Modelling Of Multi-Node Computer Networks With Task Abandonment And Transient Congestion Analysis

Abstract

Modern distributed computing environments, including cloud platforms, data centers, communication networks, web servers and edge computing systems, frequently operate under dynamic workloads, limited processing capacity, transient congestion and delay-sensitive task behavior. This paper presents a transient analysis of a finite-capacity M/M/1 Jackson-type queueing network with impatient tasks for modelling multi-node computer systems. The proposed network consists of two distributed processing nodes connected to a central server. Tasks enter the system from the outside on different nodes, are served, possibly routed to the central server or leave the system because of impatience by balking and reneging processes. The transient state probabilities are developed by Kolmogorov forward differential equations and computed numerically through forth order Runge–Kutta approximation, which is programmed in MATLAB. The performance of the node-wise and central-server is measured in terms of expected buffer occupancy, mean processing delay, congestion level and propagation of workloads. The graphical results show progressive workload accumulation during the transient period, with increasing buffer occupancy and processing delay as the system evolves. The central server has the greatest congestion due to the fact that it receives the external arrivals as well as the tasks that are routed from the distributed nodes, and thus is the main congestion point of the network. Sensitivity analysis suggests that an increase in the arrival rate and the routing probabilities will lead to an increase in congestion and delay, while an increase in service rates will lead to an improvement in processing efficiency and a decrease in waiting. Balking and reneging shorten the length of queues and delay, but are task loss in delay-sensitive applications. The proposed model would be a convenient analytical tool for transient congestion, resource allocation, bottleneck identification and service performance in multi-node computer networks.