Behavior of Coupled DEVS
Encyclopedia
DEVS is closed under coupling [Zeigper84] [ZPK00]. In other words, given a coupled DEVS model 
, its behavior is described as an atomic DEVS model 
. For a given coupled DEVS 
, once we have an equivalent atomic DEVS 
, behavior of 
can be referred to behavior of atomic DEVS
which is based on Timed Event System
.
Similar to behavior of atomic DEVS
, behavior of the Coupled DEVS class is described depending on definition of the total state set and its handling as follows.
, its behavior is described as an atomic DEVS model 
where
, its behavior is described as an atomic DEVS model . For a given coupled DEVS , once we have an equivalent atomic DEVS , behavior of can be referred to behavior of atomic DEVSBehavior of DEVS
Behaviors of a given DEVS model is a set of sequences of timed events including null events, called event segments which make the model move one state to another within a set of legal states...
which is based on Timed Event System
Timed event system
The General System has been described in [Zeigler76] and [ZPK00] with the stand points to define the time base, the admissible input segments, the system states, the state trajectory with an admissible input segment, the output for a given state....
.
Similar to behavior of atomic DEVS
Behavior of DEVS
Behaviors of a given DEVS model is a set of sequences of timed events including null events, called event segments which make the model move one state to another within a set of legal states...
, behavior of the Coupled DEVS class is described depending on definition of the total state set and its handling as follows.
View1: Total States = States * Elapsed Times
Given a coupled DEVS model, its behavior is described as an atomic DEVS model where
-
and 
are the input event set and the output event set, respectively. -
is the partial state set where 
is the total state set of component 
(Refer to View1 of Behavior of DEVS), where 
is the set of non-negative real numbers. -
is the initial state set where 
is the total initial state of component 
. 
is the time advance function, where 
is the set of non-negative real numbers plus infinity.Given 
, 
is the external state function. Given a total state 
where 
, and input event 
, the next state is given by 
where
Given the partial state
, let 
denote the set of imminent components. The firing component 
which triggers the internal state transition and an output event is determined by 
is the internal state function. Given a partial state 
, the next state is given by 
where
is the output function. Given a partial state 
, 
View2: Total States = States * Lifespan * Elapsed Times
Given a coupled DEVS model
, its behavior is described as an atomic DEVS model 
where-
and 
are the input event set and the output event set, respectively. -
is the partial state set where 
is the total state set of component 
(Refer to View2 of Behavior of DEVS). -
is the initial state set where 
is the total initial state of component 
.
is the time advance function. Given 
, 
is the external state function. Given a total state 
where 
, and input event 
, the next state is given by 
where
and
Given the partial state
, let 
denote the set of imminent components. The firing component 
which trigers the internal state transition and an output event is determined by 
is the internal state function. Given a partial state 
, the next state is given by 
where
is the output function. Given a partial state 
, 
Time Passage
Since in a coupled DEVS model with non-empty sub-components, i.e.,
, the number of clocks which trace their elapsed times are multiple, so time passage of the model is noticeable.
For View1
Given a total state
where 
If unit event segment
is the null event segment, i.e. 
, the state trajectory in terms of Timed Event SystemTimed event systemThe General System has been described in [Zeigler76] and [ZPK00] with the stand points to define the time base, the admissible input segments, the system states, the state trajectory with an admissible input segment, the output for a given state....
is
For View2
Given a total state
where 
If unit event segment
is the null event segment, i.e. 
, the state trajectory in terms of Timed Event SystemTimed event systemThe General System has been described in [Zeigler76] and [ZPK00] with the stand points to define the time base, the admissible input segments, the system states, the state trajectory with an admissible input segment, the output for a given state....
is
Remarks
- The behavior of a couple DEVS network whose all sub-components are deterministic DEVS models can be non-deterministic if
is non-deterministic.
See also
- DEVSDEVSDEVS abbreviating Discrete Event System Specification is a modular and hierarchical formalism for modeling and analyzing general systems that can be discrete event systems which might be described by state transition tables, and continuous state systems which might be described by differential...
- Behavior of Atomic DEVSBehavior of DEVSBehaviors of a given DEVS model is a set of sequences of timed events including null events, called event segments which make the model move one state to another within a set of legal states...
- Simulation Algorithms for Coupled DEVSSimulation Algorithms for Coupled DEVSGiven a coupled DEVS model, simulation algorithms are methods to generate the model's legal behaviors, which are a set of trajectories not to reach illegal states...
- Simulation Algorithms for Atomic DEVSSimulation Algorithms for Atomic DEVSGiven an atomic DEVS model, simulation algorithms are methods to generate the model's legal behaviors which are trajectories not to reach to illegal states....
- The behavior of a couple DEVS network whose all sub-components are deterministic DEVS models can be non-deterministic if
-