Cart (Loading....) | Create Account
Close category search window
 

Control of Fork-Join Networks in heavy traffic

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Atar, R. ; Fac. of Electr. Eng., Technion - Israel Inst. of Technol., Haifa, Israel ; Mandelbaum, A. ; Zviran, A.

A Fork-Join Network (FJN) is a natural model for a queueing system in which customers, or rather tasks associated with customers, are processed both sequentially and in parallel. In this paper we analyze a network that, in addition, accommodates feedback of tasks. An example of a FJN is an assembly operation, where parts are first produced and then assembled to ultimately create a final product. Another example is an emergency department, where a patient “forks” into, say, a blood test and an X-ray, which must then “join” the patient as a prerequisite for a doctor examination. There is a fundamental difference between the dynamics of these two examples: In an assembly network, parts are exchangeable while, in an emergency department, tasks are associated uniquely with patients. They are thus nonexchangeable in the sense that one cannot combine/join tasks associated with different customers. In single-server feed-forward FJNs, FCFS processing maintains a fully synchronized flow of tasks. Probabilistic feedback, however, introduces flow disruptions that give rise to task delays and ultimately a decrease in throughput rate. Nevertheless, we show that a simple flow control of tasks can render this decrease of performance asymptotically negligible (though it is not absolutely negligible). More specifically, we analyze a concrete FJN, with nonexchangeable tasks and Markovian feedback, in the conventional heavy-traffic (diffusion) regime. We prove asymptotic equivalence between this network and its corresponding assembly network (exchangeable tasks), thus establishing asymptotic throughput-optimality of our control. The analysis also reveals further interesting properties, such as state-space collapse of synchronization queues.

Published in:

Communication, Control, and Computing (Allerton), 2012 50th Annual Allerton Conference on

Date of Conference:

1-5 Oct. 2012

Need Help?


IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.