Behavior of DEVS

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.
Suppose that a DEVS model,
formula_1 has
Then the DEVS model,
formula_6 is a Timed Event System formula_7 where
For a total state formula_19 at time formula_20 and an event segment formula_21 as follows. <br>
If unit event segment formula_22 is the null event segment, i.e. formula_23
 formula_24 
If unit event segment formula_22 is a timed event formula_26 where the event is an input event formula_27,
 formula_28 
If unit event segment formula_22 is a timed event formula_30 where the event is an output event or the unobservable event formula_31,
 formula_32 
Computer algorithms to simulate this view of behavior are available at Simulation Algorithms for Atomic DEVS.
View 2: total states = states * lifespans * elapsed times.
Suppose that a DEVS model,
formula_1 has
Then the DEVS formula_41 is a timed event system formula_7 where
For a total state formula_54 at time formula_20 and an event segment formula_21 as follows. <br>
If unit event segment formula_22 is the null event segment, i.e. formula_23
 formula_59 
If unit event segment formula_22 is a timed event formula_26 where the event is an input event formula_27,
 formula_63 
If unit event segment formula_22 is a timed event formula_30 where the event is an output event or the unobservable event formula_31,
 formula_67 
Computer algorithms to simulate this view of behavior are available at Simulation Algorithms for Atomic DEVS.
Comparison of View1 and View2.
Features of View1.
View1 has been introduced by Zeigler [Zeigler84] in which given a total state formula_68 and formula_69 
where formula_70 is the remaining time [Zeigler84] [ZPK00]. In other words, the set of partial states is indeed formula_71 where formula_72 is a state set.
When a DEVS model receives an input event formula_27, View1 resets the elapsed time formula_4 by zero, if the DEVS model needs to ignore formula_75 in terms of the lifespan control, modellers have to update the remaining time
 formula_76 
in the external state transition function formula_77 that is the responsibility of the modellers.
Since the number of possible values of formula_70 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 formula_79 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 formula_80 every time any input event arrives into the DEVS model. But disadvantage might be modelers of DEVS should know how to manage formula_81 as above, which is not explicitly explained in formula_82 itself but in formula_83.
Features of View2.
View2 has been introduced by Hwang and Zeigler[HZ06][HZ07] in which given a total state formula_84, the remaining time, formula_85 is computed as
 formula_86 
When a DEVS model receives an input event formula_27, View2 resets the elapsed time formula_4 by zero only if formula_89. If the DEVS model needs to ignore formula_75 in terms of the lifespan control, modellers can use formula_91.
Unlike View1, since the remaining time formula_70 is not component of formula_93 in nature, if the number of states, i.e. formula_94 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].