Behavior of DEVS
Encyclopedia
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. To define this way, the concept of a set of illegal state as well a set of legal states are needed to be introduced.
In addition, since the behaviors of a given DEVS model needs to define how the state transition change both when time is passed by and when an event occurs, it has been described by a much general formalism, called general system [ZPK00]. In this article, we use a sub-class of General System formalism, called timed event system
instead.
Depending on how to define the total state and its external state transition function of DEVS
, two ways to define the behavior of a DEVS
model using Timed Event System
.
Since behavior of a coupled DEVS
model is defined as an atomic DEVS model, behavior of coupled DEVS class is defined by timed event system.
model,
has
Then the DEVS
model,
is a Timed Event System
where
Computer algorithms to simulate this view of behavior are available at Simulation Algorithms for Atomic DEVS
.
model,
has
Then the DEVS
is a timed event system 
where
Computer algorithms to simulate this view of behavior are available at Simulation Algorithms for Atomic DEVS
.
and 
where
is the remaining time [Zeigler84] [ZPK00]. In other words, the set of partial states is indeed 
where 
is a state set.
When a DEVS model receives an input event
, View1 resets the elapsed time 
by zero, if the DEVS model needs to ignore 
in terms of the lifepan control, modellers have to update the remaining time
in the external state transition function
that is the responsibility of the modellers.
Since the number of possible values of
is the same as the number of possible input events coming to the DEVS model, that is unlimited. As a result, the number of states 
is also unlimited that is the reason why View2 has been proposed.
If we don't care the finite-vertex reachability graph of a DEVS model, View1 has an advantage of simplicity for treating the elapsed time
every time any input event arrives into the DEVS model. But disadvantage might be modelers of DEVS should know how to manage 
as above, which is not explicitly explained in 
itself but in 
.
, the remaining time, 
is computed as
When a DEVS model receives an input event
, View2 resets the elapsed time 
by zero only if 
. If the DEVS model needs to ignore 
in terms of the lifepan control, modellers can use 
.
Unlike View1, since the remaining time
is not component of 
in nature, if the number of states, i.e. 
is finite, we can draw a finite-vertex (as well as edge) state-transition diagram [HZ06][HZ07]. As a result, we can abstract behavior of such a DEVS-class network, for example SP-DEVS
and FD-DEVS, as a finite-vertex graph, called reachability graph [HZ06][HZ07].
DEVS
DEVS 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...
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. To define this way, the concept of a set of illegal state as well a set of legal states are needed to be introduced.
In addition, since the behaviors of a given DEVS model needs to define how the state transition change both when time is passed by and when an event occurs, it has been described by a much general formalism, called general system [ZPK00]. In this article, we use a sub-class of General System formalism, called 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....
instead.
Depending on how to define the total state and its external state transition function of DEVS
DEVS
DEVS 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...
, two ways to define the behavior of a DEVS
DEVS
DEVS 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...
model using 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....
.
Since behavior of a coupled DEVS
Behavior of Coupled DEVS
DEVS is closed under coupling [Zeigper84] [ZPK00]. In other words, given a coupled DEVS model N , its behavior is described as an atomic DEVS model M...
model is defined as an atomic DEVS model, behavior of coupled DEVS class is defined by timed event system.
View 1: total states = states * elapsed times
Suppose that a DEVSDEVS
DEVS 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...
model,
has- the total state set
where 
denotes elapsed time since last event and 
denotes the set of non-negative real numbers, and - the external state transition
.
Then the DEVS
DEVS
DEVS 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...
model,
is a Timed Event SystemTimed 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....
where
- The event set
.
- The state set
.
- The initial state
.
- The set of acceptance states
- The state trajectory function
is defined for an total state
at time
and an event segment
as follows.
If unit event segmentis the null event segment, i.e.
If unit event segmentis a timed event
where the event is an input event
,
If unit event segmentis a timed event
where the event is an output event or the unobservable event
,
Computer algorithms to simulate this view of behavior are available at Simulation Algorithms for Atomic DEVS
Simulation Algorithms for Atomic DEVS
Given an atomic DEVS model, simulation algorithms are methods to generate the model's legal behaviors which are trajectories not to reach to illegal states....
.
View 2: total states = states * lifespans * elapsed times
Suppose that a DEVSDEVS
DEVS 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...
model,
has- the total state set
where 
denotes lifespan of state 
, 
denotes elapsed time since last 
update, and 
denotes the set of non-negative real numbers plus infinity, - the external state transition is
.
Then the DEVS
DEVS
DEVS 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...
is a timed event system where
- The event set
.
- The state set
.
- The initial state
.
- The set of acceptance states
.
- The state trajectory function
is defined for a total state
at time
and an event segment
as follows.
If unit event segmentis the null event segment, i.e.
If unit event segmentis a timed event
where the event is an input event
,
If unit event segmentis a timed event
where the event is an output event or the unobservable event
,
Computer algorithms to simulate this view of behavior are available at Simulation Algorithms for Atomic DEVS
Simulation Algorithms for Atomic DEVS
Given an atomic DEVS model, simulation algorithms are methods to generate the model's legal behaviors which are trajectories not to reach to illegal states....
.
Features of View1
View1 has been introduced by Zeigler [Zeigler84] in which given a total state and where
is the remaining time [Zeigler84] [ZPK00]. In other words, the set of partial states is indeed where is a state set.When a DEVS model receives an input event
, View1 resets the elapsed time by zero, if the DEVS model needs to ignore in terms of the lifepan control, modellers have to update the remaining time in the external state transition function
that is the responsibility of the modellers.Since the number of possible values of
is the same as the number of possible input events coming to the DEVS model, that is unlimited. As a result, the number of states is also unlimited that is the reason why View2 has been proposed.If we don't care the finite-vertex reachability graph of a DEVS model, View1 has an advantage of simplicity for treating the elapsed time
every time any input event arrives into the DEVS model. But disadvantage might be modelers of DEVS should know how to manage as above, which is not explicitly explained in itself but in .Features of View2
View2 has been introduced by Hwang and Zeigler[HZ06][HZ07] in which given a total state, the remaining time, is computed as When a DEVS model receives an input event
, View2 resets the elapsed time by zero only if . If the DEVS model needs to ignore in terms of the lifepan control, modellers can use .Unlike View1, since the remaining time
is not component of in nature, if the number of states, i.e. is finite, we can draw a finite-vertex (as well as edge) state-transition diagram [HZ06][HZ07]. As a result, we can abstract behavior of such a DEVS-class network, for example SP-DEVSSP-DEVS
SP-DEVS abbreviating “Schedule-Preserving Discrete Event System Specification” is a formalism for modeling and analyzing discrete event systems in both simulation and verification ways...
and FD-DEVS, as a finite-vertex graph, called reachability graph [HZ06][HZ07].
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 Coupled DEVSBehavior of Coupled DEVSDEVS is closed under coupling [Zeigper84] [ZPK00]. In other words, given a coupled DEVS model N , its behavior is described as an atomic DEVS model M...
- 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....
- 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...