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

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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

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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

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Features of View1

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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

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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

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References

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  • [Zeigler76] Bernard Zeigler (1976). Theory of Modeling and Simulation (first ed.). Wiley Interscience, New York.
  • [Zeigler84] Bernard Zeigler (1984). Multifacetted Modeling and Discrete Event Simulation. Academic Press, London; Orlando. ISBN 978-0-12-778450-2.
  • [ZKP00] Bernard Zeigler; Tag Gon Kim; Herbert Praehofer (2000). Theory of Modeling and Simulation (second ed.). Academic Press, New York. ISBN 978-0-12-778455-7.
  • [HZ06] M. H. Hwang and Bernard Zeigler, ``A Reachable Graph of Finite and Deterministic DEVS Networks``, Proceedings of 2006 DEVS Symposium, pp48-56, Huntsville, Alabama, USA, (Available at https://web.archive.org/web/20120726134045/http://www.acims.arizona.edu/ and http://moonho.hwang.googlepages.com/publications)
  • [HZ07] M.H. Hwang and Bernard Zeigler, ``Reachability Graph of Finite & Deterministic DEVS``, IEEE Transactions on Automation Science and Engineering, Volume 6, Issue 3, 2009, pp. 454–467, https://ieeexplore.ieee.org/document/5071137/;jsessionid=939E18A20B3B2411AA8CD012B44EE174?isnumber=5153598&arnumber=5071137&count=19&index=7