Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2014 Efficient communication using multiple cycles and multiple channels David Weston Lastine Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Part of the Computer Engineering Commons Recommended Citation Lastine, David Weston, "Efficient communication using multiple cycles and multiple channels" (2014). Graduate Theses and Dissertations. 14071. https://lib.dr.iastate.edu/etd/14071 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Efficient communication using multiple cycles and multiple channels by David Weston Lastine A thesis submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Computer Engineering Program of Study Committee: Arun K. Somani, Major Professor James Cochran Ahmed El-sayed Kamal Mani Mina Robert J Weber Iowa State University Ames, Iowa 2014 Copyright c David Weston Lastine, 2014. All rights reserved. ii TABLE OF CONTENTS LIST OF TABLES . vi LIST OF FIGURES . viii ABSTRACT . x CHAPTER 1. INTRODUCTION . 1 1.1 Load Balancing with Dynamic Point-to-Point Connections . .2 1.2 Cycle Finding and Dynamic Traffic . .2 1.3 Load Balancing with Static Optical Connections . .3 1.4 Scheduling . .3 CHAPTER 2. REVIEW OF LITERATURE . 5 2.1 Uses of Cycles in Networking . .5 2.1.1 Unicast Routing . .5 2.1.2 Multi-cast Routing . .6 2.1.3 Fault Tolerance . .8 2.1.4 P-Cycles . .8 2.2 Finding Cycles . 10 2.3 Wavelength Selection . 10 2.4 Traffic Models . 11 CHAPTER 3. NETWORK MODELS AND DATA STRUCTURES . 12 3.1 Network and Model . 12 3.2 Random Graphs . 12 3.3 Data Structures . 14 3.4 Random Traffic . 14 iii 3.4.1 Requests . 15 3.4.2 Wavelength Assignment . 15 CHAPTER 4. CYCLE FINDING . 17 4.1 Outline of Heuristics . 17 4.1.1 Phase I - Find Initial S-Optimal Shortest Path . 18 4.1.2 Phase II - Create an incomplete Cycle . 18 4.1.3 Phase III - Create a Complete Cycle . 18 4.2 Shortest Path Routing with Preferred Nodes used in ECBRA . 21 4.3 Variations of MCRA Heuristics . 21 4.4 Variations of CBRA Heuristics . 23 4.5 Complexity of Heuristics . 23 4.6 ILP Formulation to Find Cycles for Selected Nodes . 25 4.7 Enumeration a Non-scaling Heuristic for Comparison . 27 CHAPTER 5. ROUTING HEURISTICS ENHANCEMENT - ALTER- NATE SHORTEST PATHS . 28 5.1 Motivating Observation . 28 5.2 Possible Executions of ECBRA . 28 5.3 Blocking with Static Routing . 30 5.4 Dynamic Traffic . 31 5.4.1 Shortest Path Routing . 33 5.4.2 Cycle Finding Algorithms . 41 CHAPTER 6. ROUTING HEURISTICS ENHANCEMENT - LINK RE- MOVAL ........................................ 48 6.1 Motivating Observation . 48 6.2 Resulting Routing Heuristic Enhancement . 49 6.3 Effectiveness of Routing Heuristic Enhancement . 49 6.3.1 Experimentation with Static Traffic . 49 6.3.2 Experimentation with Dynamic Traffic . 51 iv CHAPTER 7. QUORUM CYCLES . 63 7.1 Quorums . 64 7.2 Quorum for Routing . 65 7.2.1 Analysis of Solution . 65 7.2.2 Routing Analysis . 66 7.2.3 Light-Trail on Cycle . 66 7.2.4 Hardware Cost . 68 7.2.5 Load-Balancing Discrete Requests . 68 7.2.6 Load-Balancing Fluctuating Traffic Demand . 69 7.3 Load Balancing Opportunities for Different Network Sizes . 70 7.4 Initial Load Balancing . 71 7.5 Redistributing the Load . 72 7.5.1 Informal Algorithm Description . 73 7.5.2 Pseudo-Code of Algorithm . 75 7.5.3 Optimality of Load Balance Algorithm . 75 7.5.4 Example of Redistributing Load . 76 7.5.5 Run Time of Load Balance Algorithm . 76 7.6 Required Cycle Length . 77 7.6.1 Benefits from Considering Subgraphs . 78 CHAPTER 8. MANAGING TRAFFIC ON A LIGHT-TRAIL . 90 8.1 Capacity Benefits of Light-trail Splitting . 91 8.1.1 Most Loaded Link . 92 8.2 Latency Benefits of Light-trail Splitting . 93 8.2.1 Static Schedule with Fixed Length Timeslots . 93 8.2.2 Splitting a Light-trail Once . 94 8.2.3 Worst Case Latency . 95 8.2.4 Three Way Split . 96 8.2.5 How to Select Splitting Nodes . 97 v CHAPTER 9. CONCLUSIONS AND FUTURE WORK . 100 9.1 Cycle Finding . 100 9.1.1 Intentionally Create Non-simple Cycles . 100 9.1.2 Incorporate Flow Algorithms . 101 9.1.3 Load Balancing . 101 9.2 Routing Heuristic Enhancement - Link Removal . 101 9.3 Routing Heuristic Enhancement - Alternate Shortest Path . 102 9.4 Quorum Cycles . 102 9.5 Light-trail Length . 102 BIBLIOGRAPHY . 104 vi LIST OF TABLES 3.1 Graph Types With α, β for Sixty Four Node Networks . 13 5.1 Three permutations of the example network . 29 5.2 Performance Difference . 34 6.1 Blocking of Random Requests Sizes 3,5, and 7 . 57 6.2 Blocking for different number of selected nodes in Arpanet . 58 6.3 Average length for different number of selected nodes in Arpanet . 59 6.4 Blocking for different number of selected nodes in NSFNet . 61 6.5 Average length for different number of selected nodes in NSFNet . 61 6.6 Blocking NSFNet all request have four selected nodes . 61 6.7 Blocking NSFNet request have between four to six selected nodes . 62 7.1 Cyclic Quorums and Cycles Found in NSFNet . 67 7.2 Number of Times an Element Pair Occurs in Cyclic Quorums (14 Nodes) 69 7.3 Number of Common Nodes between Cyclic Quorums (14 Nodes) . 70 7.4 Nodes shared between Quorums frequency (one time) . 71 7.5 Nodes shared between Quorums frequency (twice ) . 81 7.6 Nodes shared between Quorums frequency (three times) . 82 7.7 Nodes shared between Quorums frequency (four times) . 83 7.8 Nodes shared between Quorums frequency (five times) . 84 7.9 Nodes shared between Quorums frequency (six times) . 84 7.10 The number of times node pair occurs in cyclical quorums (one time) . 84 7.11 The number of times node pair occurs in cyclical quorums (twice) . 85 vii 7.12 The number of times node pair occurs in cyclical quorums (three times) 86 7.13 The number of times node pair occurs in cyclical quorums (four times) 87 7.14 The number of times node pair occurs in cyclical quorums (five times) 88 7.15 The number of times node pair occurs in cyclical quorums (six times) . 88 7.16 A Set of Requests to the Three Light-Trail Network . 88 7.17 The T Matrix before (after) Load Balancing . 89 7.18 Cycle lengths from a 20 node network of Type I . 89 8.1 Traffic Schedule on a Three Node Light-trail . 95 8.2 Traffic Schedule On A Two, Two Node Light-trail . 95 8.3 Traffic Schedule on a Five Node Light-trail . 95 8.4 Traffic Schedule On A Two, Three Node Light-trails . 96 8.5 Simulated Light-trail Traffic Breakdown . 97 8.6 Latency of Packet Arriving In Timeslot . 97 8.7 Latency of Packet Arriving In Timeslot (contd) . 98 8.8 Latency of Packet Arriving In Timeslot . 98 8.9 Schedule For The 3-1-3 Split . ..