140 ◾ Advances in Communications-Based Train Control Systems
process, the moving nodes communicate with the wayside nodes. e nodes’ mov-
ing speed is controlled by the train control model, and the communication latency
is determined by the communication model in Section 7.4.3. Each node looks up
the policy table to nd out the optimal action corresponding to its current state,
and then executes action. Static variables are collected in the simulations to obtain
the train control performance
H
2
norm, train travel trajectory, hando policy, and
the trip time.
We compare the performance of our proposed system with three other schemes.
e rst scheme is an existing scheme [31], where CoMP is not used. e train MT
makes hando decisions based on the immediate reward, and the optimal guid-
ance trajectory is not recalculated when the speed deviation occurs. We denote this
scheme as the existing scheme. For the second scheme, CoMP is used in the system,
but the SMDP model is not used. Instead, the decision maker makes hando deci-
sions by the reward derived from the current channel state. e optimal guidance
trajectory is not recalculated in this scheme. We denote this scheme as the CoMP-
based greedy scheme w/o updated trajectory. For the third scheme, CoMP is used in
the system, and the SMDP model is used to calculate the hando decision policy.
Unlike the proposed scheme, the optimal guidance trajectory is not recalculated in
this scheme. We denote this scheme as the CoMP-based scheme w/o updated trajec-
tory, and our proposed scheme as the proposed scheme.
7.6.1 Train Control Performance Improvement
We rst compare the train control performance
H
2
norm in dierent schemes.
Recall that the square root of the linear quadratic cost performance measure in
Equation7.4 is equivalent to the
H
2
norm. We refer to the train control perfor-
mance measure as the
H
2
norm due to this equivalence. In this simulation scenario,
the three trains depart from a station successively with interval
T
interval
s
=
16 and the
deceleration
α
that denes the ATP service braking curve is set to be
1.2 /
2
ms
. As we
can see from Figure 7.6, the existing scheme gives the highest
H
2
norm compared to
the other three schemes. is is because the existing scheme does not use CoMP in
the system, which can signicantly improve train control performance. Moreover,
it does not consider the dynamic transitions of wireless channels in CBTC systems,
which is very important information for the train Station Adapter (SA) to make
optimal hando decisions to get the optimal performance.
By contrast, the other three schemes can have signicant performance improve-
ment due to the adoption of CoMP. e two SMDP-based schemes give better
performance compared with the greedy scheme. is is because the SMDP model
considers the dynamic transitions of wireless channels in CBTC systems. e direct
optimization objective of the SMDP model is to minimize the linear quadratic cost
of train control. Our proposed scheme gives the lowest
H
2
norm. is is because
the newly calculated guidance trajectory takes full consideration of the tracking
Novel Communications-Based Train Control System ◾ 141
error caused by hando latency. As a result, it reduces the tracking error, which
further improves the
H
2
norm performance.
e train travel trajectories in our proposed scheme and the existing scheme are
shown in Figures 7.7 and 7.8, respectively. e rst, second, and third departed trains
are denoted as Train 0, Train 1, and Train 2, respectively, in our simulations. We
assume that the rst departed train travels without obstacles because there are no
trains traveling in front. As we can observe from the gure, compared with the exist-
ing scheme, the guidance trajectory in our proposed scheme for Train 1 and Train 2 is
very close to Train 0. is is because the guidance trajectory is frequently recalculated
to make up for the extra travel time caused by communication latency in this scheme.
e gure also illustrates that, given the same train departure time interval, the travel
trajectories of Train 1 and Train 2 in our proposed scheme are very close to the origi-
nal optimized guidance trajectory. Although for the existing scheme, these two trains
go through many unnecessary accelerations and decelerations during the train trip.
is is because our scheme explicitly optimizes the train control performance. e
service brake time caused by ATP subsystem is decreased to a minimum under the
proposed optimal scheme, which helps mitigate the tracking errors.
Figure 7.9 shows the error between the real travel time and the preset trip time
for Train 2 in dierent schemes. As shown in the gure, the travel time error is
signicantly increased when the trip time increases for the existing scheme and
0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45
0.50
50
60
70
80
90
100
110
120
Handoff extra delay (s)
H
2
norm
Existing scheme
CoMP-based greedy scheme w/o updated trajectory
CoMP-based SMDP scheme w/o updated trajectory
Proposed scheme
Figure7.6 Control performance
H
2
norm in different schemes.
142 ◾ Advances in Communications-Based Train Control Systems
0 500 1000 1500 2000 2500 3000 3500
4000
0
10
20
30
Train velocity
(m/s)
Train 0 guidance trajectory
Train 0 travel trajectory
Distance (m)
0 500 1000 1500 2000 2500 3000 3500
4000
0
10
20
30
Train velocity
(m/s)
Train 1 guidance trajectory
Train 1 travel trajectory
Distance (m)
0 500 1000 1500 2000 2500 3000 3500
4000
0
10
20
30
Train velocity
(m/s)
Train 2 guidance trajectory
Train 2 travel trajectory
Distance (m)
Figure7.8 Train travel trajectory in the existing CBTC system.
0 500 1000 1500 2000 2500 3000 350
04000
0
10
20
30
Train velocity
(m/s)
Train 0 guidance trajectory
Train 0 travel trajectory
Distance (m)
0 500 1000 1500 2000 2500 3000 350
04000
0
10
20
30
Train velocity
(m/s)
Distance (m)
0 500 1000 1500 2000 2500 3000 350
04000
0
10
20
30
Train velocity
(m/s)
Distance (m)
Train 1 guidance trajectory
Train 1 travel trajectory
Train 2 guidance trajectory
Train 2 travel trajectory
Figure7.7 Train travel trajectory in the proposed CBTC system with CoMP.
Novel Communications-Based Train Control System ◾ 143
the other two schemes. is travel time error severely aects the rail transit load
capacity. By contrast, the train travel time in our proposed scheme is very close to
the preset trip time. It successfully mitigates the wireless communication impacts
on CBTC performance without decreasing the utilization of railway network
infrastructure.
7.6.2 Handoff Performance Improvement
Figure 7.10 shows example hando policies when three dierent schemes are used.
In this gure, the Y axis represents the action.
Action
= 1
means the MT com-
municates with
BS1
and CoMP is not used;
Action = 2
means the MT commu-
nicates with
BS
2
and CoMP is not used; Action
= 3
means the MT is working in
the CoMP mode, and it communicates with the cluster where BS1 and BS2 are
included.
As we can observe from the gure, there are only actions 1 and 3 in the exist-
ing CBTC scheme, where CoMP is not adopted. More importantly, there are
more than one hando events when the train travels across the boundary between
two BSs, which is called ping-pong hando. is is because the hando decision
Existing scheme
CoMP-based greedy scheme w/o updated trajectory
CoMP-based SMDP scheme w/o updated trajectory
Proposed scheme
164 166 168 170 172 174 176 178
180
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Preset trip time (s)
Trip time error (s)
Figure7.9 Train travel time error in different schemes.
144 ◾ Advances in Communications-Based Train Control Systems
policy in the existing scheme makes hando decisions based on the current chan-
nel information and does not consider the dynamic transitions of wireless chan-
nels in CBTC systems, which is very important information to make hando
decisions.
By contrast, three actions all appear in the schemes when CoMP is adopted.
e ping-pong hando happens in the CoMP-based greedy scheme w/o updated
trajectory. is is because this scheme does not consider the dynamic transitions
of wireless channels in CBTC systems. In our proposed scheme, there is only a
small portion of the time when CoMP is not used. is is because the CoMP
mode performs better in most of the time. When the MT is close to a base station,
CoMP mode is not adopted. is is because the received signal is already good
enough under this circumstance. e lost and/or outdated channel state informa-
tion due to constrained backhaul network will degrade the performance. We can
also observe that a hando is performed by switching action from 1to3, and then
switching from
3
to
2
. ere are only two action switches. In other words, there is
no ping-pong hando in the proposed scheme. is is because the SMDP model is
used in the proposed scheme to calculate the hando decision policy. is model
takes full consideration of the dynamic transitions of wireless channels in CBTC
systems.
Following [32], we take service discontinuity as another performance metric to
compare the proposed scheme with other schemes. Figure 7.11 shows the average
service discontinuity time duration in dierent schemes. We can observe that the
0
5 10 15 20 25 30 35 40
45
1
2
3
Time (s)
Action
0 51015202530354
045
1
2
3
Time (s)
Action
0 51015202530354
045
Time (s)
Action
Proposed scheme
Existing scheme
CoMP-based greedy scheme w/o updated
trajectory
1
2
Figure7.10 Handoff policies in different schemes.
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