Steady-State Probabilities and Task Rejection/Failure Probability Estimation in the Multiprocessor Queueing System

Abstract

This research analyzes a multiprocessor queueing system M |M |m|n, focusing on estimating steady-state probabilities and utilizing them to calculate the probabilities of task access rejection and task failure due to waiting time restrictions. The study presents the development of numerical algorithms using the NumPy library in Python to gain insights into system performance and efficiency.Numerical algorithms were developed to evaluate the steadystate probabilities by efficiently solving the system of equations using matrix operations and tools from the NumPy library. With these probabilities in mind, calculations were performed for specific system parameters to determine the probability of task access rejection and task failure due to waiting time restrictions. The research highlights the practical applicability of these findings to real-world scenarios and discusses the potential use of high-performance computing systems for optimization.Overall, this research contributes to the understanding and enhancement of multiprocessor system efficiency. The developed numerical algorithms and implementation provide a foundation for further advancements in the field. By addressing challenges related to system performance and resource utilization, this study offers practical solutions for improving overall productivity in multiprocessor systems across various domains and applications.