Analysis of computational systems: Discrete Markov analysis of computer programs

Authors:
C. V. Ramamoorthy
Affiliations:
-
Venue:
ACM '65 Proceedings of the 1965 20th national conference
Year:
1965

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Abstract

A PROGRAM with a number of subroutines can be represented by a flow diagram; Figure 1. The nodes represent the subroutines and the directed branches indicate the allowed transitions between them. Given a program consisting of n subroutines R1, R2 .....Rn, two matrices are also assumed to be known, viz., an n × 1 matrix of execution times of each subroutine and a n × n matrix P, such that its ij-th element Pij is the branching probability that the program will branch to subroutine j from subroutine i. We shall assume Pij's are statistically independent so that the model of the computer program is that of a discrete Markov process. The expected time to complete a program is then a summation of all possible statistically weighted paths that begin at an initial or starting subroutine and end at the terminal subroutine.