Program takes a network with multi-parameter branches and reduces it to a network having a single branch connecting source nodes to sink nodes. The program calculates probability, expected time, and variance in the time to go from each source node to each sink node of the GERT network

Alan, A.

Pritsker, B.

English

NASA Technical Reports Server

December 1968	 Brief 68-10435 
NASA TECH BRIEF 
NASA Teèh Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
(GERT EXCLUSIVE-OR) Program for Combining Paths and

Loops of Electrical Networks 
The problem: 
To develop a procedure for analyzing GERT net-
works containing only EXCLUSIVE-OR nodes. 
The solution: 
The GERT EXCLUSIVE-OR program takes a net-
work with multiparameter branches and reduces it to 
a network which has only a single branch connect-
ing source nodes to sink nodes. The program cal-
culates probability, the expected time and the variance 
in the time to go from each source node to each sink 
node of the GERT network. 
How it's done: 
The GERT EXCLUSIVE-OR program determines 
the paths and loops associated with the net-
work and combines the values associated with paths 
and loops according to a topology equation to ob-
tain the parameters associated with the equivalent 
branch from the source node to the sink node. The 
program determines the source nodes, the sink nodes, 
the paths connecting the source nodes to the sink 
nodes, and the loops of the network. The standard 
output from the program includes: (I) appropriate 
problem identification headings; (2) the paths and 
loops of a network; (3) the probability of realizing 
a sink node from any source node; and (4) the mean 
and variance of the time to realize a sink node, given 
that the sink node is realized and given an initial 
source node. The option exists to delete the loop 
and/or path output for large or complex networks 
if it is so desired. The exercising of this option can 
be beneficial on machines having relatively slow prin-
ters or on high speed printers where the standard oper-
ating practice is to have a relatively low print limit.
Input to the program includes appropriate problem 
identification information and the branches of the net-
work. Information concerning each branch includes 
the start node and end node for the branch, the prob-
ability of realizing the branch, and data about the 
moment generating function of the random variable 
associated with the branch. The moment generating 
function (MGF) is described by a three-letter code and 
up to two parameters of the MGF. The program de-
termines all paths and loops of the network based on 
the input information. The desired. output statistics 
are computed using the values associated with the 
loops and paths of the network. 
The starting point for the GERT program is the 
main program, but the only program exit poi.nt is in 
subroutine INPUT. An EXIT occurs when a negative 
value is Obtained in field I of a data card. The first 
error message indicated is one that says that a bad 
input code was detected in the input data. The entire 
input network will be read in, but due to the error, 
the network will not be analyzed. The next network is 
then considered. The second error message is printed 
if the number of entries in the dimensioned variable 
LOOP exceeds the size of LOOP. 
The values associated with the loops and paths of 
the network to obtain the desired output statistics are: 
(1) the probability; (2) the mean time; and (3) the 
second moment of the time. The probability associ-
ated with the loop or path is the product of the prob-
abilities of the branches comprising the loop or path. 
The expected time to traverse a loop or path is the 
sum of the expected times of the branches of the loop 
or path. The values associated with each loop or path 
are combined through a topology equation to obtain 
(continued overleaf) 
This document was prepared under the sponsorship of the National 	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States 	 will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19680000434 2020-03-12T06:00:00+00:00Z
	the equivalent w-function between the two nodes of	 3. Inquiries concerning this innovation may be di-
	
interest for a given path. If there is more than one 	 rected to: 
	
path, the w-functions associated with each path would	 COSMIC 
be summed.	 S	 Computer Center 
Notes	 University of Georgia 
1. This program is written in Fortran IV language for	 Athens, Georgia 30601 
	
use on the IBM-I 130 machine. There is another 	 Reference: B68-10435 
version in Fortran II for use on the GE-225.
	 Patent status: 
2. The program is limited in that the number of nodes
	 No patent action is contemplated byNASA. 
	
which can be accommodated by the program is de-
	 Source: A. Alan, B. Pritsker 
	
pendent upon the storage capacity of the machine
	 of Arizona State University 
	
being used. The present version is dimensioned to
	 under contract to 
	
permit a network with 100 nodes to be analyzed.
	 Electronics Research Center 
	
The program assumes that the machine used has
	 (ERC-10206)
only 8000 words of core storage. 
Brief 68-10435	
-	
Category 06


GERT EXCLUSIVE-OR combining paths and loops of electrical networks

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