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Contents 1 Description 2 State Variables 3 Vertices 4 Initialization Conditions 5 Event Relationship Graph 6 English Translation 7 Comments

Description

NESTLOOP.MOD models two nested do-loops for I=0,...,N and J=0,...,M. The model consists of three vertices: one to start the run and initialize N and M, one that has the two nested loops, and one that ends the run when the loops are finished.

State Variables

State Variables in NESTLOOP.MOD

Variable Name	Variable Description	Size	Type
I	Inner loop index (0 TO N)	1	Integer
J	Outer loop index (O TO M)	1	Integer
N	Upper limit on inner loop	1	Integer
M	Upper limit on outer loop	1	Integer

Vertices

Vertices in NESTLOOP.MOD

Vertex Name	Vertex Description	State Changes
INITL	Initialization of the loop limits	None
LOOP	Body of the nested loop	None
OVER	End of the looping operation	None

Initialization Conditions

Initialization Conditions in NESTLOOP.MOD

Variable	Description
N	Upper limit on inner loop
M	Upper limit on outer loop

Event Relationship Graph

English Translation

An English translation is a verbal description of a model, automatically generated by SIGMA.

The SIGMA Model, NESTLOOP.MOD, is a discrete event simulation. 
It models TWO NESTED DO-LOOPS FOR I=0,...,N AND J=0,...,M.

I. STATE VARIABLE DEFINITIONS.

For this simulation, the following state variables are defined:

I: INNER LOOP INDEX (0 TO N)   (integer valued)
J: OUTER LOOP INDEX  (O TO M)   (integer valued)
N: UPPER LIMIT ON INNER LOOP   (integer valued)
M: UPPER LIMIT ON OUTER LOOP   (integer valued)

II. EVENT DEFINITIONS.

Simulation state changes are represented by event vertices (nodes or balls) in a SIGMA graph.  
Event vertex parameters, if any, are given in parentheses. Logical and dynamic relationships 
between pairs of events are represented in a SIGMA graph by edges (arrows) between event vertices.  
Unless otherwise stated, vertex execution priorities, to break time ties, are equal to 5.

1. The INITL(N,M) event occurs when INITIALIZATION OF THE LOOP LIMITS.
   Initial values for, N,M, are needed for each run.
   After every occurrence of the INITL event:
   Unconditionally, schedule the LOOP(I,J) event to occur without delay...
   using the parameter value(s) of 0,0.

2. The LOOP(I,J) event occurs when BODY OF THE NESTED LOOP.
   After every occurrence of the LOOP event:
   If I<N and J<=M, then schedule the LOOP(I,J) event to occur in 1 time units...
   using the parameter value(s) of I+1,J.
   If I==N and J<M, then schedule the LOOP(I,J) event to occur in 1 time units...
   using the parameter value(s) of 0,J+1.
   If I==N and J==M, then schedule the OVER() event to occur without delay.

3. The OVER() event occurs when END OF THE LOOPING OPERATION.
   No additional events are scheduled here.

Comments

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