General Open and Closed Queueing Networks with Blocking: A Unified Framework for Approximation

• Published in: INFORMS journal on computing Vol. 12; no. 4; pp. 299 - 316
• Main Authors: Vroblefski, Mark, Ramesh, R, Zionts, Stanley
• Format: Journal Article
• Language: English
• Published: Linthicum INFORMS 01.11.2000; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Approximation; Design; inventory-production: approximations-heuristics; Packet switched networks; Queuing theory; Studies; Systems design
• ISSN: 1091-9856; 1526-5528; 1091-9856
• DOI: 10.1287/ijoc.12.4.299.11878

In this paper, we develop a unified framework for approximating open and closed queueing networks under any general blocking protocol by extending and generalizing the approximation algorithm for open tandem queues under minimal blocking presented in Di Mascolo et al. (1996). The proposed framework is based on decomposition. We develop decomposition structures and analysis algorithms for any general blocking system using the framework. The proposed algorithms have been extensively tested using simulations as a benchmarking device. The results show that the proposed framework yields robust, reliable, and accurate estimates of system characteristics, such as throughput and Work-In-Process inventory in a wide range of system configurations. The computational load is minimal. The unified framework presents a highly useful set of tools of analysis for queueing-system designers to use in evaluating the performance under numerous design alternatives. Directions for future research are presented, with a focus on critical application areas such as packet-switching-network design and cellular manufacturing.