A Unified Framework for Transient Analysis in Queueing Networks

This paper presents a unified framework for transient analysis of cascaded M/M/c/K networks with split and merge under multiple service policies, including first-come-first-served (FCFS), priority, percentage, and circulate. A history-buffer mechanism is introduced to preserve temporal arrival composition, enabling propagation of nonstationary departures across interconnected nodes without enlarging the state space. Coupled with time-dependent Kolmogorov forward equations, a stable explicit iteration is developed to compute transient queue-length distributions. Numerical experiments verify that the proposed method can accurately reproduce full transient dynamics across multi-stage networks.

© 2026 IEEE. All rights reserved, including rights for text and data mining, and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission.