238 ◾ Advances in Communications-Based Train Control Systems
Front train
Current train
0 500 1000 1500 2000
2500
0
10
20
30
40
50
60
70
Distance (m)
Velocity (km/h)
Figure10.11 Train travel trajectory under the proposed cognitive control policy
(the headway is 15s).
0 500 1000 1500 2000
2500
0
10
20
30
40
50
60
70
Distance (m)
Velocity (km/h)
Front train
Current train
Figure10.12 Train travel trajectory under the proposed cognitive control policy
(the headway is 90s).
Cognitive Control for CBTC Systems ◾ 239
0 500 1000 1500 2000
2500
0
10
20
30
40
50
60
70
Distance (m)
Velocity (km/h)
Front train
Current train
Figure10.13 Train travel trajectory under the SMDP policy (the headway is 90s).
0 500 1000 1500 2000
2500
0
10
20
30
40
50
60
70
Distance (m)
Velocity (km/h)
Front train
Current train
Figure10.14 Train travel trajectory under the greedy policy (the headway is 90s).
240 ◾ Advances in Communications-Based Train Control Systems
we can see that the eects caused on the communication latency are less severe
when the headway is 90 s, compared to the case when the headway is 15 s.
Nevertheless, the proposed cognitive control approach can improve the perfor-
mance of train operation in both cases, compared to the existing SMDP policy
and greedy policy.
e hando performance is presented in Figure 10.15, where the
x
-axis is the
location of the train and the
y
-axis is the value of hando latency. It is obvious that
the proposed cognitive control policy can bring less hando delay, which is less
than the communication cycle
0.2s
. By contrast, the hando performance under
the greedy policy and the SMDP is worse, where the hando delay could be more
than
1s
. In addition, there are less ping-pong hando happening under the cog-
nitive control policy. erefore, the hando performance is improved due to the
application of the cognitive control approach.
As CBTC systems are safety critical, the reliability of train–ground commu-
nication is an important performance parameter. Hence, according to the hand-
o latency, we calculate the failure rate [30] of the train–ground communication
subsystem. Failure rate describes the frequency with which an engineered system
or component fails and is important in reliability engineering. Figure 10.16 shows
the failure rate with time. e cognitive control approach can keep the failure rate
less than
10
6−
, which means that the reliability is largely increased. Considering the
0.0
0.1
0.2
Handoff latency (s)
Cognitive control policy
0 500 1000 1500 2000
2500
0
1
2
Distance (m)
0 500 1000 1500 2000
2500
Distance (m)
0 500 1000 1500 2000
2500
Distance (m)
Handoff latency (s)
0
1
2
Handoff latency (s)
SMDP policy
Greedy policy
Figure10.15 Handoff latency under different policies.
Cognitive Control for CBTC Systems ◾ 241
frequency of hando and the value of hando latency, wecan derive the availability
of the train–ground communication subsystem as follows[31]:
A
av
MTTF
MTTF MTTR
=
+
(10.30)
where:
MTTF (mean time to failure) denotes the mean time between adjacent handos
MTTR (mean time to repair) denotes the mean value of hando latency
e availability of dierent policies is shown in Table 10.2.
e cognitive control approach can get the highest availability
0.9978
. In other
words, the unavailability under the cognitive control policy can be kept at an order
of magnitude
10
3−
, whereas it is
10
2
−
under the SMDP policy and
10
1
−
under the
greedy policy. We can conclude that the application of cognitive control can get
signicantly better train control performance, improved hando performance, and
reliability of CBTC systems compared with other policies.
Figure 10.17 shows the learning procedure in the proposed cognitive control
approach. Specically, the dierence between adjacent operation policies versus the
steps of Q-learning is shown in Figure 10.17. At the beginning, the learned policies
0 50 100 15
0
Time (s)
Failure rate
Cognitive control policy
SMDP policy
Greedy policy
10
−3
10
−4
10
−5
10
−6
10
−7
Figure10.16 Train–ground failure rate under different policies.
242 ◾ Advances in Communications-Based Train Control Systems
at adjacent steps are far from the optimal one, and they are quite dierent. After
about 180 steps, the dierence between adjacent policies is zero, which means that
the learned policy converges to the optimal one.
10.6 Conclusion
In this chapter, we presented a cognitive control approach to CBTC systems to
improve the train control performance, considering both train–ground commu-
nication and train control. In the proposed cognitive control approach, we intro-
duced information gap, which is dened as the dierence between the derived state
of the front train and the actual state of the front train in CBTC systems. Linear
quadratic cost for the train control performance in CBTC systems was considered
in the performance measure. In addition, information gap was formulated in the
cost function of cognitive control to quantitatively describe the eects of train–
ground communication on train control performance. Based on the cognitive con-
trol formulation, RL was used to get the optimal policy. Moreover, the wireless
channel was modeled as FSMCs with multiple state transition probability matrices,
Table 10.2 Parameters Used in the Simulations
Emergency brake deceleration 1.2m/s
2
Service brake deceleration 0.8m/s
2
Tracking acceleration 0.8m/s
2
The response time of the train 0.4s
The running resistance per unit mass 0.02m/s
2
The limited line speed 80km/h
aSifsTime
10μs
aSlotTime
9μs
anACKTime
1μs
aDifsTime aSifsTime+2aSlotTime
CW
min
16
CW
max
1024
aPacketLength 400bytes
aPropTime 1ms
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