Behavior of coupled DEVS

"DEVS is closed under coupling" [Zeigper84] [ZPK00]. In other words, given a coupled DEVS model formula_1, its behavior is described as an atomic DEVS model formula_2. For a given coupled DEVS formula_1, once we have an equivalent atomic DEVS formula_4, behavior of formula_4 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.
View1: Total States = States * Elapsed Times.
Given a coupled DEVS model formula_6, its behavior is described as an atomic DEVS model formula_7
where
 
where
 formula_26
Given the partial state formula_27, let formula_28 denote "the set of imminent components". The "firing component" formula_29 which triggers the internal state transition and an output event is determined by formula_30
where
 formula_34
View2: Total States = States * Lifespan * Elapsed Times.
Given a coupled DEVS model formula_6, its behavior is described as an atomic DEVS model formula_7
where
 
where
 formula_56
and
 formula_57
Given the partial state formula_58, let formula_59 denote "the set of imminent components". The "firing component" formula_29 which triggers the internal state transition and an output event is determined by formula_30
where
 formula_65
Time Passage.
Since in a coupled DEVS model with non-empty sub-components, i.e., formula_69, the number of clocks which trace their elapsed times are multiple, so time passage of the model is noticeable. 
Given a total state formula_70 where formula_71
If unit event segment formula_72 is the null event segment, i.e. formula_73, the state trajectory in terms of Timed Event System is 
 formula_74 
Given a total state formula_75 where formula_76
If unit event segment formula_72 is the null event segment, i.e. formula_73, the state trajectory in terms of Timed Event System is 
 formula_79 