Ph.D. - geht es zur Homepage der Informatik des Fachbereiches 3 ...

Chapter 7. openETCS Meta Model
This mathematical model is quite similar to a Moore machine [58]. According to the openETCS
meta model, the inputs are defined by Boolean data flows to guard objects (oModeGuard,
oStateGuard, oApplicationLevelType). Thus, this input can be defined as
Σ ≡ {i j ; j = 1, 2, 3, . . . , n i } ; i j ∈ {0; 1} (7.33)
The transition function δ uses the state transition vector v(s), which defines for each certain /
active state s the possible transitions to all others depending on the current inputs:
s ′ = δ(s) = δ ( v(s) T s ) (7.34)
s ′ is the new active state and s the state vector with all available states:
⎡ ⎤
s 1
s 2
s = ⎢ ⎥
⎣ . ⎦ ; ∀o : s o ∈ S (7.35)
s ns
The Sum of all available inputs multiplied by their numerical priority, which is in the meta
model a property of the related Transition relationship, are the elements of the state transition
vector v(s):
v(s) =
⎡
⎢
⎣
c 1 (s)
c 2 (s)
. . .
c ns (s)
⎤
⎥
⎦ (7.36)
If several transition to the same new state s ′ exist but under different input conditions, the
corresponding element c i of the state transition vector is the sum of the products of inputs and
their priority. In general, this means for each element
∑n i
∀l : c l = (i j (p j + 1)) ; p j ∈ N ∪ {0} (7.37)
j=0
p j is the priority of the input i j . i j = 1 means that the input i j is a condition for the
corresponding new state. Otherwise, i j = 0 is set. In the openETCS model, p j is taken from
the Transition relationship. The result of the v(s) T s operation is a sum of possible different
states s j , which have a numerical factor each. The δ function selects from this sum the state s j
with the highest factor and returns it. Therefore, it is important, that the priority is different
for all possible transitions from a certain state. Otherwise, two states with the same factor
may occur and the result of the δ function is undefined. Since not at every execution point
an input for a transition to a new state is set, the element in transition vector v(s) for a self
transition has always the value 1.
s ′ = s = s j ⇒ c j
!
= 1 (7.38)
Therefore, 1 is added to the priority p j in (7.36) in order that transitions that are not a
self transition are always preferred by the δ function. Although the state machines in the
116