1. 4-Regular Grid Networks Jens Myrup Pedersen Department of Control Engineering Center for Network Planning Center for TeleInfrastruktur Aalborg University

2. Overview Motivation – 3 flashes. Topological Routing and 4-regular grid. Future work. Conclusion.

3. Flash 1: Convergence of communications Convergence of communications (tv, radio, voice over the same single line). Increasing use of computers and computer networks. More critical data -> use of remote storage/back-up. New applications are being developed, including applications in tele- medicine, surveillance, home security, home control. Even short times without connectivity will be critical. A reliable ICT infrastructure is needed.

4. Flash 2: Another infrastructure..... (Returning to the telephony networks) 2004: 10.400 claims for compensations for cable cuts (TDC Network). 2005 (until June 3): 36 cases of large cable cuts (>1000 subscribers affected). Largest claim for compensations was in 2001, where an entrepreneur destroyed 8 fiber- and copper cables under a road in Herlev near Copenhagen. This claim exceeded 4 mio. DKR (more than ½ mio. EUR). Old fact: Single points of failures are not acceptable in the road network. New fact: Single points of failures are not acceptable in communication networks.

5. Flash 3: The demand for a new ICT infrastructure Only FTTH networks can provide sufficient bandwidth. Furthermore, FTTH networks are upgradeable by changing end equipment only. The deployment of FTTH has already begun. Bandwidth requirements: It is hard to predict - especially about the future..... Scalability: Ipv6 supports up to 655.570.793.348.866.943.898.599 IP adresses on every sqm of the surface of the earth!

6. Flashs 1+2+3 A new ICT infrastructure is about to be established. It will carry services with different demands: Reliability, bandwidth, delay, jitter. It must also support applications not known today. The physical topologies are important! No algorithms can perform better than allowed by he physical structures. Designing and implementing this infrastructure is a huge task, and it should be done right at the first attempt. Problem: Lack of methods for planning infrastructures with well- defined and describable structural properties (SQoS: Structural Quality of Service). Aim: Construct networks with global structural properties. Idea: Use regular graph structures.

7. Topological Routing and grid networks Inspiration from orienteering: Finding the direction from knowledge of current location and destination.

8. Topological Routing and grid networks Sometimes this is easy:

9. Topological Routing and grid networks Sometimes it is impossible:

10. Topological Routing and grid networks Example: Good one and bad one.

11. Topological Routing and grid networks 4-regular grid, used in multiprocessor systems. Major differences: Reliability: The network must handle short- and long term failures Scalability: Power-law connection between number of nodes and distances in the network Flexibility: The world is not square, and in some areas the networks should be more dense than in other areas. Furthermore, it must be possible to expand the network during its lifetime.

12. Topological Routing and grid networks In order to make the 4-regular grid more feasible, a number of extensions were developed: Hierarchical extension, reducing distances. Leaving out certain layers gives flexibility and expandability. Pruning, reducing costs and increasing reliability. Lake algorithms, for handling failures. Protection schemes.

13. Topological Routing and grid networks Hierarchical extension

14. Topological Routing and grid networks Hierarchical extension - variants

15. Topological Routing and grid networks Hierarchical extension - flexibility

16. Topological Routing and grid networks Pruning reduces cost and facilitates implementation (inspired by Stojmenovic and the honey comb networks).

17. Topological Routing and grid networks

18. Restoration and protection.

19. Topological Routing and grid networks The good question: How well does this toolbox support real-world implementations? Answer: It depends, but automatic methods/tools are needed to find out. Ongoing CTIF sponsored research deals with this problem, and methods are under development (Ph.D. project by Tahir Riaz).

20. Stojmenovic – Honey Comb