Formation of Community-based Multi-hop Wireless Access Networks

1. Formation of Community-based Multi-hop Wireless Access Networks Gap Nattavude Thirathon EE228A Spring 2006 Prof. Jean Walrand

2. Outline • Motivation and the problem • Background • Model and result • Conclusion

3. Motivation • Emerging results in network formation research (for overlay, P2P, social) • Does it work for other types of networks, in particular, wireless mesh? • Many cities are deploying community-based wireless networks.

4. Characterization of Wireless Access Networks • Architecture • Hotspot: not scalable • Cellular: orders of magnitude slower than WiFi. • Mesh: cost-effective, scalable • Directional or omni-directional antennas • Who deploys the system? • Centrally planned and deployed, e.g. by companies, municipal government, state, etc. • Unplanned deployment by residents.

5. Problems • How does game theory predict the outcome of this community-based wireless network? • Can the network be totally autonomous, i.e. without any central authority that deploys the wired gateway. • Develop a simple model to answer these questions.

6. Community-based Multi-hop Wireless Mesh Network • Everyone contributes resources: relay for others. • Problems to be solved • Range and capacity • Multi-hop, selfish routing • Fairness • Privacy and security • Business model • This project looks at the topology of the network and its formation.

7. Network Formation • Networks are formed by utility-maximizing nodes. Utilities depend on the network topologies. • Existing works are mostly on overlay logical network. • Choices are which links to build or remove. • Utilities/costs are routing delay, throughput, maintenance, etc.

8. Overlay Network Formation • Examples of overlay: P2P, distributed lookup service, VPN. • Nodes are connected in physical network by links and form logical overlay network on the top. • We can model the underlying network as a complete graph. Some edges have infinite cost. • Choices for each node is which other nodes to connect to.

9. Overlay Network Formation(2) • Total shortest distance cost model (Fabrikant et al, Chun et al.): • Links are two-way and are paid for by either or both of the two end nodes. • The cost for each node is α * # links built by the node + sum of shortest distances to all other nodes. (routing cost if shortest path routing is used) • Result: • α<2: SO is a clique. NE is a star. POA = 4/3. • α>2: SO is a star. NE is yet unclear. POA = O(√α) • Tree conjecture: There is A s.t. for all α>A, all non-transient NE are trees.

10. Overlay Network Formation(3) • Another cost model (Christin & Chuang): • Also assume shortest path routing. • Items are distributed among nodes. Other nodes request for items. (Think P2P.) • Cost(u) = latency + serving + routing + maintenance = l*E[tu,v] + s/N + r*E[Χv,w(u)] + m*deg(u) • tu,v = # hops (u,v) • s = cost of serving a request. Assume items are uniform. • Χv,w(u) = 1{u on path from v to w} • Result: • A clique is both SO and NE for m < l/N (Maintenance cost is relatively low.) • A star is both SO and NE for m > l/N + r/N^2 • For l/N < m < l/N + r/N^2, a clique is SO and a star is NE.

11. Model for Wireless Mesh • Nodes (houses) are placed 1 unit apart, from 1 to N. • The range of wireless connection is 1. • Route to the nearest gateway. • Nodes obey routing protocol (always relay the traffic), assuming some payment structure.

12. Model (2) • The gateway can collect some payment from connecting nodes. • Nodes choose between being gateways and wireless relays. Each node knows the entire network structure (complete information). • Consider only recurring cost and ignore fixed cost of hardware installation. • Assume utilities do not increase beyond cable speed.

13. Model (3) • Utility for gateway: • = U1 + αx • U1 = utility from connection less the cost of wired connection • x = number of connecting relays • α = payment per connecting relay • Utility for relays: • UR = U2 - f(m,n) • U2 = utility from connection less price paid • m = number of nodes to relay for • n = number of hops to the nearest gateway

14. Model (4) • f(m,n) is a reduction in utility. • f(m,n) increases with m and with n • Use f(m,n) = β1m+β2-β2/n Data from Bicket et al

15. Social Optimum Structure • If we fix # GW, the structure is as below. Each GW gets the same number of connecting nodes.So we just need to find the best # GW.

16. Nash Equilibrium Structure • We have probably heard of “concession stands on a beach” problem. The NE is all in the middle. • This problem is different. Moving a GW is not a unilateral move. People do not just move their houses. • There are many NE: GW cannot be too far. Otherwise, some relays in the middle will change to GW. • NE depends on initial condition and action order. • If view the game as multiple-stage, first mover has an advantage.

17. Nash Equilibrium Structure (2)

18. Numerical Results • Gateways: • Getting connected is like getting cable  $40 value. • Cost for T1 = $450  U1=-410, or U1=0 for cable. • Charge $10 for each connected node  α=10, or charge cable price α=40. • Relays: • Being connected to the internet at high speed give $40 value, less the price charged by GW  U2=40-α=30) • Β1=1. β2=20. As # hops increases, the utility reduces to those of dialup $10.

19. Numerical Results (2)

20. Conclusions • If residents can provide gateways and charge prices, we will reach NE, which can be inefficient. • If gateways cannot charge prices, nobody wants to be the first gateway. • Initial condition and action order determine the NE. • Planned positioning of the gateways leads to better NE. • Need to study if routing protocols and more complicated payment schemes affect the structure.