in Fig. 2. The top of Fig.3. shows an event trajectory in which the horizontal axis is a time axis so it shows an event occurs at a certain time, for example, !g:1 occurs at 0.5 and !w:0 at 1.0 time unit, and so on. The bottom of Fig. 3 shows the state trajectory associated with the above event segment in which the state is associated with its lifespan and its elapsed time in the form of . For example, (G, 30, 11) denotes that the state is G, its lifespan is and the elapsed time is 11 time units. The line segments of the bottom of Fig. 3 shows the time flow of the elapsed time which is the only one continuous variable in SP-DEVS. One interesting feature of SF-DEVS might be the preservation of schedule the restriction (3) of SP-DEVS which is drawn at time 47 in Fig. 3. when the external event ?p happens. At this moment, even though the state can change from G to GR, the elapsed time does not change so the line segment is not broken at time 47 and can grow up to which is 30 in this example. Due to this preservation of the schedule from input events as well as the restriction of the time advance to the non-negative rational number (see restriction (2) above), the height of every saw can be a non-negative rational number or infinity (as shown in the bottom of Fig. 3.) in a SP-DEVS model. SP-DEVS is a sub-class of DEVS A SP-DEVS model, is DEVS where of are the same as those of . Given a state , Given a state and an input event Given a state , if Given a state , if Advantages Applicability of Time-Line Abstraction The property of non-negative rational-valued lifespans which are not changed by input events along with finite numbers of states and events guarantees that the behavior of SP-DEVS networks can be abstracted as an equivalent finite-vertex reachability graph by abstracting the infinitely-many values of the elapsed times. To abstract the infinitely-many cases of elapsed times for each components of SP-DEVS networks, a time-abstraction method, called the time-line abstraction has been introduced [Hwang05],[HCZF07] in which the orders and relative difference of schedules are preserved. By using the time-line abstraction technique, the behavior of any SP-DEVS network can be abstracted as a reachability graph whose numbers of