論文進度報告 蔡永斌 Tsai, Yung-Pin 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Agenda Introduction Problem Formulation Lagrangean Relaxation Background Motivation Literature Survey Problem Formulation Problem Description Lagrangean Relaxation Lagrangean relaxation problem Subproblems 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Taxonomy of Wireless Networks Networking Multi-hop Infrastructure-less Single-hop Wireless Wide Area Networks (WWANs) Mesh Networks (WMNs) Infrastructure-based Wireless Local (WLANs) Metropolitan (WMANs) Personal Area Networks (WPANs) 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Infrastructure-based Taxonomy of WMNs WMNs Infrastructure-based Infrastructure-less Hybrid Infrastructure/ backbone WMNs Client WMNs Hybrid WMNs 分類方法參考自: I. F. Akyildiz, X. Wang and W. Wang, “Wireless Mesh Networks: a Survey,” Computer Networks, Vol. 47, Issue 4, Pages 445-487, March 2005. 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Infrastructure/backbone WMNs 圖擷取自: I. F. Akyildiz, X. Wang and W. Wang, “Wireless Mesh Networks: a Survey,” Computer Networks, Vol. 47, Issue 4, Pages 445-487, March 2005. 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Motivation Performance limitation of multi-hop wireless networks: Channel bandwidth is shared by a number of transmissions. Benefit gained through building relay nodes decreases when network grows. [1] Longer hop paths must bear significantly lower throughput compare with shorter paths. [2][3][4][5] The performance of the network can improve is limited, because the total network capacity has been constrained by network architecture. [1] P. Gupta and P. R. Kumar, “The Capacity of Wireless Networks,” IEEE Transactions on information theory, Vol. 46, No. 2, Pages 388-404, 2000. [2] I. F. Akyildiz, X. Wang and W. Wang, “Wireless Mesh Networks: a Survey,” Computer Networks, Vol. 47, Issue 4, Pages 445-487, March 2005. [3] B. Li, “End-to-End Fair Bandwidth Allocation in Multi-Hop Wireless Ad Hoc Networks,” Proc. IEEE ICDCS’05. [4] V. Gambiroza, B. Sadeghi and E. W. Knightly, “End-to-End Performance and Fairness in Multihop Wireless Backhaul Networks,” Proc. ACM MobiCom, Pages 287-301, Sept.-Oct. 2004. [5] Y. F. Wen and Frank Y. S. Lin, “The Top Load Balancing Forest Routing in Mesh Networks”, Proc. IEEE CCNC, pages 468-472, Jan. 2006. 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Motivation Even through during the operation stage we can deploy additional equipments or upgrade equipments to increase link capacity, throughput is not always raised[1]. The greatest motivation of our work: We consider end-to-end throughput fairness at network planning stage. Optimization issues like network deployment, channel assignment, routing and flow control are jointly considered in the WMNs deployment problem we addressed. With the objective to maximize the minimal end-to-end throughput, in other word, to maximize the total network capacity. [1] A. Tang, J. Wang and S. H. Low, “Counter-Intuitive Throughput Behaviors ini Networks Under End-to-End Control,” IEEE Transactions on Networking, Vol. 14, No. 2, Pages 355-368, April 2006. 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Literature Survey Capacity of WMNs End-to-End Fairness of WMNs IEEE 802.11s/D3 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Agenda Introduction Problem Formulation Lagrangean Relaxation Background Motivation Literature Survey Problem Formulation Problem Description Lagrangean Relaxation Lagrangean relaxation problem Subproblems 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Capacity of WMNs The capacity of WMNs is influenced by many factors including :[1] Network architecture Network topology Traffic pattern Network node density Number of channels used for each node Transmission power level [1] I. F. Akyildiz, X. Wang and W. Wang, “Wireless Mesh Networks: a Survey,” Computer Networks, Vol. 47, Issue 4, Pages 445-487, March 2005. 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Capacity of WMNs Capacity analysis of multi-hop wireless networks [1] P. Gupta and P. R. Kumar Optimal placed and random placed multi-hop wireless networks Interference models: physical model and protocol model [1] P. Gupta and P. R. Kumar, “The Capacity of Wireless Networks,” IEEE Transactions on information theory, Vol. 46, No. 2, Pages 388-404, 2000. [2] L. Kleinrock and J. Silvester, “Optimum Transmission Radii for Packet Radio Networks or Why Six Is A Magic Number,” Proc. IEEE National Telecommunications Conference, Pages 4.3.1-4.2.5, December 1978. [3] E. M. Royer, P. M. M. Smith and L. E. Moser, “An Analysis of the Optimum Node Density for Ad hoc Mobile Networks,” Proc. IEEE ICC, Vol. 3, Pages 857-861, June 2001. [4] J. Gomez and A. T. Campbell, “Variable-Range Transmission Power Control in Wireless Ad Hoc Networks,” IEEE Transaction on Mobile Computing, Vol. 6, No. 1, Pages 87-99, January 2007. 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Capacity of WMNs To increase the network capacity: Multi-hop multi-channel multi-radio wireless networks [1, 2, 3, 4, 5] Joint channel assignment, link scheduling, routing algorithms [1, 2, 4, 5] End-to-end fairness bandwidth allocation The tradeoff between fair quality of service (QoS) and network performance [6] In WMNs, competitions for resources include inter-flow contention and intra-flow contention [6]. Max-min fairness model [1] H. Yu, P. Mohapatra and X. Lin, “Channel Assignment and Link Scheduling in Multi-Radio Multi-Channel Wireless Mesh Networks,” Mobile Networks and Applications, Vol. 13, Issue 1-2, Pages 169-185, April 2008. [2] M. Kodialam and T. Nandagopal, “Characterizing the Capacity Region in Multi-Radio Multi-Channel Wireless Mesh Networks,” Proc. MobiCom’05. [3] W. Wang and X. Liu, “A Framework for Maximum Capacity in Multi-channel Multi-radio Wireless Networks,” Proc. IEEE CCNC’06. [4] X. Y. Li, A. Nusairat, Y. Wu, Y. Qi, J. Zhao, X. Chu and Y. Liu, “Joint Throughput Optimization for Wireless Mesh Networks,” IEEE Transactions on Mobile Computing, Vol. 8, Issue 7, Pages 895-909, July 2009. [5] J. Tang, G. L. Xue and W. Y. Zhang, “Cross-Layer Optimization For End-To-End Rate Allocation in Multi-Radio Wireless Mesh Networks,” Wireless Networks, Vol. 15, No. 1, January 2009. [6] B. Li, “End-to-End Fair Bandwidth Allocation in Multi-Hop Wireless Ad Hoc Networks,” Proc. IEEE ICDCS’05. 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Inter-Flow Contention In a single-hop wireless network: w2 : w1 = 1 : 2 F1 F2 2/3B 1/3B 參考自: B. Li, “End-to-End Fair Bandwidth Allocation in Multi-Hop Wireless Ad Hoc Networks,” Proc. IEEE ICDCS’05. 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Intra-Flow Contention In a multi-hop wireless mesh network F1 F2.1 F2.2 F2.3 2/3B 1/9B r2 : r1 = 1 : 6 unfair 1/9B 1/3B 1/9B 參考自: B. Li, “End-to-End Fair Bandwidth Allocation in Multi-Hop Wireless Ad Hoc Networks,” Proc. IEEE ICDCS’05. 2/5B 1/5B r2 : r1 = 1 : 2 FAIR 1/5B 3/5B 1/5B 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

End-to-End Fairness of WMNs To achieve end-to-end throughput fairness: Bandwidth allocation [1] The method extends the per-hop link bandwidth allocation to multi-hop flow fairness. This kind of approaches can be achieved through flow control [1] B. Li, “End-to-End Fair Bandwidth Allocation in Multi-Hop Wireless Ad Hoc Networks,” Proc. IEEE ICDCS’05. [2] Y.F. Wen, F.Y.S. Lin, Y.C. Tzeng and C.T. Lee, "Backhaul Assignment and Routing Algorithms with End-to-End QoS Constraints for Wireless Mesh Networks", Springer Wireless Personal Communications, Feb. 2009. 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

End-to-End Fairness of WMNs Cross-layer optimization approach [1] Rate allocation, routing, scheduling, transmission power control and channel assignment problems Max-min fairness (end-to-end throughput fairness) Multi-hop wireless network deployment [2] Backhaul and routing assignment problem which guarantees end-to-end delay fairness. In our research: Mesh router and backhaul assignment, power control, channel assignment, routing and flow control End-to-end throughput fairness [1] J. Tang, G. L. Xue and W. Y. Zhang, “Cross-Layer Optimization For End-To-End Rate Allocation in Multi-Radio Wireless Mesh Networks,” Wireless Networks, Vol. 15, No. 1, January 2009. [2] Y.F. Wen, F.Y.S. Lin, Y.C. Tzeng and C.T. Lee, "Backhaul Assignment and Routing Algorithms with End-to-End QoS Constraints for Wireless Mesh Networks", Springer Wireless Personal Communications, Feb. 2009. 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

IEEE 802.11s IEEE 802.11s/D3 Internet An enhancement of the original standard to support WLAN implementations for more flexible interoperable wireless connectivity. Internet Portal 1 Portal 2 AP MC1 MC2 MC3 MC4 MC5 MBSS infrastructure BSS Mesh STA 3 Mesh STA 7 Mesh STA 2 Mesh STA 6 Mesh STA 1 Mesh STA 8 Mesh STA 5 Mesh STA 4 圖文參考自: IEEE Standard, “Draft STANDARD for Information Technology- Telecommunications and information exchange- between systems- Local and metropolitan area networks- Specific requirements- Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications,” March 2009. infrastructure BSS 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Agenda Introduction Problem Formulation Lagrangean Relaxation Background Motivation Literature Survey Problem Formulation Problem Description Lagrangean Relaxation Lagrangean relaxation problem Subproblems 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Problem Description Multi-hop Multi-radio Multi-channel Multi-mode WMN Optimization issues: Mesh router and gateway assignment Channel assignment Routing Bandwidth allocation Objective: Maximize the total network capacity when achieve end-to-end throughput fairness 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Problem Description K - The index set of all available non-overlapping channels For example, channels 1, 6, and 11 in 2.4 GHz Wi-Fi channels (IEEE 802.11 b/g). W - The index set of all Origin-Destination pairs (OD-pairs) V - The index set of candidate locations for mesh routers N - The index set of all mobile clients L - The index set of all candidate links Q - The index set of all cliques constructed of candidate links Pw - The index set of all paths for OD-pair w 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Problem Description Candidate Links Two candidate location form a candidate link Dominated node Candidate Locations Mobile clients 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Problem Description Cliques (in the contention graph) Clique Form by one or more candidate links Clique k = 1 k = 2 k = 3 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Problem Formulation Problem Assumptions Each mesh router is stationary. Each mesh router can be equipped with multiple radios each of which operates on a particular and non-overlapping channel. Antennas are omni-directional. The routing path of each OD-pair is single path. Each mesh router has AP functionalities and can be upgraded to have gateway functionalities. Each mobile client must home to a mesh router and the selection is through system. Each mesh router and mobile client has the capability of perfect power control. Mobile clients are capable to use all available non-overlapping channels and the selection is through system. 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Problem Formulation Given CLs for mesh routers Positions and weighting factors for MCs Cost function of building a mesh router and additional cost to have gateway function Distances between nodes Maximum transmission range of each radio Limited number of available channels of each radio Budget constraint 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Problem Formulation Objective: Subject to: To maximize the minimum weighted end-to-end throughput Subject to: Budget constraint Mesh router and gateway assignment constraints Routing constraints Link constraints Channel capacity constraints Nodal capacity constraint Air-interface capacity constraint Link capacity constraints Integer constraints 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Problem Formulation 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Problem Formulation 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Problem Formulation 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Problem Formulation 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Problem Formulation 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Problem Formulation 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Lagrangean Relaxation Primal Problem Lagrangean Relaxation Problem Subproblem Lagrangean Dual Problem Optimal Solution Adjust Lagrangean Multipliers 2018/11/29

2018/11/29

Lagrangean Relaxation Problem 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Lagrangean Relaxation Problem 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Lagrangean Relaxation Problem 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Dual Problem & Subgradient Method 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Thanks For your listening 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Getting Primal Feasible Solution Heuristic 1 Mesh router, gateway and radio assignment Routing Transmission range and link capacity Flow control 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Heuristic for Mesh Router, Gateway and Radio Assignment 以LR problem中(SUB 8)所得的solution為起始值。因為這 樣的路徑規劃較有可能得到好的primal feasible solution。 將每個OD pair所選路徑上的每個mesh router建立起來， 將路徑終點的mesh router升級成gateway。並建立radio在 每個節點上。 若所花費成本大於預算，則選擇較不重要的link刪去。反 之則選擇較重要的link建立。 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Heuristic for Routing 以最大化throughput為目標做routing 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Heuristic for Setting Transmission Range and Link Capacity 將每個radio的傳輸範圍設為該radio所需負責做transmitter 的link中最大的距離。 計算每個link的capacity 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Heuristic for Flow Control 以Data Network中所提出的Max-min flow control來做 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Getting Primal Feasible Solution Heuristic 2 Mesh router, gateway and radio assignment Transmission range and link capacity flow control 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Heuristic for Mesh Router, Gateway and Radio Assignment 以(SUB 1)所得的solution為起始值。 若花費成本大於預算，則選擇較不重要的link將兩端radio 刪除。 若花費成本尚未達到預算，則選擇較重要的link建立起來。 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Heuristic for Setting Transmission Range and Link Capacity 將每個radio的傳輸範圍設為該radio所需負責做transmitter 的link中最大的距離。 計算每個link的capacity。 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University

Heuristic for Routing and Flow Control 以最大化throughput為目標做routing 以Data Network中所提出的Max-min flow control來做 2018/11/29 Network Optimization Laboratory, Information Management Department, National Taiwan University