Time Estimation Model of Concurrent Computing Systems

TL;DR

This paper introduces a mathematical model for estimating the minimum execution time of parallel processes in asynchronous computing systems, using shortest path algorithms on directed graphs.

Contribution

It presents a novel approach to model and compute the minimal execution time of concurrent instructions in asynchronous systems, reducing the problem to shortest path computation.

Findings

The model accurately predicts minimal process durations.

The shortest path approach simplifies complex timing analysis.

Applicable to various asynchronous computing scenarios.

Abstract

We consider an asynchronous system with transitions corresponding to the instructions of a computer system. For each instruction, a runtime is given. We propose a mathematical model, allowing us to construct an algorithm for finding the minimum time of the parallel process with a given trace. We consider a problem of constructing a parallel process which transforms the initial state to given and has the minimum execution time. We show that it is reduced to the problem of finding the shortest path in a directed graph with edge lengths equal to 1.