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.
Hotspot is not scalable.
3G is in order of 100 kbps
Mesh uses WiFi but extends the range by mutihop.

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: Utility for relays: = 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: Relays:
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) Scenario (100 nodes) U1 α U2 β1 β2 SO (#GW/U) NE
GW uses T1
-410 10 30 1 20
1 / 700
2 / 490
GW uses cable
20 / 2760
26 / 2683
T1GW, charge cable price 40
1 / 3550
7 / 1075
T1GW, low charge 5 35
3 / 380
1 / 350

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.