specific engineering
solution is chosen to put forward the practical implementation,
the following parameters should be taken into consideration:
•message format,
•detection range,
•and channel capability.
In order to make a quantitative evaluation, here a description
of the message format is assumed to do the illustration.
The message format has a fixed length. The message format
consists of four sections, and its size is 146 bits, as shown
in Fig. 4. The Command and Data sections are framed by
the Header and Footer. The Command section is reserved
for train control activities, such as braking command, shorten
movement authority, and so on. The Data section includes
information about the train’s current speed, estimation of
braking distance, train’s length, and track number.
Header
8 bits
Command Data Footer
30 bits 100 bits 8 bits
0XAA Train ID 0XFF
Speed Braking distance Length Track
Fig. 4: Message format
For T2T data communication system, the detection range is
an important assessment target [12]. Especially, in this pro-
posal there is no relay, BS, and the core network. Hence, the
proper selection of a carrier wave is essential. The propagation
in free-space can be estimated based on the following model
[11]:
L[dB]=20log10 f[M H z ] + 20log10d[m]−27.55 (1)
where L[dB] (in decibels) is the free-space propagation,
f[M H z] is the frequency (in megahertz), and d[m] is the
distance (in meters) between the antennas.
Note that the available operational frequency/bandwidth
for wireless communication is usually under control by the
government/semi-government agencies, e.g., Federal Commu-
nications Commission (FCC) in the USA. The selection of
carrier wave will be depended on the channel availability. We
suggest that the bandwidth reserved as industrial, scientific and
medical (ISM) radio bands can be chosen.
However, the train is running in various scenarios, and extra
loss should be taken into account. Take the tunnel as a case
study, the propagation is mainly determined by the geometry
4
and material of tunnel, straight and curved lines. Hence, the
total propagation loss inside curved tunnels is given by [22]:
Lt un nel [dB]=LS(d[m])[dB]+LC[dB/100m]· d[m]
100 !(2)
where Lt un nel [dB] is the total propagation inside tunnels,
LC[dB/100m] is the typical value of the extra losses 1.
Based on the equation (1), it can be noticed that the
higher the frequency of carrier wave will cause a higher
propagation. With the summary conclusions in literature, the
finding is that a higher frequency wave in straight tunnels
has a better performance than it in curved line [23], [24].
Hence, based on the equation (2), the Lt un ne l [dB] of various
frequencies tend to be similar. Thus, which frequency is more
suitable for the T2T data communication and has the relatively
lower attenuation rate depends on the application scenarios,
frequency, etc. The frequency selection of carrier wave be-
longs to the engineering implementation level, which needs
specific mathematical calculation and software simulation to
be applied. Hence, the bit error rate under different operating
frequencies is not further discussed in this paper.
What is more, trains operate in different situations, such as
two trains can run on the same or opposite direction. The
data communication system makes different reaction based
on the specific movement authority (MA) of each train. The
details discussion of the different scenarios can be found in our
previous publication [12], which also presents an application
demo of MA+ on the Driver Machine Interface (DMI) of the
onboard equipment.
After the communication link is established, the channel ca-
pability limits the performance of the communication system.
Based on the Shannon-Hartley theorem, as shown in equation
(3), the channel capacity is related to the bandwidth of the
channel.
C=B·log2(1 + S
N) (3)
where Cis the channel capacity (in bits per second), B
is the bandwidth of the channel (in hertz), and S/Nis the
signal-to-noise ratio. Normally, if the carrier wave has a lower
frequency, the data transition rate is also slower. Hence, the
low data stream can be implemented by various carrier waves.
Besides engineering parameters, two of the critical perfor-
mance indicators of T2T data communication system are the
data update interval and system availability. If the communica-
tion link is not available or can not provide a correct message
when needed, there will be a significant adverse impact on the
performance of train operation.
III. MODELING OF T2T DATA COMMUNICATION SYSTEM
In practice, various descriptive means and software tools are
used to perform a RAMS analysis (Reliability, Availability,
Maintainability, Safety). However, using Petri net models, all
four aspects can be evaluated using only one model.
1In the measurements, 0.86.7 dB/100 m extra losses resulting from the
tunnel curve are observed in [22].
A. Petri nets modeling methodology
For the system availability and performance analysis, the
numerical results can intuitively indicate the system behavior.
The modeling methodology proposed in this paper emphasizes
the following four objectives [14]:
•Model building: the system logical structure has to be
transferred into a computerized model.
•Qualitative system properties: properties represent the
abstraction of characteristics, which is fundamental ob-
jectively determinable.
•Quantitative performance properties: quantitative per-
formance is physically and numerically deducted from
properties; based on the results, optimization and optimal
control can be carried out.
•Robustness: robustness results from measurements and
calculations of quantitative properties, which result in
values and units.
Petri nets method uses transitions and places to represent
the system’s actions and states, respectively. By using Petri
nets, the system states and activities can be transformed into a
computerized model. Different kind of Petri nets are available
to use, and one has to be picked as the suitable method. Take
the SPNs and Colored Petri nets (CPNs) as case studies, SPNs
are more appropriate to do the numerical and stochastic related
analysis, while CPNs can be applied to do a deeper functional
safety verification.
The basic symbols of stochastic Petri nets are shown in
Fig. 5. In Petri nets model, system states are represented
by places (P), which are drawn as circles and used to store
tokens. Tokens, which are drawn as dots, represent objects
or flags. Tokens can be created and consumed by the firing
of transitions. Transitions (T) are used to indicate activities
during the operation, and have an associated or random firing
rate (Λ). Places and transitions are connected by arcs (I,O),
which determined the enabling of transition and can have a
multiplicity. Normal arcs allow the modifications of states by
transferring tokens among places through transitions. Test arcs,
which are drawn as the dashed arrow, have the same function
as normal arcs but not lead to consuming the tokens. Inhibitor
arcs are drawn as arrows with circular heads, and can disable
transitions when places are occupied.
Symbol
Type
(1)
(2)
Place Place with
Token Transition
Meaning Activities during
the operation
Locations or states
(1) Normal arc allows the modifications
of s tates by transf erring tokens am ong
places through transitions.
(2) Tes t arc has the same functio n as
normal arc , but not leads to c onsuming
the tokens.
(3 ) I nhi bi tor ar c disables transitions
when enough tokens are in place
Normal arc, test arc, inhibitor arc
(3)
Fig. 5: Basic symbols of stochastic Petri nets
The overall system state after execution of enabled tran-
sitions is represented by marking (M). Hence, the formal
5
definition of an SPNs model is given by equation 4, which
has six-tuples: [25]
SP N ={P,T,I,O,M,Λ}(4)
•P={p1,p2, ..., pm}is the set of places;
•T={t1,t2, ... ,tn}is the set of transitions;
•I⊂P×Tis the set of input arcs;
•O⊂T×Pis the set of output arcs;
•Mis the markings;
•and Λ=(λ1, λ2, . .., λ n) is the array of firing rates
associated with transitions.
As shown in the Fig. 6, the transition is associated with a
deterministic time delay of 10 seconds. In Colored Petri nets
(CPNs), time is consumed as holding in a specific state after a
transition [26]. Different from the time factors treated in CPNs,
the time consumption in SPNs is reflected by time delay trough
transitions, which is the actual time interruption behavior of
a communication system. The firing action of a transition is
an atomic event, which is associated with a firing delay τ, as
shown in Fig. 6. If the transition is fired, a specific amount of
time τmust be elapsed in its input place. Hence, stochastic
Petri nets are chosen to model the T2T data communication
system.
Stochastic Petri nets
Colored Petri nets
Time attribution
20
10
0
Fig. 6: Time consumption in different Petri nets
The most interesting result of SPNs is the steady state. In
this paper, the following two performance parameters of SPNs
are selected to evaluate the T2T data communication system.
•probability of place occupancy;
•frequency of transition firing rate.
The reliability of a system (R) can be calculated by sum-
ming up the probabilities of all Mthat the specific place is
occupied.
R=X
Mi∈M
πi[Mi](5)
Xiπi[Mi]=1 (6)
where πi[Mi] denotes the steady-state probability of marking
Mi;Miis the marking that the system hods in a specific
condition (i.e. the system is working properly); Mis the all
available markings of a SPN model.
The frequency of transition firing rate (Fti) can be used to
check the average number of times that the transition tmfires
in a unit time. In numerical value it is given by:
Fti
=X
Mi∈E(Mi)
λi[Mi]πi[Mi](7)
where E(Mi)is the set of transition tienabled in Mi;λi[Mi]
means the firing rate of tiin Mi. By calculating the frequency
of firing of a transition, it can be applied to numerically
analyze the performance of a specific event. For example, the
data update frequency.
B. SPN model solutions of the train-to-train communication
system
In the data communication procedure, the following as-
sumptions are made:
•the downtime requires the system to send acknowledge
is negligible;
•the system is treated as unreliable after it continuously
received more than five uncompleted messages;
•as long as one bit of the message is wrong, a new message
is required.
Given that no robust modulation scheme or redundant error
correction strategy is taken into consideration, the aforemen-
tioned assumptions are rather harsh. In actual engineering
implementation, the T2T data communication system can have
a better performance.
The data update mainly depends on the integrity of mes-
sages, as shown in Fig. 7. One successful round data commu-
nication is that a full message packet can be received. Hence,
the buffer, which is used to count the number of uncompleted
messages, has four input transitions. These four transitions
H_loss,C_loss,D_loss, and F_loss indicate the losses
of sections Header,Command,Data, and Footer of the
message, respectively 2.
Fig. 7: Uncompleted message controller model
Based on the received messages, T2T data communication
system has a different status. Fig. 8 shows an SPN model of
the described the failure and recovery behavior. The places
corresponding meanings in SPN model are shown in Table
I. The right part model represents the data receiving process,
which can be interrupted by four aforementioned transitions
and then return to IDEL.
2The transition with a prefix PN. means it is a fusion one
6
Fig. 8: Failure and recovery model for T2T data communication channel
The initial state of T2T data communication system is
available, and the buffer is empty. When a com-
pleted message is received, the system state will maintain
available through transition update2. At the same time,
the message is updated. The buffer is reset through transi-
tion T2. Transition T1 is reserved for the time consumed by
hardware processing. When there are five tokens on the place
buffer, the system will be modified to “unavailable” through
the transition fail. If there is still no completed message
receiving, the token will hold on the place unavailable
through the transition T3. Once a completed message is ob-
tained, the system state will be changed from unavailable
to available through transition update1.
TABLE I: Places corresponding meanings in SPN model
Items Type Meaning
buffer Place Failure counter
successful Place Continually successful
available Place The system is available
unavailable Place The system is unavailable
completed! Place A completed message is received
IDLE Place Initial state
The data receiving process model starts from IDLE, as
shown in Fig. 9. Places with suffixes “?” and “!” represent
the message section loss and receive detection, respectively,
which is assumed to be negligible. For each section of the
message, it has three transitions. Take the Header section as
an example. The transition H_time represents time needed to
receive a full Header section; transitions H_success and
H_loss model the probabilities of successful reception and
transmission error, respectively.
IV. NUMERICAL ANALYSIS OF T2T DATA
COMMUNICATION SYSTEM
Combining the aforementioned three models, the overall
SPN model of the T2T data communication is shown in Fig.
10. In this section, the model will be parameterized with values
Fig. 9: Date receiving process model
to do the numerical simulation. The time delay and probability
of a transition depend on the transmission rate and bit error
rate.
A. Communication availability
There are different transmission bit rates (Rb) for the radio
modems. For an mbits serial data, the time consumed (Tm)
to send it is given by:
Tm=
m
Rb
(8)
In digital transmission, due to transmission channel noise,
interference, attenuation, there is a probability that the data
can not be received correctly. The bit error rate (BER) is the
number of bit errors per unit time. The BER is also affected
by the modulation scheme, signal energy, and redundant error
correction codes [19]. Here BER is chosen as 10−3, which is
7
Fig. 10: Petri nets model
relatively more stringent value, and its engineering risk is very
small and the feasibility is very high. Hence, for the mbits
serial data, the probabilities of receiving correctly (Pr) and
transmission error (Pl) are given by equations (9) and (10):
Pr=(1 −BE R)m(9)
Pl=1−(1 −BE R)m(10)
take the Header section as an example, we can calculate the
necessary parameters Tm,Pr, and Plfor transitions H_time,
H_success, and H_loss, respectively. Here we set the
transmission rate Rb=9600 bit/s. Hence,
Tm=
m
Rb
=
8
9600 ≈0.833 ms (11)
Pr=(1 −BE R)m≈9.92 ×10−3(12)
Pl≈7.97 ×10−3(13)
π−Tool provides Markovian analysis and Monte Carlo Sim-
ulation. The markovian analysis is possible only for nets con-
taining immediate transitions and transitions with exponential
distributions. Hence, in this paper Monte Carlo Simulation is
applied. For each simulation, the max samples are set to 1050.
In order to obtain the performance of T2T data communication
system under various technology solutions, different BER and
transmission rates are applied in the model.
Given that the system is treated as “unavailable” when it
continuously received more than five uncompleted messages,
which has been mentioned in section III-B, the modification
of BER will have effects on the system availability. The BER
is usually expressed as an equation of carrier-to-noise ratio, as
shown in equation (14):
BE R =
1
2er f c
rEb
N0
(14)
er f c (x)=
2
√π∞
x
e−η2dη(15)
where Eb
N0
is the energy per bit to noise power spectral density
ratio. By calculating the probability of place available
occupancy, the result of T2T data communication availability
under different BER is shown in Fig. 11. As shown in this
figure, given BER <3×10−3, the system availability is greater
than 99.44%. This means that a lower BER results in higher
system availability.
10−5 10−4 10−3 10−2 10−1 100
0
0.2
0.4
0.6
0.8
1
X: 0.003
Y: 0.9944
Bit error rate (BER)
System availability
Fig. 11: T2T data communication availability under different
BER
8
Another key performance indicator is the data update inter-
val, which can be evaluated by calculating the frequency of
transition firing rate. In the simulation, we choose five different
transmission rates 9600, 19200, 38400, 57600, and 115200
bit/s. The data update intervals under different transmission
rates are shown in Fig. 12. The simulation results show that
the update interval decreases with the increase of transmission
rate. This is because the update frequency is highly dependent
on the time consumed by receiving a completed message. It
is clear that a higher update frequency means the system has
a lower probability of triggering unnecessary braking actions,
which caused by communication interruption [20]. However, it
should be noted that the higher communication rate normally
requires a wide bandwidth. As a result, a higher frequency
carrier wave is needed. Based on the discussion in section II,
the benefits will be nullified by a greater propagation. Hence,
the practical solution can be modified based on the targets of
system availability, update interval, communication range, and
so on.
0 2 4 6 8 10 12
x 104
0
5
10
15
20
25
Transmission rate (bit/s)
Update interval (ms)
Simulate results
Fitting line
Fig. 12: Transmission rates impact on the data update interval
B. Communication efficiency
Take the package transmission delay as a case study. The
transmission rate and B E R are 9600 bit/s and 3 ×10−3,
respectively. As shown in Fig. 11 and 12, the update interval
(Tu) and system availability (Am) are 16.84 ms and 0.9944,
respectively. Hence, to transfer a 128 bytes information, at
least seven messages (k) need to be transferred successfully.
The overall availability (Aal l ) and time delay (Tdela y ) are
given:
Aal l =Ak
m(16)
Tdel ay =k∗Tu(17)
hence, Aal l =0.9614 and Tdel a y =117.8 ms.
Following the specification, the time delay, which follows
an exponential distribution, in actual Global System for Mo-
bile Communications Railway (GSM-R) is assumed to be
memoryless. What is more, the specification requires it to be
smaller than 500 ms in 99% of all cases when transferring a
128 bytes information with an 8000 bit/s [17]. Based on the
definitions of density ( f(x) ) and distribution (F(x)) functions
of the exponential distribution:
f(x)=λe−λx(18)
F(x)=1−e−λx(19)
The time delay comparison of T2T communication and
GSM-R is shown in Fig. 13, which indicates that the T2T
data communication system can be more efficient than the
current train-to-ground communication strategy when both of
them hold similar parameters.
100101102103
Time delay (ms)
0
0.2
0.4
0.6
0.8
1
Cumulative distribution function
T2T
GSM-R
Fig. 13: Time delay distribution of T2T and GSM-R
C. Sensitivity analysis
With a specific transmission rate, the probability of system
reliability will tend to a stable value with time increasing.
Hence, there are two parameters which influence the results,
and they are:
•the size of design packet;
•and the number of consecutive uncompleted messages
(n).
the selection of these two numbers will significantly affect the
calculated system availability/reliability. Hence, the sensitivity
analysis of the output is carried out by using one-at-a-time
(OAT/OFAT) technology, which moves one input variable
while keeping others at the initial values. The length of
Command (LC) and Data (LD) sections are set as:
LC+LD=LT(20)
where LT∈{200,260},LC∈[60,160]⊂N; for consecutive
uncompleted messages n∈{3,4,5,6,7}. By modifying Tm,
Pr, and Plof corresponding transitions in Fig. 10, the system
availabilities can be calculated as shown in Fig. 14.
The results indicate that the data length LTwill affect the
availability, as more data needs to be transferred means more
probability to cause the error. What is more, with a fixed
packet length the availability will be the highest when LCand
LDhave the same bit length. However, the system availability
is not sensitive to the number of consecutive uncompleted
messages (n) when n≥4. A proper selection of ncan not only
increase the system’s robustness but also reduce the frequency
of triggering unnecessary false warnings.
9
50 60 70 80 90 100 110 120 130 140 150
Length of the Command section
0.97
0.975
0.98
0.985
0.99
0.995
1
System availability
Total length of the Command and Data sections =200 bits
90 95 100 105
0.996
0.997
0.998
0.999
1
n=3
n=4
n=5
n=6
n=7
60 70 80 90 100 110 120 130 140 150 160
Length of the Command section
0.93
0.94
0.95
0.96
0.97
0.98
System availability
Total length of the Command and Data sections =260 bits
120 125 130 135
0.965
0.97
0.975
n=3
n=4
n=5
n=6
n=7
Fig. 14: System availability with different data format and
length
V. CONCLUSION AND FUTURE WORKS
The current CBTC systems are based on the train-to-ground
communication, which suffer from having too many inter-
faces and subsystems. With involving the T2T communication
channel, the following train can obtain the information of
preceding train, and calculate its own MA with the assistance
of ZC. What is more, based on the TOA method the train to
train distance can be estimated during the data communication
procedure. It is clear that T2T communication will contribute
benefits to the next generation CBTC system.
The paper presents the structure of the T2T data communi-
cation system, and its potential implementation for the train to
train distance measurement. For engineering implementation,
three main parameters are discussed. Stochastic Petri nets
are used to model and evaluate the system availability and
performance. Numerical results are presented under different
parameters, which consider both bit error and transmission
rates. The simulation results provide intercorrelations among
system availability, update interval, communication range, and
so on.
The limitation of this paper is that there is no practical
experiment data to validate the simulation results. Hence, in
the future we are going to build a physical platform, which
will involve actual channel simulator, to obtain the actual
data, and compare the simulation results with the actual data.
In the next step, T2T data communication system will be
merged into the collaborative train control system. As one
of a common design criterion in control systems, survival
time, the time that an application consuming a communication
service may continue without an anticipated message, will be
further discussed and modeled system. For the model-based
analysis, an extended SPN model, which involves the train
control functions, will be built. What is more, a more complex
train operation scenario will be taken into consideration. For
example, when 2 trains running on the same or opposite
direction, the response time (or survival time) would be of
significant difference. By considering this attribute in the
design of numerical analysis, the discussion will be much more
practical for the practitioners/train operators.
ACKNOWLEDGMENT
I hereby present my gratitude to the iVA, Technische Uni-
versit¨
at Braunschweig, Germany. This work is supported by
the “Fundamental Research Funds for the Central Universitie”
(2019RC003).
We would also like to thank the Editors and all anonymous
reviewers for their valuable comments.
REFERENCES
[1] G. Cavone, M. Dotoli, and C. Seatzu, “A survey on petri net models
for freight logistics and transportation systems,” IEEE Transactions on
Intelligent Transportation Systems, vol. 19, no. 6, pp. 1795–1813, jun
2018.
[2] S. Fathi-Kazerooni, Y. Kaymak, R. Rojas-Cessa, J. Feng, N. Ansari,
M. Zhou, and T. Zhang, “Optimal positioning of ground base stations
in free-space optical communications for high-speed trains,” IEEE
Transactions on Intelligent Transportation Systems, vol. 19, no. 6, pp.
1940–1949, jun 2018.
[3] M. Taheri, N. Ansari, J. Feng, R. Rojas-Cessa, and M. Zhou, “Provi-
sioning internet access using FSO in high-speed rail networks,” IEEE
Network, vol. 31, no. 4, pp. 96–101, jul 2017.
[4] R. Robidoux, H. Xu, L. Xing, and M. Zhou, “Automated modeling
of dynamic reliability block diagrams using colored petri nets,” IEEE
Transactions on Systems, Man, and Cybernetics - Part A: Systems and
Humans, vol. 40, no. 2, pp. 337–351, mar 2010.
[5] A. Lehner, T. Strang, and P. Unterhuber, “Train-to-train propagation at
450 mhz,” in Antennas and Propagation (EUCAP), 2017 11th European
Conference on. IEEE, 2017, pp. 2875–2879.
[6] B. Ai, K. Guan, M. Rupp, T. Kurner, X. Cheng, X.-F. Yin, Q. Wang, G.-
Y. Ma, Y. Li, L. Xiong et al., “Future railway services-oriented mobile
communications network,” IEEE Communications Magazine, vol. 53,
no. 10, pp. 78–85, 2015.
[7] P. Fraga-Lamas, T. M. Fern´
andez-Caram´
es, and L. Castedo, “Towards
the internet of smart trains: a review on industrial iot-connected rail-
ways,” Sensors, vol. 17, no. 6, p. 1457, 2017.
[8] A. Lehner, C. R. Garc´
ıa, and T. Strang, “On the performance of tetra dmo
short data service in railway vanets,” Wireless personal communications,
vol. 69, no. 4, pp. 1647–1669, 2013.
[9] D. He, B. Ai, K. Guan, Z. Zhong, B. Hui, J. Kim, H. Chung, and I. Kim,
“Channel measurement, simulation, and analysis for high-speed railway
communications in 5g millimeter-wave band,” IEEE Transactions on
Intelligent Transportation Systems, 2017.
[10] A. Lehner, T. Strang, and P. Unterhuber, “Direct train-to-train com-
munications at low uhf frequencies,” IET Microwaves, Antennas &
Propagation, vol. 12, no. 4, pp. 486–491, 2017.
[11] H. Song and E. Schnieder, “Development and validation of a distance
measurement system in metro lines,” IEEE Transactions on Intelligent
Transportation Systems, 2018.
[12] T. Shen and H. Song, “A new movement authority based on vehicle-
centric communication,” Wireless Communications and Mobile Com-
puting, vol. 2018, 2018.
[13] C. Lijie, T. Tao, Z. Xianqiong, and E. Schnieder, “Verification of the
safety communication protocol in train control system using colored
petri net,” Reliability engineering & system safety, vol. 100, pp. 8–18,
2012.
10
[14] H. Song, “Development and analysis of a train-centric distance mea-
surement system by means of colored petri nets,” Ph.D. dissertation,
Technische Universit¨
at Braunschweig, 2018.
[15] A. Zimmermann and G. Hommel, “A train control system case study
in model-based real time system design,” in Parallel and Distributed
Processing Symposium, 2003. Proceedings. International. IEEE, 2003,
pp. 8–pp.
[16] L. Lei, Y. Zhang, X. Shen, C. Lin, and Z. Zhong, “Performance analysis
of device-to-device communications with dynamic interference using
stochastic petri nets,” IEEE transactions on wireless communications,
vol. 12, no. 12, pp. 6121–6141, 2013.
[17] A. Zimmermann, “Reliability modelling and evaluation of dynamic
systems with stochastic petri nets (tutorial),” in Proceedings of the 7th
International Conference on Performance Evaluation Methodologies and
Tools. ICST (Institute for Computer Sciences, Social-Informatics and
Telecommunications Engineering), 2013, pp. 324–327.
[18] A. Heindl and R. German, “Performance modeling of ieee 802.11 wire-
less lans with stochastic petri nets,” Performance Evaluation, vol. 44,
no. 1-4, pp. 139–164, 2001.
[19] H. Song, T. Shen, and W. Wang, “Train-centric communication-based
close proximity driving train movement authority system,” IEEE Intelli-
gent Transportation Systems Magazine, vol. 10, no. 3, pp. 22–34, 2018.
[20] H. Song, J. Liu, and E. Schnieder, “Validation, verification and eval-
uation of a train to train distance measurement system by means of
colored petri nets,” Reliability Engineering & System Safety, vol. 164,
pp. 10–23, 2017.
[21] X. Mao, D. Inoue, S. Kato, and M. Kagami, “Amplitude-modulated
laser radar for range and speed measurement in car applications,” IEEE
Transactions on Intelligent Transportation Systems, vol. 13, no. 1, pp.
408–413, 2012.
[22] B. Ai, K. Guan, Z. Zhong, C. F. L´
opez, L. Zhang, C. Briso-Rodr´
ıguez,
and R. He, “Measurement and analysis of extra propagation loss of
tunnel curve,” IEEE Transactions on Vehicular Technology, vol. 65,
no. 4, pp. 1847–1858, 2016.
[23] K. Guan, B. Ai, Z. Zhong, C. F. L´
opez, L. Zhang, C. Briso-Rodr´
ıguez,
A. Hrovat, B. Zhang, R. He, and T. Tang, “Measurements and analysis
of large-scale fading characteristics in curved subway tunnels at 920
mhz, 2400 mhz, and 5705 mhz,” IEEE Transactions on Intelligent
Transportation Systems, vol. 16, no. 5, pp. 2393–2405, 2015.
[24] K. Guan, Z. Zhong, B. Ai, R. He, B. Chen, Y. Li, and C. Briso-
Rodriguez, “Complete propagation model in tunnels,” IEEE Antennas
and Wireless Propagation Letters, vol. 12, pp. 741–744, 2013.
[25] M. A. Marsan, “Stochastic petri nets: an elementary introduction,” in
European Workshop on Applications and Theory in Petri Nets. Springer,
1988, pp. 1–29.
[26] H. Song and E. Schnieder, “Modeling of railway system maintenance
and availability by means of colored petri nets,” Eksploatacja i Nieza-
wodnosc - Maintenance and Reliability, vol. 20, no. 2, pp. 236–243,
mar 2018.
Haifeng Song received his B.Sc. degree in 2011
from Beijing Jiaotong University (China), the Mas-
ter degree in Traffic Information Engineering and
Control from the same university in 2014. He re-
ceived his Dr.-Ing degree from Technische Univer-
sit¨
at Braunschweig, Germany in 2018. He has joined
the Institute for Traffic Safety and Automation
Engineering, Technische Universit¨
at Braunschweig
(Germany) as a visiting scientist since 2014. He
is with the School of Electronic and Information
Engineering, Beijing Jiaotong University, China.
He specializes in safety and security of transportation systems, his current
research interests include railway control system, formal method, intelligent
control, and transportation modeling. He has been involved in several national
and international research projects dealing with system safety and system
evaluation. He is a member of the China Institute of Communications and a
reviewer for international journals.
Eckehard Schnieder received his diploma degree in
electrical engineering with a major in control engi-
neering and his doctoral degree from the Technische
Universit¨
at Braunschweig, Braunschweig, Germany,
in 1972 and 1978, respectively. From 1979 to 1989,
he was the Division Manager for new transport sys-
tems at Siemens. In 1989, he was offered a Profes-
sorship for Control and Automation Engineering at
TU Braunschweig. Since 2002, he has been the Head
of the Institute for Traffic Safety and Automation
Engineering, TU Braunschweig.
Dr. Schnieder directed the first formal modeling of the European Railway
Control System, the basic research on satellite-assisted railway location
systems, and other German and European projects for traffic safety and
automation in cooperation with operators, suppliers, and safety authorities. He
was offered several professorships, e.g., as the Dean of Volkswagen AutoUni
and, recently, as a Visiting Professor of Beijing Jiaotong University in China.
In 1998, he received the Carl Adam Petri Award of the Society of Design
and Process Science. In 2005, he received the Doctor Honoris Causa from
Todor Kableshkov University of Transportation in Sofia, Bulgaria followed
by another Doctor Honoris Causa from the University of Zilina in Zilina,
Slovakia and the Otto von Guericke University Magdeburg in Magdeburg,
Germany, both in 2010, honoring his achievements both in the educational
and the scientific sector within the cooperation between the universities. He
is currently the spokesman of the German Academy of Technical Science.
