Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Event segment
open-in-new
<h2 id="event-segments">Event segments</h2> <h3>Time base</h3> <p>The <i>time base</i> of the concerning systems is denoted by T {\displaystyle \mathbb {T} } , and defined </p> T = [ 0 , ∞ ) {\displaystyle \mathbb {T} =[0,\infty )} <p>as the set of non-negative real numbers. </p> <h3>Event and null event</h3> <p>An <i>event</i> is a label that abstracts a change. Given an event set Z {\displaystyle Z} , the <i>null event</i> denoted by ϵ ∉ Z {\displaystyle \epsilon \not \in Z} stands for nothing change. </p> <h3>Timed event</h3> <p>A <i>timed event</i> is a pair ( t , z ) {\displaystyle (t,z)} where t ∈ T {\displaystyle t\in \mathbb {T} } and z ∈ Z {\displaystyle z\in Z} denotes that an event z ∈ Z {\displaystyle z\in Z} occurs at time t ∈ T {\displaystyle t\in \mathbb {T} } . </p> <h3>Null segment</h3> <p>The <i>null segment</i> over time interval [ t l , t u ] ⊂ T {\displaystyle [t_{l},t_{u}]\subset \mathbb {T} } is denoted by ϵ [ t l , t u ] {\displaystyle \epsilon _{[t_{l},t_{u}]}} which means nothing in Z {\displaystyle Z} occurs over [ t l , t u ] {\displaystyle [t_{l},t_{u}]} . </p> <h3>Unit event segment</h3> <p>A <i>unit event segment</i> is either a <a href="/facts/Event_Segment/kdrhDIu1">null event segment</a> or a <a href="/facts/Event_Segment/kdrhDIu1">timed event</a>. </p> <h3>Concatenation</h3> <p>Given an event set Z {\displaystyle Z} , <i>concatenation</i> of two <a href="/facts/Event_Segment/kdrhDIu1">unit event segments</a> ω {\displaystyle \omega } over [ t 1 , t 2 ] {\displaystyle [t_{1},t_{2}]} and ω ′ {\displaystyle \omega '} over [ t 3 , t 4 ] {\displaystyle [t_{3},t_{4}]} is denoted by ω ω ′ {\displaystyle \omega \omega '} whose time interval is [ t 1 , t 4 ] {\displaystyle [t_{1},t_{4}]} , and implies t 2 = t 3 {\displaystyle t_{2}=t_{3}} . </p> <h3>Event trajectory</h3> <p>An <i>event trajectory</i> ( t 1 , z 1 ) ( t 2 , z 2 ) ⋯ ( t n , z n ) {\displaystyle (t_{1},z_{1})(t_{2},z_{2})\cdots (t_{n},z_{n})} over an event set Z {\displaystyle Z} and a time interval [ t l , t u ] ⊂ T {\displaystyle [t_{l},t_{u}]\subset \mathbb {T} } is concatenation of <a href="/facts/Event_Segment/kdrhDIu1">unit event segments</a> ϵ [ t l , t 1 ] , ( t 1 , z 1 ) , ϵ [ t 1 , t 2 ] , ( t 2 , z 2 ) , … , ( t n , z n ) , {\displaystyle \epsilon _{[t_{l},t_{1}]},(t_{1},z_{1}),\epsilon _{[t_{1},t_{2}]},(t_{2},z_{2}),\ldots ,(t_{n},z_{n}),} and ϵ [ t n , t u ] {\displaystyle \epsilon _{[t_{n},t_{u}]}} where t l ≤ t 1 ≤ t 2 ≤ ⋯ ≤ t n − 1 ≤ t n ≤ t u {\displaystyle t_{l}\leq t_{1}\leq t_{2}\leq \cdots \leq t_{n-1}\leq t_{n}\leq t_{u}} . </p><p>Mathematically, an event trajectory is a mapping ω {\displaystyle \omega } a time period [ t l , t u ] ⊆ T {\displaystyle [t_{l},t_{u}]\subseteq \mathbb {T} } to an event set Z {\displaystyle Z} . So we can write it in a function form : </p> ω : [ t l , t u ] → Z ∗ . {\displaystyle \omega :[t_{l},t_{u}]\rightarrow Z^{*}.} <h2 id="timed-language">Timed language</h2> <p>The <i>universal timed language</i> Ω Z , [ t l , t u ] {\displaystyle \Omega _{Z,[t_{l},t_{u}]}} over an event set Z {\displaystyle Z} and a time interval [ t l , t u ] ⊂ T {\displaystyle [t_{l},t_{u}]\subset \mathbb {T} } , is the set of all event trajectories over Z {\displaystyle Z} and [ t l , t u ] {\displaystyle [t_{l},t_{u}]} . </p><p>A <i>timed language</i> L {\displaystyle L} over an event set Z {\displaystyle Z} and a timed interval [ t l , t u ] {\displaystyle [t_{l},t_{u}]} is <i>a set of event trajectories</i> over Z {\displaystyle Z} and [ t l , t u ] {\displaystyle [t_{l},t_{u}]} if L ⊆ Ω Z , [ t l , t u ] {\displaystyle L\subseteq \Omega _{Z,[t_{l},t_{u}]}} . </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Outline_of_computing/TSLlWDFh">Outline of computing</a></li></ul> <ul><li>[Zeigler76] Bernard Zeigler (1976). <i>Theory of Modeling and Simulation</i> (first ed.). Wiley Interscience, New York.</li> <li>[ZKP00] Bernard Zeigler; Tag Gon Kim; Herbert Praehofer (2000). <i>Theory of Modeling and Simulation</i> (second ed.). Academic Press, New York. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-12-778455-7.</li> <li>[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. 216–229, dec 2001</li> <li>[Hwang13] M.H. Hwang, ``Revisit of system variable trajectories``, <i>Proceedings of the Symposium on Theory of Modeling & Simulation - DEVS Integrative M&S Symposium </i>, San Diego, CA, USA, April 7–10, 2013</li></ul>