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 km per hour for speed). Mathematically, a segment is a function mapping from a set of times which can be defined by a real interval, to the set [Zeigler76], [ZPK00], [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 Systems such as DEVS, timed automata, and timed petri nets.

Event segments

edit

Time base

edit

The time base of the concerning systems is denoted by  , and defined

 

as the set of non-negative real numbers.

Event and null event

edit

An event is a label that abstracts a change. Given an event set  , the null event denoted by   stands for nothing change.

Timed event

edit

A timed event is a pair   where   and   denotes that an event   occurs at time  .

Null segment

edit

The null segment over time interval   is denoted by   which means nothing in   occurs over  .

Unit event segment

edit

A unit event segment is either a null event segment or a timed event.

Concatenation

edit

Given an event set  , concatenation of two unit event segments   over   and   over   is denoted by   whose time interval is  , and implies  .

Event trajectory

edit

An event trajectory   over an event set   and a time interval   is concatenation of unit event segments   and   where  .

Mathematically, an event trajectory is a mapping   a time period   to an event set  . So we can write it in a function form :

 

Timed language

edit

The universal timed language   over an event set   and a time interval  , is the set of all event trajectories over   and  .

A timed language   over an event set   and a timed interval   is a set of event trajectories over   and   if  .

See also

edit

References

edit
  • [Zeigler76] Bernard Zeigler (1976). Theory of Modeling and Simulation (first ed.). Wiley Interscience, New York.
  • [ZKP00] Bernard Zeigler; Tag Gon Kim; Herbert Praehofer (2000). Theory of Modeling and Simulation (second ed.). Academic Press, New York. ISBN 978-0-12-778455-7.
  • [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
  • [Hwang13] M.H. Hwang, ``Revisit of system variable trajectories``, Proceedings of the Symposium on Theory of Modeling & Simulation - DEVS Integrative M&S Symposium , San Diego, CA, USA, April 7–10, 2013