Towards a Science of Networks: Communication Networks I

1. Towards a Science of Networks:Communication Networks I Report on workshop held at the University of Birmingham, UK, 3 – 4 November 2005 (including brief comments on Rome and Budapest workshops) Costas Constantinou

2. Workshop aims • Examine communication network theory from different perspectives – physics, engineering and computer science • Take stock of state of the art • Challenge “conventional wisdom” assumptions for network design/operation (strong held opinions versus fundamental properties) • Define a set of grand challenges to enable the creation of a coherent scientific theory of networks

3. Some background history • Workshop was preceded by a U.S. workshop on the complex behaviour of adaptive, network-centric systems, hosted by the University of Maryland on 12 – 14 July 2005 • Interdisciplinary aspects of complexity science • Applicability to predictable emergent behaviour in distributed systems/networks • Very strong emphasis on wireless networks

4. Workshop presentations • Report on Workshop on the Complex Behaviour of Adaptive, Network-Centric SystemsDr. Stuart D. Milner, University of Maryland • Logical Network Abridgement leading to Diversity and Resilience Measures on NetworksDr Costas Constantinou, University of Birmingham • Spreading Processes on Complex Networks: Theory and ApplicationsMaziar Nekovee Complexity Group, Mobility Research Centre, BT

5. Workshop presentations (cont.) • Algorithms and Survivable Protocols for Scale-Free and Scale-Free Small World NetworksAndrás Lörincz, Eötvös Loránd University • Information flow issues in cross-layer models of wireless communication networksProfessor Leandros Tassiulas, University of Thessaly • MAC-Layer Selfish Behaviour in Wireless Networks: A Repeated Game ApproachJerzy Konorski, Gdansk University of Technology

6. Workshop presentations (cont.) • Transmit beamforming strategies for PHY-layer multicasting with QoS guaranteesProfessor Nikos Sidiropoulos, Technical university of Crete – Greece • Traffic theory for the Internet and its implications on network designJim Roberts, France Telecom • Congestion and CentralityRaul J. Mondragón, Queen Mary, University of London

7. Workshop presentations (cont.) • Physics of networks: state of the artJosé F. F. Mendes, University of Aveiro • Large-Scale Behaviour of Packet-Switched NetworksSanya Stepanenko, University of Birmingham

8. Workshop panel discussions • The first panel session concentrated on the network properties that need to be predicted reliably • Conclusion: Nearly all observable variables are either data rates, such as capacity, throughput, loss rate, etc., or delays, such as packet transport delay, start-up and recovery times, etc., all of which should be predicted statistically to estimate their distributions & correlations, as their mean values are not sufficient

9. Workshop panel discussions (cont.) • The second panel session attempted to list the ingredients for a viable theory of networks • Four main components to such a theory: • Input traffic demand to a network • Network topology • Routing protocol operation and • Interaction between above three components • A clean separation of time-scales for the various component processes would make the formulation of a theory of networks easier, but the discussion did not go into establishing whether such a separation is applicable

10. Workshop panel discussions (cont.) • Conclusion: The individual components of a theory of networks already exist and are well understood in isolation. However, these partial theories fall short of an overall theory of networks in two ways: • The interactions between different components need to be specified in a unified framework, taking particular care to determine the relevant time-scales pertinent to the problem under study • Even though in principle current formalisms can be used to describe networks in all their aspects, the number of variables becomes intractably large even for modest sized networks

11. Rome Workshop • Biologically Inspired Information Systems Workshop • Held in Rome, 24 – 26 July 2006 • Organised by the Università di Roma – La Sapienza • Funded by ONR

12. Rome Workshop • Biologists largely working with neural networks (NN) • NN nodes are non-linear and have non-linear interactions • NN are viewed as computation circuits • Unlike communication networks coarse-graining is meaningless within our current framework of understanding • Neuroplasticity, i.e. the brain's ability to reorganize itself by forming new neural connections to compensate for injury and disease and to adjust its activities in response to new situations or to changes in their environment, is an interesting unexplored mechanism that could be exploited in self-healing networks

13. Rome Workshop (cont.) • Analogies with some biological networks are useful: • Routing based on social insect paradigm (ants) • Synchronisation based on coupled oscillators (fireflies) • Topology management in overlay networks based on differential cell adhesion • Immune system inspired security • Game theory [not really biology, but economics] for emergence of self-organised cooperation

14. Rome Workshop (cont.) • General problem is the very restricted range of known/predictable emergent behaviour from local interaction rules • Concept of time/time-scales and their impact on dynamics is often based on educated guesswork • Strict adherence to biological analogies not always sensible – should only be used as starting point

15. Budapest workshop • Social Networks and Complexity Workshop • Held in Budapest, 31 July – 2 August 2006 • Organised by the Institute for Advanced Study at the Collegium • Co-funded by AFOSR and ONR

16. Budapest workshop (cont.) • Social scientists are heavily concerned with the study of social network structures: either that of static topologies (e.g. clustering, cliques, etc.), or the topology evolution “dynamics” • Theory (random, scale-free and small world graph [growth process] models dominate); eigenvector spectrum of connectivity matrix • Numerical simulations (node/link decimation/addition, percolation thresholds) • Measurements

17. Budapest workshop (cont.) • Simple coupled dynamical process node models (agents as local dynamical processes – often based on Game Theory) • Co-clustering of overlay processes on network topology using bi-partite graphs – A bipartite network can be used as a (general) mapping between two interacting networked processes • Smallpox epidemic dynamics (not social networks) has strong similarities to mobile ad hoc networks • Many social networks tend to be “networks” in a not very precise sense

18. Common problems across disciplines • Topology and overlay processes are both dynamic – but often on different time scales • Layering of processes (more than one overlays) • The predictable mapping local interaction behaviours to emergent global observable properties is poorly understood • Not enough effort goes towards identifying differences as opposed to similarities (not everything is scale-free symptom)

19. Common problems across disciplines (cont.) • Identifying and modelling the sources of stochasticity is often incompletely done • Too many types of topology classification (taxonomy), but no fundamental understanding of topology groups/types • No identified order parameters for emergent properties – conversely we know nothing about invariants

20. Differences between disciplines • Exaggerated view: • Communications • Data flow networks • Routing process • Biology • Neural networks • Topology re-construction and pattern identification • Social sciences • Agent networks • Static topology analysis

21. State of the art? • All three disciplines are currently posing problems • New problems that arise could lead to a convergence in the posing of the fundamental problems in network science