國立臺灣大學資訊管理學研究所碩士論文審查 Backhaul Assignment and Routing Algorithms with End-to-End QoS Constraints in Wireless Mesh Networks 無線網狀網路下考量端對端服務品質之 出口閘道設施指定及路由演算法 指導教授：林永松 博士 研究生：曾勇誠 中華民國95年10月23日

Outline Introduction Problem Description & Formulation Background Motivation Problem Description & Formulation Solution Approach Lagrangean Relaxation Method Getting Primal Feasible Solution Computational Experiments Conclusion and Future Work 2018/11/15

Outline Introduction Problem Description & Formulation Solution Approach Getting Primal Feasible Solution Computational Experiments Conclusion and Future Work 2018/11/15

Introduction WiFi networks have become increasingly popular Clients need to be in the immediate vicinity of the Internet Hot Spot Have to deploy hot spots at well-chosen locations Wireless Mesh Network (WMN) Release hot spot deployment problem Components Backhaul Transit Access Point (TAP) Mobile Host (MH) 2018/11/15

Introduction (cont’d) Issues: WMNs deployment Wireless multi-hop performance EXIT TAP 3 TAP 2 TAP 1 BH 2018/11/15

Background Wireless Mesh Networks (WMNs) I. F. Akyildiz, X. Wang, and W. Wang. Wireless Mesh Networks: A Survey. Computer Networks Journal (Elsevier), 47(4), 2005. Present a survey on recent advances and open research issues in WMNs Point out an important research topic: Backhaul deployment Routing protocols QoS requirements 2018/11/15

Background (cont’d) End-to-end Performance V. Gambiroza, B. Sadeghi, and E. Knightly, “End-to-End Performance and Fairness in Multihop Wireless Backhaul Networks”. in Proceedings of MobiCom 2004. Temporal fairness (max min channel access time) Chain topology N. Ben Salem and JP Hubaux, “A Fair Scheduling for Wireless Mesh Networks”. in Proceedings of WiMesh 2005. Based on TDMA End-to-end QoS 2018/11/15

Motivation Tradeoff Backhaul deployment and end-to-end performance To propose a resource allocation algorithm that achieves: Optimize backhaul deployment Assign routing path with considering end-to-end QoS constraints Internet Backhaul TAP Mobile host Wireless con. Wired line 2018/11/15

Outline Introduction Problem Description & Formulation Solution Approach Getting Primal Feasible Solution Computational Experiments Conclusion and Future Work 2018/11/15

Problem Description Backhaul Deployment Problem Backhaul TAP Mobile host Wireless con. TAP 9 TAP 1 TAP 2 TAP 3 TAP 4 TAP 5 TAP 6 TAP 7 TAP 11 2018/11/15 TAP 10

Problem Description (cont’d) QoS Routing Problem T=0 T=4 T=3 T=3 T=0 TAP 5 Backhaul TAP Mobile host Wireless con. 1 1 1 2 1 TAP 1 TAP 2 TAP 3 TAP 4 1 1 TAP 6 2018/11/15

Problem Description (cont’d) Assumption: The backhauls integrate both functions of access and backhaul All flows are transmitted to Internet through backhauls There is no additional round trip time from the wired Internet Mobile hosts to TAPs and TAP to TAP transmission occurs on orthogonal channels The average delay and jitter from one MH to any TAPs can be formulate as a function of required data rate and link capacity The average delay and jitter from one TAP to another can be formulate as a function of link aggregate flow and capacity 2018/11/15

Problem Description (cont’d) Given: The set of all TAPs - also the set of candidate backhauls The set of all backhaul configurations The cost of backhaul installation and configuration The set of all candidate paths from each TAP to reach backhauls The set of all mobile hosts The required data rate of each mobile host The QoS requirements including end-to-end mean delay and delay jitter Objective: To minimize the total cost of backhaul deployment 2018/11/15

Problem Description (cont’d) Subject to: Backhaul assignment constraints Routing constraints Link constraints Mobile host constraints Capacity constraints QoS constraints To determine: Backhaul deployment and configuration Routing assignment of each O-D pairs The source TAP assignment of each mobile host Bandwidth allocation on each link 2018/11/15

Problem Formulation (cont’d) Given Parameters Notation Description V The set of TAPs which is also the set of candidate backhauls, where v  V. K The set of backhaul configurations, where k  K. cb The fixed cost to install candidate backhaul b into a backhaul. Pbs The set of paths from original TAP s to destination TAP b, where p  Pbs. puv The indication function, which denote link uv on path p. Cuv (packets/sec) The capacity of link uv. (packets/sec) The nodal capacity of TAP s. 2018/11/15

Problem Formulation (cont’d) Given Parameters Notation Description (packets/sec) The air-interface capacity of TAP s. Φb(k) The cost of building the wired line on backhaul b, which is a function of backhaul configuration k. Qb(k) The capacity of the wired line on backhaul b, which is a function of backhaul configuration k. Fuv(fuv,Cuv) The average delay on link uv, which is a function of aggregate flow fuv and link capacity Cuv. Muv(fuv,Cuv) The delay jitter on link uv, which is a function of aggregate flow fuv and link capacity Cuv. T The end-to-end delay requirement. J The end-to-end jitter requirement. 2018/11/15

Problem Formulation (cont’d) Given Parameters Notation Description N The set of mobile hosts, where n  N. θn(packets/sec) The data rate required to be transmitted of mobile host n. rns(packets/sec) The link capacity from mobile host n to TAP s. The average delay from mobile host n to source TAP s, which is a function of required data rate θn and link capacity rns. The delay jitter from mobile host n to source TAP s, which is a function of required data rate θn and link capacity rns. M1 An arbitrarily large number. M2 M3 2018/11/15

Problem Formulation (cont’d) Decision Variables Notation Description bk 1 if TAP b is selected to be a backhaul with configuration k; otherwise 0. zbs 1 if TAP s connects to the wired network via backhaul b; otherwise 0. xp 1 if path p from TAP s to TAP b is selected; otherwise 0. ysuv 1 if link uv is on the path adopted by TAP s; otherwise 0. κns 1 if mobile host n associates to TAP s; otherwise 0. as(packets/sec) The data rate required to be transmitted of TAP s. γsuv The bandwidth allocation of TAP s on link uv. fuv The aggregate flow on link uv. 2018/11/15

Problem Formulation (cont’d) Objective function subject to: (IP) Backhaul assignment constraints Installation cost Wired line cost (IP 1) (IP 2) (IP 3) Routing constraints (IP 4) (IP 5) (IP 6) (IP 7) 2018/11/15

Problem Formulation (cont’d) Link constraints (IP 8) (IP 9) (IP 10) (IP 11) Mobile host constraints (IP 12) (IP 13) (IP 14) (IP 15) (IP 16) 2018/11/15

Problem Formulation (cont’d) Link capacity constraints (IP 17) (IP 18) (IP 19) (IP 20) (IP 21) Nodal capacity constraints (IP 22) (IP 23) QoS constraints (IP 24) (IP 25) 2018/11/15

Problem Formulation (cont’d) (IP 26) (IP 27) (IP 28) (IP 29) (IP 30) 2018/11/15

Outline Introduction Problem Description & Formulation Solution Approach Getting Primal Feasible Solution Computational Experiments Conclusion and Future Work 2018/11/15

Lagrangean Relaxation Method Relax Constraints (1), (3), (5), (7), (8), (9), (10), (13), (14), (17), (18), (19), (23), (24), (25) and we can obtain the following Lagrangean relaxation problem (LR) Primal Problem Adjust Multipliers Lagrangean Dual Problem Lagrangean Relaxation Problem ηbk zbs xp as γsuv ysuv fuv κns Optimal Solution Optimal Solution Optimal Solution Optimal Solution Optimal Solution Optimal Solution Optimal Solution 2018/11/15

Outline Introduction Problem Description & Formulation Solution Approach Getting Primal Feasible Solution Computational Experiments Conclusion and Future Work 2018/11/15

Getting Primal Feasible Solution The proposed heuristic algorithm is described as follows Step1: Initiate backhaul deployment according to decision variableηbk. Step2: Run Assign_Mobile_Host_Heuristic. Step3: Run Routing_Heuristic. Step4: Go to step 5 if all TAPs can route to associated backhauls without violating end-to-end QoS requirements. Step4.1: Run Add_Backhaul_Heuristic. Step4.2: Go back to step 2. Step5: Calculate total cost of backhaul deployment. 2018/11/15

Getting Primal Feasible Solution (cont’d) Assign Mobile Host Heuristic κns Backhaul TAP Mobile host Wireless con. 2018/11/15

Getting Primal Feasible Solution (cont’d) Routing Heuristic 1 2 1 2 1 TAP 1 Backhaul TAP Mobile host Wireless con. TAP 2 TAP 3 TAP 4 BH=4,T=3 BH=8,T=4 BH=4,T=2 BH=8,T=3 1 T=5 T=3 T=3 T=4 TAP 5 1 BH=4,T=5 BH=8,T=2 1 2 1 T=3 TAP 6 TAP 7 TAP 8 2018/11/15

Getting Primal Feasible Solution (cont’d) Add Backhaul Heuristic - Reachability 1 1 2 1 Backhaul TAP Mobile host Wireless con. TAP 1 TAP 3 TAP 5 TAP 8 3 2 1 TAP 6 1 2 1 2 1 TAP 4 TAP 2 TAP 9 2 1 TAP 7 2018/11/15

Outline Introduction Problem Description & Formulation Solution Approach Getting Primal Feasible Solution Computational Experiments Conclusion and Future Work 2018/11/15

Experiment Environment Experiment Environment and Parameters Parameter Value Number of Iterations 2000 Improvement Counter 40 Initial Upper Bound Solution of 1st Getting Primal Feasible Initial Upper Multiplier Initial Scalar of step size 2 Test Platform CPU: Intel(R) Pentium-IV 3GHz RAM: 1024MB OS: Windows 2000 SP 4 2018/11/15

Experiment Scenarios Different topologies Different data flow Grid, Random, Hexagon network 9-91 no. of TAPs with triple MHs 1 unit data flow per MH Different data flow 49 TAPs with 49x3 MHs 0.25-1.75 unit data flow per MH 2018/11/15

Simple Algorithms Algorithm Backhaul Deployment Routing Sequence LR-based Reachability Closest to QoS Req. SA1 Random SA2 Min. Cost Min. Flow SA3 Min. Resource Usage 2018/11/15

Experimental Results Gird Network 2018/11/15

Experimental Results (cont’d) Random Network 2018/11/15

Experimental Results (cont’d) Hexagon Network 2018/11/15

Experimental Results (cont’d) Different Data Flow 2018/11/15

Discussion Deployment Cost The Location of Backhaul Deployment Linear Increasing The Location of Backhaul Deployment Reachability The Sequence of Paths Selection Closest to QoS Requirement, First Selection 2nd 1st 2nd 1st 2018/11/15

Outline Introduction Problem Description & Formulation Solution Approach Getting Primal Feasible Solution Computational Experiments Conclusion and Future Work 2018/11/15

Conclusions Contribution Backhaul deployment Propose a mathematical formulation to model this complicated problem. By Lagrangean Relaxation and the heuristics we proposed , we can nearly-optimally solve this problem. Backhaul deployment Reachablity Routing Paths Selection Sequence Closest to QoS Requirement, First Selection 2018/11/15

Future Work Routing - Sequence of Paths Selection Backhaul Deployment - Clustering Mobile Hosts - Mobility 2018/11/15

Q & A -Thanks for your listening 2018/11/15

Appendix 2018/11/15

Lagrangean Relaxation method Relax Constraints (1), (3), (5), (7), (8), (9), (10), (13), (14), (17), (18), (19), (23), (24), (25) and we can obtain the following Lagrangean relaxation problem (LR) 2018/11/15

Lagrangean Relaxation method (cont’d) (LR) subject to: (IP 2) (IP 4) 2018/11/15

Lagrangean Relaxation method (cont’d) (IP 6) (IP 11) (IP 12) (IP 15) (IP 16) (IP 20) (IP 21) (IP 22) 2018/11/15

Lagrangean Relaxation method (cont’d) (IP 26) (IP 27) (IP 28) (IP 29) (IP 30) We can decomposed this LR problem into 7 subproblems. 2018/11/15

Subproblem 1 (related to decision variable ηbk) subject to: (IP 2) (IP 26) 1. Decompose into |V| independent subproblems. One for each candidate backhaul b. 2. Calculate the coefficient of ηbk for each configuration k. 3. Find the smallest negative coefficient, then set the associated ηbk to 1, others 0. 2018/11/15

Subproblem 2 (related to decision variable zbs) subject to: (IP 4) (IP 27) 1. Decompose into |V| independent subproblems. One for each TAP s. 2. Calculate the coefficient of zbs for each candidate backhaul b. 3. Find the smallest coefficient, then set the associated zbs to 1 , others 0. 2018/11/15

Subproblem 3 (related to decision variable xp) subject to: (IP 6) (IP 28) (SUB 3) can be decomposed into |V| independent shortest path problems. One for each TAP s. 2018/11/15

Subproblem 4 (related to decision variable as) subject to: (IP 15) (IP 16) 1. Reset all as to 0. 2. Calculate the coefficient of as for each TAP s. 3. Find the unset as with smallest coefficient. If found, then set it to , else stop. 4. Repeat step 3 until the total data rate required to be transmitted of all TAPs equal to or large than the total incoming flow of all mobile hosts. 2018/11/15

Subproblem 5 (related to decision variable γsuv) subject to: (IP 21) (IP 22) 1. Decompose into |V| independent subproblems. One for each TAP v. 2. Reset all TAP v’s incoming flow, γsuv, to 0. 3. Calculate the coefficient of γsuv for all incoming flow of TAP v. 4. Find the unset γsuv with smallest negative coefficient. If found, then set it to , else stop. 5. Repeat step 4 while the total incoming flow of TAP v not exceed . 2018/11/15

Subproblem 6 (related to decision variable ysuv and fuv) subject to: (IP 11) (IP 20) (IP 29) Decompose into |VxV | independent subproblems. One for each uv link. Complicated due to two coupled decision variables Can be solved analytically * * K. T. Cheng and F. Y. S. Lin, “Minimax End-to-end Delay Routing and Capacity Assignment for Virtual Circuit Networks”, Proc. IEEE Globecom, pp. 2134-2138, 1995 2018/11/15

Subproblem 6 (related to decision variable ysuv and fuv) 1. Solve for each TAP s, call them the break points of fuv. 2. Sorting these break points and denoted as fuv1, fuv2, …, fuvn. 3. At each interval, fuvi ≤ fuv ≤ fuvi+1, ysuv(fuv) is 1 if 　 and is 0 otherwise. 4. Find the local minimum within each interval. 5. The global minimum point can be found by comparing these local minimum points. f 1uv f 2uv f 3uv … f *uv f iuv … Cuv fuv y1uv(fuv) y1uv = 0, if y1uv(fuv) > 0 y1uv = 1, if y1uv(fuv) ≤ 0 fuv y1uv(fuv) Sub 6.1 f *uv 2018/11/15

Subproblem 7 (related to decision variable κns) subject to: (IP 12) (IP 30) 1. Decompose into |N| independent subproblems. One for each MH n. 2. Calculate the coefficient of κns for each TAP s. 3. Find the smallest coefficient, then set the associated κns to 1, others 0. 2018/11/15