Advanced Queueing Model of a Multiprocessor Computing System

Abstract

This paper presents an advanced queueing model for a multiprocessor computing system, where tasks require a random number of processors and are subject to constraints on waiting times in the queue. Unlike classical multi-server queueing systems, this model accounts for both resource requirements and queue waiting time restrictions, making it more suitable for real-world computing environments. By incorporating the probabilistic behavior of task arrival, service, and waiting constraints, the expressions are derived for key performance metrics, including the probabilities of task rejection and failure, system throughput, and resource utilization. An algorithm for determining the optimal queue length is also developed to enhance system efficiency by minimizing the probability of task losses. The proposed model provides a framework for analyzing and optimizing resource allocation in multiprocessor systems, improving their capability to handle dynamic and complex workloads.