Model of a System for Servicing Multiprocessor Tasks without a Queue

This paper investigates a multiprocessor queueing system where tasks require varying numbers of processors for service i.e., unlike classical multiserver queuing systems, here, to service each task needs a specific required number of service nodes. It presents a detailed model and derives analytical solutions for the steady-state probabilities of the system. The study addresses the challenges of organizing computations in multiprocessor environments, considering factors such as task arrivals, service times, and resource constraints. Through rigorous mathematical analysis, this work provides insights into the dynamics of task scheduling and resource utilization in such systems. Our findings contribute to advancing queueing theory applications in multiprocessor systems and offer valuable implications for optimizing resource allocation and system performance in practical computing scenarios.