Behavior of DEVS

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The behavior of a given DEVS model is a set of sequences of timed events including null events, called event segments, which make the model move from one state to another within a set of legal states. To define it this way, the concept of a set of illegal state as well a set of legal states needs to be introduced.

In addition, since the behavior 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 the total state and the external state transition function of a DEVS model are defined, there are two ways to define the behavior of a DEVS model using Timed Event System. Since the behavior of a coupled DEVS model is defined as an atomic DEVS model, the behavior of coupled DEVS class is also defined by timed event system.

View 1: total states = states * elapsed times[edit]

Suppose that a DEVS model, has

  1. the external state transition .
  2. the total state set where denotes elapsed time since last event and denotes the set of non-negative real numbers, and

Then the DEVS model, is a Timed Event System where

  • The event set .
  • The state set where .
  • The set of initial states .
  • The set of accepting states
  • The set of state trajectories is defined for two different cases: and . For a non-accepting state , there is no change together with any even segment so

For a total state at time and an event segment as follows.

If unit event segment is the null event segment, i.e.

If unit event segment is a timed event where the event is an input event ,

If unit event segment is 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.

View 2: total states = states * lifespans * elapsed times[edit]

Suppose that a DEVS model, has

  1. 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,
  2. the external state transition is .

Then the DEVS is a timed event system where

  • The event set .
  • The state set where .
  • The set of initial states.
  • The set of acceptance states .
  • The set of state trajectories is depending on two cases: and . For a non-accepting state , there is no changes together with any segment so

For a total state at time and an event segment as follows.

If unit event segment is the null event segment, i.e.

If unit event segment is a timed event where the event is an input event ,

If unit event segment is 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.

Comparison of View1 and View2[edit]

Features of View1[edit]

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 lifespan 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[edit]

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 lifespan 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].

See also[edit]

References[edit]