1. Optimal Placement of Relay Infrastructure in Heterogeneous Wireless Mesh Networks by Bender’s Decomposition Aaron So, Ben Liang University of Toronto, Canada ACM International conference on Quality of service in heterogeneous wired/wireless networks ( QShine 2006)

2. Outline  Introduction  System model  Optimization  Numerical results  Conclusion

3. Introduction Broadband wireless has long held the promise of delivering a wide range of cost-effective data services. Because of the size of the coverage area, the base station usually cannot serve every subscriber by a single-hop communication. As a result, several relay stations (RSs) are installed in the network to relay traffic from the base station.

4. Introduction Motivation The placement of wireless network equipments can have significant impact on network performance. Goal Place the minimum number of relay stations in the network such that the demands of the subscribers can be met.

5. System Model Suppose there are N users and one base station in the system, and they are represented by the set V = {0, 1,..., N}, where the base station is represented by the index 0. For each user i, there is a pre-specified uplink demand, u i, and downlink demand, d i.

6. Optimization – Inputs and decision variables ParameterValue BC ij Capacity from node i to node j by using the backbone technology. LC ij Capacity from node i to node j by using the local technology. XiXi 1: if an RS is installed at node i. 0: otherwise 0 < i ≤ N Downlink flow from node i to node j by using backbone technology (bps). Uplink flow from node i to node j by using backbone technology (bps). Downlink flow from node i to node j by using local technology (bps). Uplink flow from node i to node j by using local technology (bps).

7. Optimization – Inputs and decision variables ParameterValue BC ij Capacity from node i to node j by using the backbone technology. LC ij Capacity from node i to node j by using the local technology. XiXi 1: if an RS is installed at node i. 0: otherwise 0 < i ≤ N Downlink flow from node i to node j by using backbone technology (bps). Uplink flow from node i to node j by using backbone technology (bps). Downlink flow from node i to node j by using local technology (bps). Uplink flow from node i to node j by using local technology (bps).

8. Optimization – Inputs and decision variables ParameterValue BC ij Capacity from node i to node j by using the backbone technology. LC ij Capacity from node i to node j by using the local technology. XiXi 1: if an RS is installed at node i. 0: otherwise 0 < i ≤ N Downlink flow from node i to node j by using backbone technology (bps). Uplink flow from node i to node j by using backbone technology (bps). Downlink flow from node i to node j by using local technology (bps). Uplink flow from node i to node j by using local technology (bps).

9. Optimization – Inputs and decision variables ParameterValue BC ij Capacity from node i to node j by using the backbone technology. LC ij Capacity from node i to node j by using the local technology. XiXi 1: if an RS is installed at node i. 0: otherwise 0 < i ≤ N Downlink flow from node i to node j by using backbone technology (bps). Uplink flow from node i to node j by using backbone technology (bps). Downlink flow from node i to node j by using local technology (bps). Uplink flow from node i to node j by using local technology (bps).

10. Optimization Formulation Objective function: s.t. BS RS MS RS MS

11. Optimization Formulation Objective function: s.t. BS RS MS RS MS

12. Optimization Formulation RS MS RS MS

13. Optimization Formulation RS MS RS MS

14. Optimization Formulation RS MS BS

15. Optimization Formulation RS MS BS

16. Optimization by Bender’s Decomposition Because this problem is NP-hard, we propose an efficient optimization algorithm based on Bender’s decomposition to iteratively compute converging bounds to the problem solution. Site 1 Site 2 Site 3 User 1 User 2 User 3 User 4

17. Optimization by Bender’s Decomposition Add new constraints ex: Distance, signal strength

18. Optimization by Bender’s Decomposition

19. Numerical results ParameterValue Backbone networksIEEE 802.16 Wireless MAN-SC technology Local networksIEEE 802.16 Wireless MAN-OFDM technology Path loss exponentLocal networks: 2.8 Backbone networks: 2.4 ChannelLocal networks: 5 MHz Backbone networks: 20 MHz User demandUplink: 1Mbps Downlink: 2Mbps

20. Numerical results

23. Conclusion They propose to use Bender’s decomposition to compute the minimum number and placement of RSs of a heterogeneous wireless mesh network. The proposed optimization technique can be used by network designers to provide design guidelines and maintenance cost estimations.

24. Thank you!