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Mathematical Challenges in Telecommunicati on a Tutorial

Mathematical Challenges in Telecommunicati on a Tutorial. Martin Grötschel IMA workshop on Network Management and Design Minneapolis, MN, April 6, 2003. Comment. This is an abbreviated version of my presentation. The three films I showed are not included.

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Mathematical Challenges in Telecommunicati on a Tutorial

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  1. Mathematical Challenges in Telecommunicationa Tutorial Martin Grötschel IMA workshop on Network Management and Design Minneapolis, MN, April 6, 2003

  2. Comment • This is an abbreviated version of my presentation. • The three films I showed are not included. • I also deleted many of the pictures and some of the tables: • in some cases I do not have permission to publish them since they contain some confidential material or information not for public use, • in other cases I am not sure of the copy right status (and do not have the time and energy to check it). Martin Grötschel

  3. The ZIB Telecom Group Andreas Bley Andreas Eisenblätter Martin Grötschel Thorsten Koch Arie Koster Roland Wessäly  Adrian Zymolka ZIB Associates Manfred Brandt Sven Krumke Frank Lutz Diana Poensgen Jörg Rambau and more: Clyde Monma(BellCore, ...) Mechthild Opperud (ZIB, Telenor) Dimitris Alevras (ZIB, IBM) Christoph Helmberg (Chemnitz) ZIB Telecom Team Martin Grötschel

  4. Bell Communications Research Telenor (Norwegian Telecom) E-Plus (acquired by KPN in 01/2002) DFN-Verein Bosch Telekom (bought by Marconi) Siemens Austria Telekom (controlled by Italia Telecom) T-Systems Nova (T-Systems, Deutsche Telekom) KPN Telecel-Vodafone Atesio (ZIB spin-off company) ZIB Partners from Industry Martin Grötschel

  5. Contents • Telecommunication: The General Problem • The Problem Hierarchy: Cell Phones and Mathematics • The Problem Hierarchy: Network Components and Math • Network Design: Tasks to be solvedAddressing Special Issues: • Frequency Assignment • Locating the Nodes of a Network • Balancing the Load of Signaling Transfer Points • Integrated Topology, Capacity, and Routing Optimization as well as Survivability Planning • Planning IP Networks • Optical Networks • Summary and Future Martin Grötschel

  6. Contents • Telecommunication: The General Problem • The Problem Hierarchy: Cell Phones and Mathematics • The Problem Hierarchy: Network Components and Math • Network Design: Tasks to be solvedAddressing Special Issues: • Frequency Assignment • Locating the Nodes of a Network • Balancing the Load of Signaling Transfer Points • Integrated Topology, Capacity, and Routing Optimization as well as Survivability Planning • Planning IP Networks • Optical Networks • Summary and Future Martin Grötschel

  7. What is the Telecom Problem? Design excellent technical devices and a robustnetworkthatsurvives all kinds offailuresandorganize the trafficsuch that high quality telecommunication between very many individual units at many locationsis feasible atlow cost! Speech Data Video Etc. Martin Grötschel

  8. What is the Telecom Problem? Design excellent technical devices and a robustnetworkthatsurvives all kinds offailuresandorganize the trafficsuch that high quality telecommunication between very many individual units at many locationsis feasible atlow cost! This problem is too general to be solved in one step. • Approach in Practice: • Decompose whenever possible • Look at a hierarchy of problems • Address the individual problems one by one • Recompose to find a good global solution Martin Grötschel

  9. Contents • Telecommunication: The General Problem • The Problem Hierarchy: Cell Phones and Mathematics • The Problem Hierarchy: Network Components and Math • Network Design: Tasks to be solvedAddressing Special Issues: • Frequency Assignment • Locating the Nodes of a Network • Balancing the Load of Signaling Transfer Points • Integrated Topology, Capacity, and Routing Optimization as well as Survivability Planning • Planning IP Networks • Optical Networks • Summary and Future Martin Grötschel

  10. Cell Phones and Mathematics • Computational logic • Combinatorial • optimization • Differential algebraic • equations • Designing mobile phones • Task partitioning • Chip design (VLSI) • Component design cellphonepicture • Operations research • Linear and integer programming • Combinatorial optimization • Ordinary differential equations • Producing Mobile Phones • Production facility layout • Control of CNC machines • Control of robots • Lot sizing • Scheduling • Logistics Marketing and Distributing Mobiles • Financial mathematics • Transportation optimization Martin Grötschel

  11. CMOS layout for four-transistor static-memory cell CMOS layout for two four-transistor static-memory cells. Compacted CMOS layout for two four-transistor static-memory cells. Chip Design Schematic for four-transistor static-memory cell Placement Routing Compactification ZIB-Film 9:01 – 9:41

  12. Design and Production of ICs and PCBs Printed Circuit Board (PCB) Integrated Circuit (IC) Problems: Logic Design, Physical Design Correctness, Simulation, Placement of Components, Routing, Drilling,... Martin Grötschel

  13. Production and Mathematics: Examples CNC Machine for 2D and 3D cutting and welding (IXION ULM 804) Sequencing of Tasks and Optimization of Moves Mounting Devices Minimizing Production Time via TSP or IP SMD Printed Circuit Boards Optimization of Manufacturing

  14. Drilling 2103 holes into a PCB Significant Improvements via TSP (Padberg & Rinaldi) Martin Grötschel

  15. Siemens Problem printed circuit board da1 after before Martin Grötschel

  16. Siemens Problem printed circuit board da4 before after Martin Grötschel

  17. Mobile Phone Production Line Fujitsu Nasu plant Martin Grötschel

  18. Contents • Telecommunication: The General Problem • The Problem Hierarchy: Cell Phones and Mathematics • The Problem Hierarchy: Network Components and Math • Network Design: Tasks to be solvedAddressing Special Issues: • Frequency Assignment • Locating the Nodes of a Network • Balancing the Load of Signaling Transfer Points • Integrated Topology, Capacity, and Routing Optimization as well as Survivability Planning • Planning IP Networks • Optical Networks • Summary and Future Martin Grötschel

  19. Network Components Design, Production, Marketing, Distribution: Similar math problems as for mobile phones • Fiber (and other) cables • Antennas and Transceivers • Base stations(BTSs) • Base Station Controllers(BSCs) • Mobile Switching Centers(MSCs) • and more... Martin Grötschel

  20. Component „Cables“ Martin Grötschel

  21. Component „Antennas“ Martin Grötschel

  22. Component „Base Station“ Nokia MetroSite Nokia UltraSite Martin Grötschel

  23. Component„Mobile Switching Center“:Example of an MSC Plan

  24. Contents • Telecommunication: The General Problem • The Problem Hierarchy: Cell Phones and Mathematics • The Problem Hierarchy: Network Components and Math • Network Design: Tasks to be solvedAddressing Special Issues: • Frequency Assignment • Locating the Nodes of a Network • Balancing the Load of Signaling Transfer Points • Integrated Topology, Capacity, and Routing Optimization as well as Survivability Planning • Planning IP Networks • Optical Networks • Summary and Future Martin Grötschel

  25. Network Design: Tasks to be solved Some Examples • Locating the sites for antennas (TRXs) and base transceiver stations (BTSs) • Assignment of frequencies to antennas • Cryptography and error correcting encoding for wireless communication • Clustering BTSs • Locating base station controllers (BSCs) • Connecting BTSs to BSCs Martin Grötschel

  26. Network Design: Tasks to be solved Some Examples (continued) • Locating Mobile Switching Centers (MSCs) • Clustering BSCs and Connecting BSCs to MSCs • Designing the BSC network (BSS) and the MSC network (NSS or core network) • Topology of the network • Capacity of the links and components • Routing of the demand • Survivability in failure situations Most of these problems turn out to be Combinatorial Optimization or Mixed Integer Programming Problems Martin Grötschel

  27. Connecting Mobiles: What´s up? BSC MSC MSC BSC Location Routing MSC Network BSC BSC BSC Network MSC MSC BSC BSC MSC MSC Location Cryptography BSC BSC Frequency Assignment BTS Martin Grötschel

  28. Connecting Computers or other Devices X Location IP Routing Y Network X Network Y Location Cryptography Bandwidth Allocation The mathematical problems are similarbut not identical Martin Grötschel

  29. Contents • Telecommunication: The General Problem • The Problem Hierarchy: Cell Phones and Mathematics • The Problem Hierarchy: Network Components and Math • Network Design: Tasks to be solvedAddressing Special Issues: • Frequency Assignment • Locating the Nodes of a Network • Balancing the Load of Signaling Transfer Points • Integrated Topology, Capacity, and Routing Optimization as well as Survivability Planning • Planning IP Networks • Optical Networks • Summary and Future Martin Grötschel

  30. FAPFilm Martin Grötschel

  31. Antennas & Interference x x x x x x x x co- & adjacent channel interference cell antenna site cell backbone network Martin Grötschel

  32. Interference Level of interference depends on • distance between transmitters • geographical position • power of the signals • direction in which signals are transmitted • weather conditions • assigned frequencies • co-channel interference • adjacent-channel interference Martin Grötschel

  33. Separation Frequencies assigned to the same location (site) have to be separated Parts of the spectrum forbidden at some locations: • government regulations, • agreements with operators in neighboring regions, • requirements military forces, etc. Site Blocked channels Martin Grötschel

  34. Frequency Planning Problem Find an assignment of frequencies to transmitters that satisfies • all separation constraints • all blocked channels requirements and either • avoids interference at all or • minimizes the (total/maximum) interference level Martin Grötschel

  35. Minimum InterferenceFrequency Assignment Problem Integer Linear Program: Martin Grötschel

  36. A Glance at some Instances E-Plus Project Martin Grötschel

  37. Region Berlin - Dresden 2877 carriers 50 channels Interference reduction: 83.6% Martin Grötschel

  38. Region Karlsruhe 2877 Carriers 75 channels Interference Reduction: 83.9 % Martin Grötschel

  39. The UMTS Radio Interface • Completely new story • see talk by Andreas Eisenblätter on Monday Martin Grötschel

  40. Contents • Telecommunication: The General Problem • The Problem Hierarchy: Cell Phones and Mathematics • The Problem Hierarchy: Network Components and Math • Network Design: Tasks to be solvedAddressing Special Issues: • Frequency Assignment • Locating the Nodes of a Network • Balancing the Load of Signaling Transfer Points • Integrated Topology, Capacity, and Routing Optimization as well as Survivability Planning • Planning IP Networks • Optical Networks • Summary and Future Martin Grötschel

  41. G-WiN Data • G-WiN = Gigabit-Wissenschafts-Netz of the DFN-Verein • Internet access of all German universities and research institutions • Locations to be connected: 750 • Data volume in summer 2000: 220 Terabytes/month • Expected data volume in 2004: 10.000 Terabytes/month • Clustering (to design a hierarchical network): • 10 nodes in Level 1a 261 nodes eligible for • 20 nodes in Level 1b Level 1 • All other nodes in Level 2 Martin Grötschel

  42. G-WiN Problem • Select the 10 nodes of Level 1a. • Select the 20 nodes of Level 1b. • Each Level 1a node has to be linked to two Level 1b nodes. • Link every Level 2 node to one Level 1 node. • Design a Level 1a Network such that • Topology is survivable (2-node connected) • Edge capacities are sufficient (also in failure situations) • Shortest path routing (OSPF) leads to balanced capacity use (objective in network update) • The whole network should be „stable for the future“. • The overall cost should be as low as possible. Martin Grötschel

  43. Potential node locations for the 3-Level Network of the G-WIN Rednodes are potential level 1 nodes Bluenodes are all remaining nodes Cost: Connection between nodes Capacity of the nodes Martin Grötschel

  44. Demand distribution The demand scales with the height of each red line Aim Select backbone nodes and connect all non-backbone nodes to a backbone node such that the overall network cost is minimal (access+backbone cost) Martin Grötschel

  45. G-WiN Location Problem: Data Martin Grötschel

  46. G-WiN Location/Clustering Problem Each location i must be connected to a Level 1 node Capacity at p must be large enough Only one configuration at each Location 1 node # of Level 1a nodes All variables are 0/1. Martin Grötschel

  47. Solution: Hierarchy & Backbone Martin Grötschel

  48. G-WiN Location Problem: Solution Statistics The DFN problem leads to ~100.000 0/1-variables. Typical computational experience: Optimal solution via CPLEX in a few seconds! A very related problem at Telekom Austria has ~300.000 0/1-variables plus some continuous variables and capacity constraints. Computational experience (before problem specific fine tuning): 10% gap after 6 h of CPLEX computation, 60% gap after „simplification“ (dropping certain capacities). Martin Grötschel

  49. Contents • Telecommunication: The General Problem • The Problem Hierarchy: Cell Phones and Mathematics • The Problem Hierarchy: Network Components and Math • Network Design: Tasks to be solvedAddressing Special Issues: • Frequency Assignment • Locating the Nodes of a Network • Balancing the Load of Signaling Transfer Points • Integrated Topology, Capacity, and Routing Optimization as well as Survivability Planning • Planning IP Networks • Optical Networks • Summary and Future Martin Grötschel

  50. Re-Optimization of Signaling Transfer Points Telecommunication companies maintain a signaling network (in adition to their communication transport network). This is used for management tasks such as: • Basic call setup or tear down • Wireless roaming • Mobile subscriber authentication • Call forwarding • Number display • SMS messages • Etc. Martin Grötschel

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