![](bg3.png)
formalisms. Connections between the different
formalisms can then be achieved through a multi-
formalism to perform the whole system
specification.
In this study, subsystems are specified using
DEVS, DTSS (Discrete Time System Specification)
and DSDTSS formalisms. Connections between the
different models are achieved using a Multi-
formalism Network (MFN). A structure description
of each model is provided hereafter.
A DEVS atomic model is a structure:
DEVS = (X, Y, Q, q
0
, δ
int
, δ
ext
, λ, t
a
)
where X is the input events set, Q is the set of state,
q
0
is the initial state, Y is the output events set, δ
int
:
Q
Æ
Q is the internal transition function, δ
ext
: Q×X
Æ
Q is the external transition function,
λ
: Q
Æ
Y
the output function, t
a
is the time advance function.
DSDTSS basic models are DTSS atomic model:
DTSS = (X, Y, Q, q
0
,
δ
,
λ
, h)
where X, Y are the input and output sets, Q is the
set of state, q
0
is the initial state,
δ
: Q×X
Æ
Q is
the state transition function,
λ
: Q
Æ
Y is the
output function (considering a Moore machine) and
h is a constant time advance.
At a periodic rate, this model checks its inputs
and, based on its state information, produces an
output and changes its internal state.
The network of simple DTSS models is referred
to as a Dynamic Structure Discrete Time Network
(DSDTN) (Barros, 1997). We introduce here input
and output sets to allow connections with the
network. Formally, a DSDTN is a 4-tuple:
DSDTN = (X
DSDTN
,Y
DSDTN
,
χ
, M
χ
)
where X
DSDTN
is the network input values set, Y
DSDTN
is the network input values set,
χ
is the name of the
DSDTN executive, M
χ
is the model of the executive
χ
.
The model of the executive is a modified DTSS
defined by the 8-tuple:
M
χ
= (X
χ
,Q
χ
, q
0,
χ
, Y
χ
,
γ
,
Σ
*
,
δ
χ
,
λ
χ
)
where
γ
: Q
χ
Æ
Σ
*
is the structure function, and
Σ
*
is
the set of network structures. The transition function
δ
χ
computes the executive state q
χ
. The network
executive structure
Σ
, at the state q
χ
∈
Q
χ
is given by
Σ
=
γ
(q
χ
) = (D, {M
i
}, {I
i
}, {Z
i,j
}), for all i
∈
D, M
i
=
(X
i
, Q
i
, q
0,i
, Y
i
,
δ
i
,
λ
i
), where D is the set of model
references, I
i
is the set of influencers of model i, and
Z
i,j
is the i to j translation function.
Because the network coupling information is
located in the state of the executive, transition
functions can change this state and, in consequence,
change the structure of the network. Changes in
structure include changes in model interconnections,
changes in system definition, and the addition or
deletion of system models.
Formally, a multiformalism network (Zeigler et
al., 2000) is defined by the 7-tuple:
MFN = (X
MFN
,Y
MFN
, D, {M
i
}, {I
i
}, {Z
i,j
},select)
where X
MFN
=X
discr
×X
cont
is the network input values
set, X
discr
and X
cont
are discrete and continuous input
sets, Y
MFN
=Y
discr
×Y
cont
is the network input values
set, Y
discr
and Y
cont
are discrete and continuous output
sets, D is the set of model references,
For each i
∈
D,
M
i
is are DEVS, DEVN, DTSN, DTSS,
DESS, DEV&DESS or other MFN models.
As DSDTSS proved to be closed under
coupling, M
i
can also be dynamic structure
models or networks,
I
i
is the set of influencers of model i,
Z
i,j
is the i to j translation function,
select is the tie-breaking function.
3 DSCA MODELLING
Models composing a DSCA are specified here using
the previous model definitions. As described in the
modeling part of Figure 1, external events are
simulated using a DEVS atomic model: the
Generator. The latter can asynchronously generate
data information to the DSCA during the simulation.
The cell space is embedded in a DSDTN. Each cell
is defined as a DTSS model. Using its transition
function, the DSCA executive model (containing
every cells) achieves changes in structure directly
accessing to the attributes of cells. A mathematical
description of each model is provided here after.
We define the MFN by the structure:
MFN = (X
MFN
,Y
MFN
, D, {M
i
}, {I
i
}, {Z
i,j
}, select)
where D={G,DSDTN}, M
G
= (X
G
, Q
G
, q
0,G
, Y
G
,
δ
G
,
λ
G,
τ
G
), M
DSDTN
=DSDTN, I
G
={}, I
DSDTN
={G}, and
Z
DSDTN,MFN
: Y
DSDTN
Æ
Y
MFN
, Z
G,DSDTN
: Y
G
Æ
X
DSDTN
.
DYNAMIC STRUCTURE CELLULAR AUTOMATA IN A FIRE SPREADING APPLICATION
145