1. Adviser: Frank,Yeong-Sung Lin Present by Limin Zheng Gunhak Lee, Alan T. Murray

2. Agenda  Introduction  Backgroud  Problem description  Mathematical formulation  Application details  Results & Discussion  Conclusions

3. Intorduction

4. Introduction Many US cities and Countries are attempting to build wireless broadband networks for communication and service in their communities as basic infrastructure to facilitate local economic development and enable much wider service provision to more people.  wireless networks in municipalities have been widely utilized for a range of public applications, such as public hotspots, public safety and general communication  Wireless broadband networks would play an important role in improving the quality of our life, giving people the freedom and capability to communicate with the world anytime, anywhere  Advanced wireless broadband technologies, such as Wi-Fi, WiMax and cellular systems, relying on mesh or multi-hop networking.  Wireless broadband is attractive to municipalities willing to construct their own communication network given limited budgets.

5. Introduction What is the primary concern in providing wireless broadband services ?  When local governments attempt to provide wireless broadband services to their communities, the primary concern is where to place relevant facilities and how to connect them. What is the purpose of this paper ?  In this paper, we address location modeling approaches for integrating maximal covering and survivable network design in planning citywide wireless broadband services. More specifically, we propose a mathematical formulation of the maximal covering problem with survivability constraints based on wireless mesh network topology.

6. Backgroud

7. Background Survivable network design  What is survivable network ?  What is disjoint path?

8. Background Wi-Fi based mesh networks  What is mesh networks

9. Problem Description

10. For the purpose of this paper, we specifically address two issues: (1)how to locate Wi-Fi equipment to maximally cover demand given a specified number of units. (2)how to connect Wi-Fi equipment to ensure survivable networking. Solution: For(1)Maximal Covering Location Problem (MCLP) For(2) Number of node disjoint paths for any pair of nodes

11. Problem Description  Regarding the architecture of a mesh wireless network, some of nodes (gateways) must be connected to hard, land based infrastructure and thus reliable performance of network is dependent on the existence of duplicated paths between a general node and gateway node.

12. Mathematical Formulation

13. Model: Maximal Covering problem with Survivability Constraints (MCSC) Assumed based on equipment capabilities : 1.Maximum distance of wireless access form the Wi-Fi router. 2.Maximum distance for wired access from the exiting backbone infrastructure. 3.Maximum distance for interconnection between the Wi-Fi routers.

14. Mathematical Formulation Something need to predefined or given when using this model : 1.Potentially eligible sites to provide wireless broadband services constitute a discrete set of locations. 2.Set of points is predefined to represent aggregate population to be covered by the Wi-Fi router. 3.A number of facilities, p, is given exogenously. 4.a number of Wi-Fi routers, q, providing wired connection to the existing backbone infrastructure, is also specified in advance.

15. Mathematical Formulation Based on the hierarchy of a wireless broadband network, parameters and sets are defined as follows: Iset of demand nodes Jset of potential sites for Wi-Fi router Mset of existing DSL central offices aiai population at demand node I prequired number of Wi-Fi routers to be deployed qrequired number of Wi-Fi routers for wired connections to existing central offices Krequired number of disjoint paths d ij shortest distance from demand node i to Wi-Fi router at j d jc shortest distance from Wi-Fi router at j to DSL central office at c d jl shortest distance between Wi-Fi routers at j and l

16. Mathematical Formulation NiNi {j єJ|d ij ≤ R} Ψ{j єJ|d cj ≤ L, c є M} ΩjΩj {l єJ|d jl ≤ W, j ≠ l} Rcoverage standard for Wi-Fi; Lcoverage standard for DSL central office Wmaximum distance for Wi-Fi router point to point interconnection

17. Mathematical Formulation Decision variables are defined as follows:

18. Mathematical Formulation

21. Application Details

22. 1.It is assumed that wireless routers must be within 12,000 feet (L) from a central office. 2.The coverage standard of a Wi-Fi router (R) is specified as 3465 feet, so 6930 feet is used for the maximum distance for Wi-Fi point to point interconnection (W) 3.The required number of Wi-Fi routers (p) is specified to be in the range of 8–29. 4.It is assumed that 20% of Wi-Fi routers satisfy the required number of wired connections to existing central offices (q). 5.Two cases of disjoint paths, K = 1 and K = 2, are examined for survivable network design.

24. Application Details The MCSC was solved exactly using a commercial optimization solver, named CPLEX 10.0 (ILOG) on an Intel Xeon 3 GHz CPU with 3 GB memory. ArcGIS 9.1 was used to manage needed input information (Ni, W, xj) through spatial analysis functionality. Also, Visual Basic Application (VBA) with ArcObjects was used to create the necessary text file of the MCSC that is read into CPLEX. Further, GIS provides capabilities for visualizing and evaluating solutions.

25. Results & Discussion

31. Discussion In this paper, we focus on system reliability for comparison between two different network configurations. For each network configuration, there are specific source and destination nodes. Accordingly, sets are defined as follows:

32. Evaluating system reliability Reliability of a node can be defined as the probability that it functions during a specified time period. Given node reliability, the probability of a disjoint path for a pair of source and destination nodes can be derived by the joint probability of nodes along the disjoint path, based upon the assumption of independence. Since there could be a number of disjoint paths between source and destination nodes, system reliability is the sum of the probabilities of all possible disjoint paths between source and destination nodes.

33. Evaluating system reliability The standard mathematical formulation of system reliability can be found in Shier (1991), and stated as follows:

34. Evaluating system reliability Average system reliability for entire network, Raverage, is computed by averaging the reliabilities for all pairs of source and destination nodes as follows: where Q is the number of all pairs of source and destination nodes.

35. Evaluating system reliability Node reliability probabilities are assumed (0.8 in our case) Kp(s)q(t) S-t pairs (Q) Disjoint path R average 111660710.69 211440800.41 For examining these two configurations in cases of a specific node failure, we calculate reliability after simulating any single node failure. K=1, average reliability = 0.5 K=2, average reliability = 0.61

36. Conclusions

37. Adequately positioning wireless access points is crucial in order to extend service coverage with a given budget limit. Another significant consideration for building wireless broadband networks is the provision of reliable broadband service. However, it is difficult to cover a large area reliably because a more reliable broadband network ecessarily requires a more interconnected network topology to ensure redundancy in routing.

38. Conclusions To deal with these considerations simultaneously, we introduced the maximal covering problem with survivability requirements (MCSC). This approach extends classical facility location and network design problems by explicitly integrating covering and network survivability. For more practical use of this approach, several related technical issues, such as radio coverage planning, traffic and routing controls and channel assignment, must be taken into account. This paper, however, focuses on general methodological issues concerning maximal covering and survivable network design. Thus, this paper is expected to help decision makers and network planners understand coverage and design issues through the use of a method for obtaining solutions and presenting expected network configurations.

39. Conclusions The application found that a wireless network can be designed to provide citywide wireless broadband services to an urban area, ensuring network survivability to a high degree. Comparatively, we also highlighted two types of tradeoffs. One tradeoff exits between coverage and the level of survivability. Another one exits between coverage and total cost.

40. Thanks for your listening.