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Chapter 7. openETCS Meta Model
and the only final state is marked with doubled circled dot
F ≡ {s END } (7.43)
There are seven transitions, which also corresponds to the number of inputs:
n i = 7 (7.44)
The transition between the initial state, drawn by the black spot, is not counted because it
does not have any condition / input and is always passed in the beginning. The conditions and
inputs are numbered as follows:
Transition Condition Input, Priority
Starting −→ Sleeping c 1 i 1 , p 1 = 0
Starting −→ Running c 2 i 2 , p 2 = 1
Sleeping −→ Running c 3 i 3 , p 3 = 0
Running −→ Sleeping c 4 i 4 , p 4 = 0
Sleeping −→ Terminating c 5 i 5 , p 5 = 1
Running −→ Terminating c 6 i 6 , p 6 = 1
Terminating −→ END c 7 i 7 , p 7 = 0
Accordingly, the transition vector v(s) can be build for each state s:
s =
⎡
⎢
⎣
s Starting
s Sleeping
s Running
s Terminating
s END
⎤
⎥
⎦
(7.45)
v(s Starting ) T = [1; i 1,k ; 2i 2,k ; 0; 0] (7.46)
v(s Sleeping ) T = [0; 1; i 3;,k 2i 5,k ; 0] (7.47)
v(s Running ) T = [0; i 4,k ; 1; 2i 6,k ; 0] (7.48)
v(s Terminating ) T = [0; 0; 0; 1; i 7,k ] (7.49)
A transition vector for the final state s END is not required. Since s Starting is the initial state s 0 ,
the corresponding transition function can be defined as
⎛
⎡
s Starting
⎤⎞
s k = s Starting : s k+1 = δ
⎜
⎝ [1; 2i s Sleeping
1,k; 3i 2,k ; 0; 0]
⎢ s Running
⎥⎟
⎣ s Terminating
⎦⎠
s END
= δ (s Starting + 2i 1,k s Sleeping + 3i 2,k s Running ) (7.50)
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