Event segment: Difference between revisions

Revision as of 19:30, 3 March 2014

Revision as of 19:32, 3 March 2014

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A '''segment''' of a system variable shows a homogenous status of system dynamics over a time period. Here, a homogenous status of a variable is a state which can be described by one coefficient of a simple formula. For example of homogenous statuses, we can bring status of constant ('ON' of a switch) and linear (60 miles or 96km per hour for speed). Mathematically, a segment is a function mapping from a set of times which can be defined by an real interval, to the set <math>Z</math> [[Event_Segment#References|[Zeigler76]]] and [[Event_Segment#References|[ZPK00]]]. A '''trajectory''' of a system variable is a concatenation of segments. We call it a trajectory of constant-segments (respectively linear-segments) if its concatenating segments are constant (respectively linear).

An event segment is a special class of the constant segment thatwith a constraint in which the constant segment is either one of a timed event or a null-segment. The event segments are used to define [[Timed Event System]]s such as [[DEVS]], [[timed automaton|timed automata]], and [[timed petri nets]].

== Event segments ==

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A ''timed event'' <math> (z,t) </math> over an event set <math> Z </math> and the time base <math> \mathbb{T}</math> denotes that an event <math> z \in Z</math> occurs at time <math> t \in \mathbb{T}</math>.

=== Null event segment ===

The ''null event segment'' over time interval <math> [t_l, t_u] \subset \mathbb{T} </math> is denoted by <math> \epsilon_{[t_l, t_u]}</math> which means that there is no event over <math> [t_l, t_u] </math>.

=== Unit event segment ===