Event segment: Difference between revisions

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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 a set of coefficients of a formula. For example, of homogenous statuses, we can bring status of constant ('ON' of a switch) and linear (60 miles or 96&nbsp;km 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]]],[[Event_Segment#References|[ZPK00]]], [[Event_Segment#References|[Hwang13]]]. A '''trajectory''' of a system variable is a sequence of segments concatenated. We call a trajectory constant (respectively linear) if its concatenating segments are constant (respectively linear).

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{{Short description|Computational modeling concept}}

A '''segment''' of a system variable in [[computing]] 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 a set of coefficients of a formula. For example, of homogenous statuses, we can bring status of constant ('ON' of a switch) and linear (60 miles or 96&nbsp;km per hour for speed). Mathematically, a segment is a function mapping from a set of times which can be defined by ana real interval, to the set <math>Z</math> [[Event_Segment#References|[Zeigler76]]], [[Event_Segment#References|[ZPK00]]], [[Event_Segment#References|[Hwang13]]]. A '''trajectory''' of a system variable is a sequence of segments concatenated. We call a trajectory constant (respectively linear) if its concatenating segments are constant (respectively linear).

An '''event segment''' is a special class of the constant segment with 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]].

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The ''time base'' of the concerning systems is denoted by <math> \mathbb{T} </math>, and defined

<{{center>|1=<math> \mathbb{T}=[0,\infty) </math> </center>}}

as the set of non-negative real numbers.

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Mathematically, an event trajectory is a mapping <math>\omega</math> a time period <math>[t_l,t_u] \subseteq \mathbb{T} </math> to an event set <math>Z</math>. So we can write it in a function form :

<{{center>|1=<math> \omega:[t_l,t_u] \rightarrow Z^* .</math></center>}}

== Timed language ==

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t_u]</math> if <math>L

\subseteq \Omega_{Z, [t_l, t_u]}</math>.

== See also ==

* [[Outline of computing]]

== References ==

* [Zeigler76] {{cite book|author = Bernard Zeigler | year = 1976| title = Theory of Modeling and Simulation| publisher = Wiley Interscience, New York | id = |edition=first}}

* [ZKP00] {{cite book|author1=Bernard Zeigler |author2=Tag Gon Kim |author3=Herbert Praehofer | year = 2000| title = Theory of Modeling and Simulation| publisher = Academic Press, New York | isbn= 978-0-12-778455-7 |edition=second}}

* [Giambiasi01] Giambiasi N., Escude B. Ghosh S. “Generalized Discrete Event Simulation of Dynamic Systems”, in: Issue 4 of SCS Transactions: Recent Advances in DEVS Methodology-part II, Vol. 18, pp.&nbsp;216–229, dec 2001