Network Optimization 網路最佳化

1. Network Optimization網路最佳化 Chih-Hao Lin (林志浩) Department of Information Management Chung Yuan Christian University December 20, 2019

2. 林志浩 (Chih-Hao Lin) • 學歷：國立台灣大學 資訊管理學 博士 • 現職：中原大學 資管系 助理教授 • 專長：系統最佳化、演化式計算、效能評估、無線通訊網路、網路規劃與容量管理 • 課程：系統最佳化、資源規劃與管理、網路規劃與管理、資源管理實務、企業資料通訊、管理數學 • 聯絡方式： • Tel: (03) 265-5410 • E-mail: linch@cycu.edu.tw Chih-Hao Lin

3. Outline • Introduction • Motivation: the bridges of Koenigsberg • Network flow applications • Possible problems in developing decision models • Shortest path problem • Maximum flow problem • Minimum cost flow problem • Network optimization issues • Two research examples • Conclusion Chih-Hao Lin

4. Introduction • Deterministic mathematical model • All parameter values are assumed to be certainty • Mathematical programs which decide how to plan or “program” activities. • “Netform” • Network flow-based formulation • Network-related formulation. • Deterministic network optimization • Solve deterministic network-related formulation by optimization technique Chih-Hao Lin

5. Outline • Introduction • Motivation: the bridges of Koenigsberg • Network flow applications • Possible problems in developing decision models • Shortest path problem • Maximum flow problem • Minimum cost flow problem • Network optimization issues • Two research examples • Conclusion Chih-Hao Lin

6. The Bridges of Koenigsberg: Eüler 1736 (from J.B. Orlin in MIT) • “Graph Theory” began in 1736 • Leonard Eüler • Visited Koenigsberg • People wondered whether it is possible to take a walk, end up where you started from, and cross each bridge in Koenigsberg exactly once • Generally it was believed to be impossible Chih-Hao Lin

7. The Bridges of Koenigsberg: Eüler 1736(cont’d)(from J.B. Orlin in MIT) Chih-Hao Lin

8. The Bridges of Koenigsberg: Eüler 1736 (cont’d)(from J.B. Orlin in MIT) Chih-Hao Lin

9. The Bridges of Koenigsberg: Eüler 1736 (cont’d)(from J.B. Orlin in MIT) Chih-Hao Lin

10. The Bridges of Koenigsberg: Eüler 1736 (cont’d)(from J.B. Orlin in MIT) Chih-Hao Lin

11. The Bridges of Koenigsberg: Eüler 1736(cont’d)(from J.B. Orlin in MIT) Chih-Hao Lin

12. Outline • Introduction • Motivation: The Bridges of Koenigsberg • Network flow applications • Possible problems in developing decision models • Shortest path problem • Maximum flow problem • Minimum cost flow problem • Network optimization issues • Two research examples • Conclusion Chih-Hao Lin

13. Network Flow Applications • Communications • Design and expansion of communication systems • Flow of information across networks • Transportation • Transportation of goods over transportation networks • Scheduling of fleets of airplanes: time/space networks • Manufacturing • Scheduling of goods for manufacturing • Flow of manufactured items within inventory systems • Personnel assignment • Assignment of crews to airline schedules • Assignment of drivers to vehicles Chih-Hao Lin

14. Outline • Introduction • Motivation: The Bridges of Koenigsberg • Network flow applications • Possible problems in developing decision models • Shortest path problem • Maximum flow problem • Minimum cost flow problem • Network optimization issues • Two research examples • Conclusion Chih-Hao Lin

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16. Defining the Problem • Conflicting viewpoints • Analysts may often have to consider conflicting viewpoints in defining the problem • Impact on correlative part of system • Problems do not exist in isolation and are not owned • Assumptions • To state problems in terms of solutions • State of the art • Problem can change during the development Chih-Hao Lin

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18. Developing a Model • Fitting and modifying the textbooks models • Not always match the textbook approach • Understanding the models • Most readers will not use the results of a model they do not understand Chih-Hao Lin

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20. Acquiring Input Data • Using trustworthy data • For example, most data generated in a firm come from basic accounting reports • Validity of data Chih-Hao Lin

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22. Developing a Solution • Illustrating the mathematical models with pictures • Hard-to-understand mathematics • Considering multi-objective problems • The limitation of only one answer Chih-Hao Lin

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24. Testing the Solution • Convince the reader of the validity of the results • Review every assumption Chih-Hao Lin

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26. Analyzing the Results • The results must be analyzed in terms of how they will affect the total organization Chih-Hao Lin

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28. Outline • Introduction • Motivation: the bridges of Koenigsberg • Network flow applications • Possible problems in developing decision models • Shortest path problem • Maximum flow problem • Minimum cost flow problem • Network optimization issues • Two research examples • Conclusion Chih-Hao Lin

29. Shortest Path Problem • R.K. Ahuja, T.L. Magnanti and J.B. Orlin, Network Flows: Theory, Algorithms, and Applications, Prentice-Hall, 1993. • Consider a network G = (N, A) • There is an origin node 1 and a destination node 6. • What is the shortest path from 1 to 6? Chih-Hao Lin

30. Shortest Path Problem (cont’d) • Label-setting algorithms: Non-negative arc lengths • Dijkstra’s Algorithm (1959)  O(n2) • Radix heap implementation (1990)  O(m+n log(nC)) • Label correcting algorithm: Negative costs permitted • Bellman–Ford algorithm (1956) O(min(n2mC, m2n)) • FIFO implementation (1958)  O(mn) • Dynamic lot sizing application • All-pairs shortest path problem • Repeated shortest path algorithm  O(nm+n2 log C) • Floyd–Warshall algorithm (sometimes known as the Roy–Floyd algorithm or WFI Algorithm) O(n3) Chih-Hao Lin

31. Outline • Introduction • Motivation: the bridges of Koenigsberg • Network flow applications • Possible problems in developing decision models • Shortest path problem • Maximum flow problem • Minimum cost flow problem • Network optimization issues • Two research examples • Conclusion Chih-Hao Lin

32. Maximum Flow Problem • Directed Graph G = (N, A) • A source node s and a sink node t • Capacities uij on arc (i, j) • Maximize the flow out of s • Subject to flow out of i= flow into i, for i≠s or t. Chih-Hao Lin

33. Maximum Flow Problem (cont’d) • Labeling algorithm • Ford-Fulkerson algorithm (1956)  O(nmU) • Edmonds-Karp algorithm (1972) • The largest augmenting path algorithm  O(m2 log U) • The shortest augmenting path algorithm  O(nm2) • Generic preflow-push algorithm • Push-relabel algorithm (1970)  O(n2 m) • FIFO preflow-push algorithm (1982)  O(n3) • Applications • Network reliability and maximum flow Chih-Hao Lin

34. Outline • Introduction • Motivation: the bridges of Koenigsberg • Network flow applications • Possible problems in developing decision models • Shortest path problem • Maximum flow problem • Minimum cost flow problem • Network optimization issues • Two research examples • Conclusion Chih-Hao Lin

35. 0 10, $4 2 4 30, $7 25, $5 25 1 20, $2 20, $6 20, $1 3 5 25, $2 -25 0 Minimum Cost Flow Problem • Consider a network G = (N, A) • Flow out of i -Flow into i = b(i) • Each arc has a linear cost and a capacity 5 5 5 20 20 Chih-Hao Lin

36. Minimum Cost Flow Problem (cont’d) • Basic algorithms • Cycle-canceling algorithm (1967)  O(nm2CU) • Successive shortest path algorithm (1961)  O(nU S(n, m, nC)) • Polynomial-time algorithm • Capacity scaling algorithm (1972)  O((m logU)  S(n, m, nC))) • Cost scaling algorithm (1980)  O(n3log(nC)) • Network simplex algorithms • Minimum cost flow applications Chih-Hao Lin

37. Outline • Introduction • Motivation: the bridges of Koenigsberg • Network flow applications • Possible problems in developing decision models • Shortest path problem • Maximum flow problem • Minimum cost flow problem • Network optimization issues • Two research examples • Conclusion Chih-Hao Lin

38. Network Planning Performance Optimization Network Monitoring Network Capacity Expansion Network Servicing Network Optimization Issues • Network planning & capacity management Chih-Hao Lin

39. Network Optimization Issues (cont’d) • Network planning • To design a network with the minimum installation and operation cost subject to performance (QoS), survivability / reliability and other constraints • Communication networks • GSM (The 2G digital cellular system) • WCDMA (The 3G wideband cellular system) • Wireless LAN (i.e. IEEE 802.11, WiFi) • Wireless MAN (i.e. IEEE 802.16, WiMAX) Chih-Hao Lin

40. A Wireless Cell Planning Algorithmfor Adaptive Beam and SDMA Systems Chih-Hao Lin

41. Network Optimization Issues (cont’d) • Network performance optimization • For an in-service traffic network, to assure pre-specified QoS requirements and/or to optimize certain performance measures, e.g. to minimize the total system throughput/revenue or to minimize the average cross-network packet delay • Networking mechanisms • Channel assignment • Resource management • Admission control • Quality of service routing • Multipath and multicast routing Chih-Hao Lin

42. User 2 4 3 1 2 1 2 1 1 2 2 2 4 4 1 1 2 3 2 4 3 1 4 4 3 3 2 3 2 An Adaptive Resource Allocation Algorithmin OFDMA Networks Sub-carrier Resource Allocation Algorithm OFDM time slot Chih-Hao Lin

43. Network Optimization Issues (cont’d) • Network monitoring • For an in-service traffic network, by using traffic measurements or performance modeling techniques (or a combination of the two) to identify potential performance exceptions and to activate corrective actions • To collect traffic measurements for load forecasting purposes (to feed the servicing and the capacity expansion processes) Chih-Hao Lin

44. An Optimal Monitoring Scheme • Three typical questions: • What engineering thresholds for network elements to use when end-to-end performance objectives are concerned? • When/How often to monitor the network? • What parts of network (or the whole network) to monitor? Chih-Hao Lin

45. Network Optimization Issues (cont’d) • Network servicing • Using corrective actions to alleviate the performance exceptions identified by the monitoring process • Three typical approaches • Traffic rerouting/load balancing • Resource reallocation • Sizing (minimal-cost capacity augmentation to satisfy the current demand) Chih-Hao Lin

46. A Bandwidth Reservation Algorithm for Wireless Cellular Networks Considering Mobility Characteristic and Service Level Agreement Chih-Hao Lin

47. Network Optimization Issues (cont’d) • Network capacity expansion • For an in-service traffic network, to determine the capacity augmentation strategy at each decision stage over a pre-specified time horizon such that the total cost, considering the effect of economies of scale and composite cost of money, is minimized • Communication networks • Wireless LAN (i.e. IEEE 802.11, Wi-Fi) • Wireless MAN (i.e. IEEE 802.16, WiMAX) • WSN (Wireless sensor network) Chih-Hao Lin

48. Network Capacity Expansion S.R. Saunders, Antennas and Propagation for Wireless Communication Systems, John Wiley & Sons, Ltd., 1999. Chih-Hao Lin

49. Our Research Results • Communication networks • GSM (The 2G digital cellular system) • WCDMA (The 3G wideband cellular system) • Wireless LAN (i.e. IEEE 802.11, Wi-Fi) • Wireless MAN (i.e. IEEE 802.16, WiMAX) • OFDMA (Orthogonal frequency division multiple access) • WSN (Wireless sensor network) Chih-Hao Lin

50. Our Research Results (cont’d) • Topics • Network design and expansion • Performance assurance and optimization • Resource allocation and management • Mobility management • Admission control • Quality of service routing • Network servicing • Reliability and survivability Chih-Hao Lin