Ranking-Based performance Analysis of Hierarchical Computing Network under Task Impatience

Abstract

Computer networks and distributed processing systems often operate under uncertain traffic conditions, where arrival rates, service rates and task abandonment cannot be represented precisely by crisp parameters. This study presents a ranking-based performance analysis of an M/M/1 Jackson-type network queueing system with task impatience under fuzzy and intuitionistic fuzzy environments. The proposed model consists of two processing nodes and one Central Server with finite capacity, external arrivals, routing from nodes to the Central Server, balking and reneging. Triangular fuzzy, trapezoidal fuzzy, triangular intuitionistic fuzzy and trapezoidal intuitionistic fuzzy numbers are used to represent uncertain arrival and service rates. The transient state probabilities are formulated through Kolmogorov forward equations and solved numerically using the fourth-order Runge–Kutta method in MATLAB. Expected system length and mean waiting time are evaluated for Node-1, Node-2 and the Central Server. Robust ranking and wingspan methods are applied to convert fuzzy and intuitionistic fuzzy performance measures into comparable ranked values. The results show that uncertainty decreases as the α-cut value increases in fuzzy models, while β-cut based intuitionistic fuzzy models provide more compact and stable intervals. Trapezoidal fuzzy and trapezoidal intuitionistic fuzzy models give more controlled uncertainty ranges than triangular fuzzy models. Node-1 shows the lowest congestion, Node-2 shows moderate congestion and the Central Server shows the highest congestion. The proposed approach is useful for congestion-aware task scheduling, routing control and capacity planning in computer networks, cloud systems and distributed computing environments.