1. 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

2. 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

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

4. 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

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

6. 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

7. 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

8. 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

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

10. 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

11. 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

12. 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

13. 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

14. 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

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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

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

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

24. 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

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

26. 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

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

28. 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

29. 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

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

31. 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

32. 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
unit data flow per MH
2018/11/15

33. 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

34. Experimental Results
Gird Network
2018/11/15

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

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

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

38. 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

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

40. 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

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

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

43. Appendix
2018/11/15

44. 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

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

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

47. 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

48. 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

49. 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

50. 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

51. 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

52. 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

53. 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.  , 1995
2018/11/15

54. 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

55. 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