IN
DEGREE PROJECT ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS
,
STOCKHOLM SWEDEN 2019
Link Criticality Characterization
for Network Optimization
An approach to reduce packet loss rate in
packet-switched networks
FARHAD ZAREAFIFI
KTH ROYAL INSTITUTE OF TECHNOLOGY
Link Criticality Characterization for Network Optimization
An approach to reduce packet loss rate in packet-switched networks
Farhad Zareafifi
Master Thesis
Communication Systems
School of Electrical Engineering and Computer Science KTH Royal Institute of Technology
Stockholm, Sweden
01 December 2019
Examiner: Professor Dejan Kostic
Abstract
Network technologies are continuously advancing and attracting ever-growing interests from the industry and society. Network users expect better experience and performance every day. Consequently, network operators need to improve the quality of their services. One way to achieve this goal entails over-provisioning the network resources, which is not economically efficient as it imposes unnecessary costs. Another way is to employ Traffic Engineering (TE) solutions to optimally utilize the current underlying resources by managing traffic distribution in the network. In this thesis, we consider packet-switched Networks (PSN), which allows messages to be split across multiple packets as in today’s Internet. Traffic engineering in PSN is a well-known topic yet current solutions fail to make efficient utilization of the network resources.
The goal of the TE process is to compute a traffic distribution in the network that optimizes a given objective function while satisfying the network capacity constraints (e.g., do not overflow the link capacity with an excessive amount of traffic). A critical aspect of TE tools is the ability to capture the impact of routing a certain amount of traffic through a certain link, also referred as the link criticality function. Today’s TE tools rely on simplistic link criticality functions that are inaccurate in capturing the network-wide performance of the computed traffic distribution. A good link criticality function allows the TE tools to distribute the traffic in a way that it achieves close-to-optimal network performance, e.g., in terms of packet loss and possibly packet latencies. In this thesis, we embark upon the study of link criticality functions and introduce four different criticality functions called: 1) LeakyCap, 2) LeakyReLU, 3) SoftCap, and 4) Softplus. We compare and evaluate these four functions with the traditional link criticality function defined by Fortz and Thorup, which aims at capturing the performance degradation of a link given its utilization.
To assess the proposed link criticality functions, we designed 57 network scenarios and showed how the link criticality functions affect network performance in terms of packet loss. We used different topologies and considered both constant and bursty types of traffic. Based on our results, the most reliable and effective link criticality function for determining traffic distribution rates is Softplus. Softplus outperformed Fortz function in 79% of experiments and was comparable in the remaining 21% of the cases.
Keywords: Network Optimization, Traffic Engineering, Link Criticality, QoS.
Sammanfattning
N¨atverksteknik ¨ar ett omr˚ade under snabb utveckling som r¨oner ett stort och v¨axande intresse fr˚an s˚av¨al industri som samh¨alle. Anv¨andare av n¨atverkskommunikation f¨orv¨antar sig st¨andigt ¨okande prestanda och d¨arf¨or beh¨over n¨atverksoperat¨orerna f¨orb¨attra sina tj¨anster i motsvarande grad. Ett s¨att att m¨ota anv¨andarnas ¨okade krav ¨ar att ¨overdimensionera n¨atverksresurserna, vilket dock leder till on¨odigt h¨oga kostnader. Ett annat s¨att ¨ar att anv¨anda sig av trafikstyrningl¨osningar med m˚alet att utnyttja de tillg¨angliga resurserna s˚a bra som m¨ojligt. I denna avhandling unders¨oker vi paketswitchade n¨atverk (PSN) i vilka meddelanden kan delas upp i multipla paket, vilket ¨ar den r˚adande paradigmen f¨or dagens Internet. ¨Aven om trafikstyrning (TS) f¨or PSN ¨ar ett v¨alk¨ant ¨amne s˚a finns det utrymme f¨or f¨orb¨attringar relativt de l¨osningar som ¨ar k¨anda idag.
M˚alet f¨or TS-processen ¨ar att ber¨akna en trafikf¨ordelning i n¨atverket som optimerar en given m˚alfunktion, samtidigt som n¨atverkets kapacitetsbegr¨ansningar inte ¨overskrids. En kritisk aspekt hos TS-verktygen ¨ar f¨orm˚agan att f˚anga p˚averkan av att s¨anda en viss m¨angd trafik genom en specifik l¨ank, vilket vi kallar l¨ankkritikalitetsfunktionen. Dagens TS-verktyg anv¨ander sig av f¨orenklade l¨ankkritikalitetsfunktioner som inte v¨al nog beskriver trafikf¨ordelningens p˚averkan p˚a hela n¨atverkets prestanda. En bra l¨ankkritikalitetsfunktion m¨ojligg¨or f¨or TS-verktygen att f¨ordela trafiken p˚a ett s¨att som n¨armar sig optimal n¨atverksprestanda, till exempel beskrivet som l˚ag paketf¨orlust och l˚ag paketlatens. I denna avhandling unders¨oker vi l¨ankkritikalitetsfunktioner och f¨oresl˚ar fyra olika funktioner som vi kallar 1) LeakyCap, 2) LeakyReLU, 3) SoftCap, och 4) Softplus. Vi j¨amf¨or och utv¨arderar dessa fyra funktioner och inkluderar ¨aven klassiska l¨ankkritikalitetsfunktioner som Fortz och Thorup, vilka avser f˚anga prestandadegraderingen av en l¨ank ¨over graden av utnyttjande.
Vi har unders¨okt 57 olika n¨atverksscenarier f¨or att best¨amma hur de olika l¨ank kritikalitets funktionerna p˚averkar n¨atverksprestanda i form av paketf¨orlust. Olika topologier har anv¨ants och vi har studerat s˚av¨al konstant som st¨otvis fl¨odande trafik. Enligt v˚ara resultat ¨ar Softplus den mest tillf¨orlitliga och effektiva l¨ankkritikalitetsfunktionen f¨or att f¨ordela trafiken i ett n¨atverk. Softplus presterade b¨attre ¨an Fortz i 79% av v˚ara tester, och var j¨amf¨orbar i ¨ovriga 21%.
Nyckelord: N¨atverksoptimering, trafikdesign, l¨ankkritikalitet, QoS.
Acknowledgements
First, I would like to express my deep gratitude to my supervisors, Giovanni Fiaschi and Assistant Professor Marco Chiesa. It has been a great pleasure to work under their supervision. They were very supportive and always helped me whenever I ran into problems or had a question about any subject related to the work.
I would like to offer my special thanks to my examiner, Professor Dejan Kostic, for his guidance and constructive suggestions during the development of the thesis. I am also grateful to Yngve Sel´en for helping me with the Swedish abstract. Finally, I would like to thank my family for their love, support, and encouragement throughout the thesis.
Farhad Zareafifi,
Stockholm, December 2019
Contents
1 Introduction 1 1.1 Overview . . . 1 1.2 Problem . . . 2 1.3 Purpose . . . 3 1.4 Goals . . . 3 1.5 Deliverables . . . 3 1.6 Research Methodology . . . 4 1.7 Delimitations . . . 4 1.8 Sustainability . . . 51.9 Risks, Consequences and Ethics . . . 5
1.10 Report Structure . . . 5
2 Background 7 2.1 Traffic Engineering . . . 7
2.2 Traffic Engineering Systems . . . 10
2.3 Link Criticality Function . . . 11
2.3.1 Fortz Link Criticality Function . . . 13
2.4 Traffic Estimation . . . 14
2.4.1 Gravity Model . . . 15
2.5 Traffic Generation Model and Characteristics . . . 15
2.5.1 Poisson Pareto Burst Process . . . 16
2.6 Discrete-event Network Simulator . . . 17
2.6.1 The ns-3 Network Simulator . . . 17
2.7 Related Work . . . 18
3 Definition of Link Criticality Functions 20 3.1 Rectified Linear Unit (ReLU) . . . 20
3.2 Leaky Rectified Linear Unit (LeakyReLU) . . . 21
3.3 Softplus . . . 22
3.4 Link Capacity Injection into Functions . . . 23
viii CONTENTS
3.5.1 Two Paths with the Same Number of Links . . . 28
3.5.2 Two Paths with Different Number of Links . . . 31
3.5.2.1 Uniform Network . . . 32 3.5.2.2 Non-uniform Network . . . 33 4 Methodology 36 4.1 Research Process . . . 36 4.2 Data Collection . . . 37 4.3 Data Measurement . . . 38 4.4 Scenarios . . . 39 4.4.1 Topologies . . . 39 4.4.2 Traffic Generators . . . 42 4.4.3 Pre-computed Paths . . . 43 4.4.4 Applied Modifications . . . 43 4.5 Experimental Design . . . 44 4.5.1 Testbed . . . 44 4.5.2 Hardware Platform . . . 44 4.5.3 Software Platform . . . 44
4.6 Reliability and Validity . . . 45
4.6.1 Reliability. . . 45
4.6.2 Validity . . . 46
5 Implementation 47 5.1 Initialization of Network Parameters . . . 47
5.2 Topology Creation . . . 49
5.3 Criticality Module - Phase 1 . . . 49
5.3.1 Network Modelling . . . 49
5.3.2 Path Computation. . . 51
5.4 Traffic Estimation . . . 52
5.5 Path Installation . . . 53
5.6 Criticality Module - Phase 2 . . . 53
5.6.1 Traffic Generator . . . 53
5.6.2 Criticality functions . . . 54
5.7 Traffic Engineering System (TES) . . . 56
5.7.1 Initialization Process . . . 56
5.7.2 Optimization Process . . . 57
5.7.3 Reset Process . . . 58
CONTENTS ix
6 Results and Analysis 60
6.1 Results on Packet Loss . . . 60
6.1.1 Triangle (1:1) with High Degree of Burstiness . . . 64
6.1.2 Triangle (1:4) with High Degree of Burstiness . . . 66
6.1.3 Diamond (1:4) with High Degree of Burstiness . . . 68
6.1.4 Europe-Uniform with Low Degree of Burstiness . . . 69
6.1.5 U.S.-Good with Low Degree of Burstiness . . . 69
6.1.6 B4-Bad with Low Degree of Burstiness . . . 71
6.1.7 B4-Good with Low Degree of Burstiness . . . 72
6.2 Results of Modification Impacts on Packet Loss . . . 74
6.3 Results on Average Delay . . . 76
6.3.1 Triangle (1:4) with High Degree of Burstiness . . . 77
6.3.2 Europe-Random with High Degree of Burstiness . . . 79
6.3.3 Europe-Uniform with Low Degree of Burstiness . . . 80
6.3.4 U.S.-Bad with Low Degree of Burstiness . . . 80
6.3.5 U.S.-Good with Low Degree of Burstiness . . . 82
6.4 Reliability Analysis . . . 83
6.4.1 Duration of Traffic Generation and Monitoring Process . . 83
6.4.2 Fair Comparison . . . 84
6.4.3 No Significant Impact due to Applied Modifications . . . 84
6.5 Validity Analysis . . . 84
7 Conclusions and Future Work 86 7.1 Conclusion . . . 86
7.2 Limitations . . . 87
7.3 Future Work . . . 88
7.4 Sustainability and Ethical Aspects . . . 88
7.4.1 Sustainability . . . 88
7.4.2 Ethical Aspect . . . 89
Bibliography 90 A Plots of Packet Loss Ratio 96 A.1 High Bursty Traffic . . . 96
A.2 Medium Bursty Traffic . . . 104
A.3 Low Bursty Traffic . . . 111
List of Figures
2.1 Sample of ECMP routing.. . . 8
2.2 Routing based on shortest path algorithms (a) and traffic engineering solutions (b). . . 9
2.3 Generic view of TE system.. . . 11
2.4 An example of a link criticality function. . . 12
2.5 Fortz function.. . . 13
2.6 Drawback of Fortz function. . . 14
3.1 ReLU function. . . 21
3.2 LeakyReLU function. . . 21
3.3 Smooth approximation of unit step function. . . 22
3.4 Softplus with three different β values. . . 23
3.5 LeakyCap for 1Gbps and 2Gbps links . . . 24
3.6 SoftCap for two links with different capacities (C and 2C). . . 25
3.7 Network with two paths between n1 and n2 . . . 26
3.8 Network with 2 nodes and 2 paths with same number of links . . . 29
3.9 The behavior of linear criticality functions against the different amount of traffic in a simple network discussed in Subsection 3.5.1: (a) LeakyCap, (b) LeakyReLU, (c) Fortz . . . 31
3.10 Two triangle networks: (a) uniform, (b) non-uniform. . . 32
3.11 The behavior of linear criticality functions against the different amount of traffic in a simple uniform network with three links discussed in Subsection 3.5.2.1: (a) LeakyCap, (b) LeakyReLU, (c) Fortz . . . 33
3.12 The behavior of linear criticality functions against the different amount of traffic in a simple non-uniform network with three links discussed in Subsection 3.5.2.2: (a) LeakyCap, (b) LeakyReLU, (c) Fortz . . . 34
4.1 Research process steps. . . 37
4.2 Simple topologies: (a) Triangle, (b) Diamond . . . 40
LIST OFFIGURES xi
4.4 Four cases of Europe Zone topology (capacities are in Mbps): (a) Uniform, (b) Good, (c) Bad, (d) Random . . . 41
4.5 Google B4 topology (red links connect different continents). . . . 42
6.1 Loss ratio for Softplus with different β values and Fortz function. 65
6.2 Loss ratio of criticality functions and Fortz function in Triangle (1:1) topology with high bursty traffic. . . 66
6.3 Loss ratio of criticality functions and Fortz function in Triangle (1:4) topology with high bursty traffic. . . 67
6.4 Loss ratio of criticality functions and Fortz function in Diamond (1:4) topology with high bursty traffic. . . 68
6.5 Loss ratio of criticality functions and Fortz function in Europe-Uniform topology with low bursty traffic. . . 70
6.6 Loss ratio of criticality functions and Fortz function in U.S.-Good topology with low bursty traffic. . . 71
6.7 Loss ratio of criticality functions and Fortz function in B4-Bad topology with low bursty traffic. . . 72
6.8 Loss ratio of criticality functions and Fortz function in B4-Good topology with low bursty traffic. . . 73
6.9 Loss ratio of the criticality functions in four scenarios using Europe-Uniform topology with low bursty traffic: (1) without modification, (2) buffer size modification, (3) capacity modification, (4) random seed modification. . . 76
6.10 Loss ratio of the criticality functions in four scenarios using Europe-Random topology with medium bursty traffic: (1) without modification, (2) buffer size modification, (3) capacity modification, (4) random seed modification. . . 77
6.11 Average delay of criticality functions and Fortz function in Triangle (1:4) topology with high bursty traffic. . . 78
6.12 Average delay of criticality functions and Fortz function in Europe-Random topology with high bursty traffic. . . 79
6.13 Average delay of criticality functions and Fortz function in Europe-Uniform topology with low bursty traffic. . . 81
6.14 Average delay of criticality functions and Fortz function in U.S.-Bad topology with low bursty traffic. . . 81
6.15 Average delay of criticality functions and Fortz function in U.S.-Good topology with low bursty traffic. . . 82
xii LIST OFFIGURES
A.2 Loss ratio of criticality functions and Fortz function in Triangle (1:2) topology with high bursty traffic. . . 97
A.3 Loss ratio of criticality functions and Fortz function in Triangle (1:4) topology with high bursty traffic. . . 97
A.4 Loss ratio of criticality functions and Fortz function in Diamond (1:2) topology with high bursty traffic. . . 98
A.5 Loss ratio of criticality functions and Fortz function in Diamond (1:4) topology with high bursty traffic. . . 98
A.6 Loss ratio of criticality functions and Fortz function in Europe-Uniform topology with high bursty traffic. . . 99
A.7 Loss ratio of criticality functions and Fortz function in Europe-Good topology with high bursty traffic.. . . 99
A.8 Loss ratio of criticality functions and Fortz function in Europe-Bad topology with high bursty traffic. . . 100
A.9 Loss ratio of criticality functions and Fortz function in Europe-Random topology with high bursty traffic. . . 100
A.10 Loss ratio of criticality functions and Fortz function in U.S.-Uniform topology with high bursty traffic. . . 101
A.11 Loss ratio of criticality functions and Fortz function in U.S.-Good topology with high bursty traffic. . . 101
A.12 Loss ratio of criticality functions and Fortz function in U.S.-Bad topology with high bursty traffic. . . 102
A.13 Loss ratio of criticality functions and Fortz function in B4-Uniform topology with high bursty traffic. . . 102
A.14 Loss ratio of criticality functions and Fortz function in B4-Good topology with high bursty traffic. . . 103
A.15 Loss ratio of criticality functions and Fortz function in B4-Bad topology with high bursty traffic. . . 103
A.16 Loss ratio of criticality functions and Fortz function in Triangle (1:1) topology with medium bursty traffic. . . 104
A.17 Loss ratio of criticality functions and Fortz function in Triangle (1:2) topology with medium bursty traffic. . . 104
A.18 Loss ratio of criticality functions and Fortz function in Triangle (1:4) topology with medium bursty traffic. . . 105
A.19 Loss ratio of criticality functions and Fortz function in Diamond (1:2) topology with medium bursty traffic. . . 105
A.20 Loss ratio of criticality functions and Fortz function in Diamond (1:4) topology with medium bursty traffic. . . 106
LIST OFFIGURES xiii
A.22 Loss ratio of criticality functions and Fortz function in Europe-Good topology with medium bursty traffic.. . . 107
A.23 Loss ratio of criticality functions and Fortz function in Europe-Bad topology with medium bursty traffic. . . 107
A.24 Loss ratio of criticality functions and Fortz function in Europe-Random topology with medium bursty traffic. . . 108
A.25 Loss ratio of criticality functions and Fortz function in U.S.-Uniform topology with medium bursty traffic. . . 108
A.26 Loss ratio of criticality functions and Fortz function in U.S.-Good topology with medium bursty traffic. . . 109
A.27 Loss ratio of criticality functions and Fortz function in U.S.-Bad topology with medium bursty traffic. . . 109
A.28 Loss ratio of criticality functions and Fortz function in B4-Uniform topology with medium bursty traffic. . . 110
A.29 Loss ratio of criticality functions and Fortz function in B4-Good topology with medium bursty traffic. . . 110
A.30 Loss ratio of criticality functions and Fortz function in B4-Bad topology with medium bursty traffic. . . 111
A.31 Loss ratio of criticality functions and Fortz function in Triangle (1:1) topology with low bursty traffic. . . 111
A.32 Loss ratio of criticality functions and Fortz function in Triangle (1:2) topology with low bursty traffic. . . 112
A.33 Loss ratio of criticality functions and Fortz function in Triangle (1:4) topology with low bursty traffic. . . 112
A.34 Loss ratio of criticality functions and Fortz function in Diamond (1:2) topology with low bursty traffic. . . 113
A.35 Loss ratio of criticality functions and Fortz function in Diamond (1:4) topology with low bursty traffic. . . 113
A.36 Loss ratio of criticality functions and Fortz function in Europe-Uniform topology with low bursty traffic. . . 114
A.37 Loss ratio of criticality functions and Fortz function in Europe-Good topology with low bursty traffic. . . 114
A.38 Loss ratio of criticality functions and Fortz function in Europe-Bad topology with low bursty traffic. . . 115
A.39 Loss ratio of criticality functions and Fortz function in Europe-Random topology with low bursty traffic. . . 115
A.40 Loss ratio of criticality functions and Fortz function in U.S.-Uniform topology with low bursty traffic. . . 116
xiv LIST OFFIGURES
A.42 Loss ratio of criticality functions and Fortz function in U.S.-Bad topology with low bursty traffic. . . 117
A.43 Loss ratio of criticality functions and Fortz function in B4-Uniform topology with low bursty traffic. . . 117
A.44 Loss ratio of criticality functions and Fortz function in B4-Good topology with low bursty traffic. . . 118
A.45 Loss ratio of criticality functions and Fortz function in B4-Bad topology with low bursty traffic. . . 118
A.46 Loss ratio of criticality functions and Fortz function in Europe-Uniform topology with constant traffic. . . 119
A.47 Loss ratio of criticality functions and Fortz function in Europe-Good topology with constant traffic. . . 119
A.48 Loss ratio of criticality functions and Fortz function in Europe-Bad topology with constant traffic. . . 120
A.49 Loss ratio of criticality functions and Fortz function in U.S.-Uniform topology with constant traffic. . . 120
A.50 Loss ratio of criticality functions and Fortz function in U.S.-Good topology with constant traffic. . . 121
A.51 Loss ratio of criticality functions and Fortz function in U.S.-Bad topology with constant traffic. . . 121
A.52 Loss ratio of criticality functions and Fortz function in B4-Uniform topology with constant traffic. . . 122
A.53 Loss ratio of criticality functions and Fortz function in B4-Good topology with constant traffic. . . 122
List of Tables
5.1 Propagation delay of each link in B4 topology (see Figure 4.5) . . 48
6.1 Results of comparison for high bursty traffic. . . 61
6.2 Results of comparison for medium bursty traffic. . . 61
6.3 Results of comparison for low bursty traffic. . . 62
6.4 Results of comparison for constant traffic. . . 62
6.5 Overall performance of criticality functions in 57 scenarios comparing to Fortz function. . . 63
6.6 Overall performance of two Softplus functions compared to Fortz function. . . 64
6.7 Comparison ratio of each criticality function against Fortz after modification to Europe-Uniform topology. . . 74
6.8 Comparison ratio of each criticality function against Fortz after modification to Europe-Random topology. . . 75
6.9 Comparison rates for Softplus with β set to 20 and 30. . . 83
List of Listings
1 Topology creation in ns-3 simulator. . . 50
2 Link class in Criticality module. . . 51
3 Path class in Criticality module. . . 52
4 TrafficGenerator class in Criticality module. . . 54
5 Method for link cost measurement using Fortz function. . . 55
6 Method for link cost measurement using Soft function. . . 56
7 Method for link cost measurement using Leaky function. . . 57
8 pseudo-code of optimization process.. . . 59
List of Acronyms and Abbreviations
CSMA Carrier-Sense Multiple Access ECMP Equal Cost Multipath
FIFO First In First Out
IS-IS Intermediate System to Intermediate System LDP Label Distribution Protocol
LP Linear Programming
LRD Long-Range Dependent LSP Label Switched Path LSR Label Switching Routers MLU Maximum Link Utilization MPLS Multiprotocol Label Switching NS-3 Network Simulator 3
OSPF Open Shortest Path First
P2P Point-to-Point
PPBP Poisson Pareto Burst Process PSN packet-switched Network ReLU Rectified Linear Unit TE Traffic Engineering
TES Traffic Engineering System
Chapter 1
Introduction
This chapter aims to motivate the thesis by providing an overview of the work, describing today’s existing TE problems, and clarifying the purpose that has been followed in the entire work. This chapter also presents the adopted research methodology and describes the scope of the project. Issues concerning project sustainability, consequences, and ethics are described.
1.1
Overview
In recent years, Internet traffic has grown at a fast pace and every day attracts more users [1]. In 2009, the Minnesota Internet Traffic Studies (MINTS) indicated that Internet traffic increased by 40% to 50% compared to 2008 [2]. Moreover, in 2018, the Malaysian Communications and Multimedia Commission (MCMC) conducted a survey to collect information about Internet users in Malaysia. This survey presents 10.5% percentage increase in percentage of Internet users from 76.9% in 2016 to 87.4% in 2018 [3]. End-users use data networks to exchange and share information and they demand multimedia services and applications with high quality for their communications. This means it is essential for service providers to enhance the quality of their communication services regularly. Results presented in [4] indicates that there are bottlenecks in both intra-domain and inter-domain interconnections at the Internet backbone. Therefore, network and service providers need to adopt a method in order to eliminate the bottlenecks. One method is over-provisioning in network resources; However, this approach imposes unnecessary high network costs and increases power consumption which is not efficient from an energy point of view. Another method is to adopt traffic engineering techniques [5].
2 CHAPTER 1. INTRODUCTION
traffic through the packet-switched network (PSN) and utilizes this information with the aim of evaluating and optimizing the performance. The performance of a PSN can be defined based on different metrics such as packet loss rate, packet delay, delay variation, and throughput. This performance and the service quality to end-users can be severely affected by congestion in any PSN. Thus, as one can find in RFC 3272 [5], traffic engineering techniques tend to minimize congestion to improve performance and resource utilization. Congestion is a state where a network node or link tries to carry data beyond its capacity which may cause packet loss or worsen packet delay [6].
One of the actions taken by traffic engineering mechanisms to obviate or mitigate congestion is to control traffic routing among nodes and determine distribution rates for each demand among available paths in the most effective way [5]; However, finding the best routes and distribution rates for traffic demands can be challenging according to different congestion symptoms. For example, if network providers do not properly select demand distribution rates among available paths, it will lead to degradation in the quality of their network services. Therefore, a mechanism is required to discover the rates effectively and orchestrate the traffic distribution over the PSN.
1.2
Problem
Network optimization can be conducted by TE systems with different objective functions. One of the previously proposed objective functions entails minimizing the sum of “link costs” in PSN. This objective function needs a cost function to compute the cost of each link. Henceforth, the cost function is defined as link criticality function in this thesis.
By monitoring the traffic and analyzing the statistics, it is possible to predict congestion in PSN. In order to avoid unnecessary costs due to resource over-provisioning, network operators need to employ TE solutions with an effective link criticality function to deliver more efficiency to network sensitive services; However, current link criticality functions are simplistic and have not been thoroughly analyzed. We believe that TE solutions need new and well-explained link criticality functions. Therefore, the major questions of the thesis are:
1.3. PURPOSE 3
1.3
Purpose
The purpose of the thesis is to investigate and discuss new link criticality functions and try to find good criticality function(s) for TE systems. A good link criticality function can lead TE solutions to close-to-optimal network performance in terms of packet loss and possibly average delay.
Any network provider with the aim of enhancing the network performance may benefit from a good criticality function as part of their objective function. Therefore, in case the outcome of the thesis is promising, our defined criticality function will be useful in the area of network performance optimization.
1.4
Goals
In order to satisfy the purpose of the thesis, we need to meet the following goals: 1. Studying recent researches which are mainly about different traffic
engineering approaches and network performance optimization using different objective functions.
2. Specifying alternative link criticality functions.
3. Developing a simulated environment with some well-known traffic generation models.
4. Implementing a traffic engineering system to perform the optimization process.
5. Running the experiments for each link criticality function to assess the effectiveness of each function in the network.
6. Comparing the defined link criticality function(s) with a well-known criticality function to emphasize the positive effects achieved in this work.
1.5
Deliverables
• A project proposal. • Four criticality functions.4 CHAPTER 1. INTRODUCTION
• All of the results and plots collected during the projects.
• A written thesis containing background information, details of the project environment and implementation, and the result analysis.
• Oral presentation of the project.
1.6
Research Methodology
In this thesis, the conducted simulations provide measured data for different criticality functions. The main purpose of this thesis is to compare these criticality functions according to the values obtained from these simulations and to illustrate that a good criticality function can improve the performance of IP networks in terms of packet loss and possibly packet delay. Accordingly, this thesis follows a quantitative approach [7].
1.7
Delimitations
In this project, all of the experiments are performed in a simulated environment. The network considered for the experiments and evaluation is a path-based network where there are exactly two pre-computed link-disjoint paths between each pair of nodes, a common scenario to support reliable communication in the presence of single-link failures. Also, in each experiment, we assume there is a single traffic scenario and the average demands are known to the TE system, which optimizes the traffic distribution according to this knowledge. As the focus of the thesis is on evaluating link criticality and not TE systems, dynamic TE optimization is orthogonal to the scope of this thesis project. Additionally, node and link failures are not considered in the experiments. Hence, all of the nodes and links are always up in the network.
1.8. SUSTAINABILITY 5
1.8
Sustainability
This thesis can have a positive impact on sustainability. The purpose of this thesis is to improve the performance of the current networks and enhance the quality of network services without changing network resources. If we can satisfy this purpose, then network providers do not need to use more power-hungry devices to deliver better services which will lead to reduced power consumption and a decrease in greenhouse gas emissions. Moreover, network providers can economically benefit from this thesis since they can use their resources efficiently and avoid over-provisioning. Also, delivering a better quality of services with the same resources will result in satisfying end-users and making their lives more enjoyable.
1.9
Risks, Consequences and Ethics
Since all of the experiments are intended to be done in a simulated environment, there are no consequences such as device breakdown or network failure. The only platforms that can be affected during this work are one virtual operating system (OS), Ubuntu 18.04, run on top of Windows 10 OS and one physical machine running Ubuntu 16.04 used for the experiments.
The whole thesis is an attempt to improve network performance using open source academic materials, software, and tools. Therefore, there was no need to provide any license agreement. Also, this thesis is not conducted to be used against any user or organization. Since it is not related to any security topics, it is completely harmless.
This thesis is industrial and is organized by Ericsson, a Swedish multinational networking and telecommunications company. Hence, the outcome of the thesis belongs to Ericsson. Since it is necessary to publish the thesis and make the codes and resources publicly available, informed consent was given by Ericsson which allows to only share the information relevant to this project.
1.10
Report Structure
The rest of this report is organized as follows: Chapter 2 provides background information required to understand this project. Chapter 3 defines different criticality functions used in the project traffic engineering system. Chapter 4
6 CHAPTER 1. INTRODUCTION
the problem. Chapter5 describes the implementation of the traffic engineering system used in this project. Chapter6presents the results and analysis. Chapter7
Chapter 2
Background
This chapter provides relevant background information to ease understanding of the selected methods and thesis implementation. First, it gives basic background information about traffic engineering concepts to present why network operators tend to use traffic engineering tools. Then, it defines traffic engineering systems and the process of network optimization. Afterward, it describes a well-know link criticality function used as the benchmark of this work. Subsequently, it provides information about a method for estimating demand among the nodes required for implementation. Then, it provides information about traffic characteristics and a method used for generating estimated demand matrices. Also, in this chapter, a brief introduction of discrete-event simulators is given. This chapter ends with stating the works done in the past that are related to this degree project.
2.1
Traffic Engineering
Traffic engineering (TE) is a technique used by network operators and service providers to improve resource utilization in their networks and to satisfy end-users by delivering better services [5]. In many IP networks, dynamic routing protocols such as OSPF [8] and IS-IS [9] are widely used. These protocols calculate the shortest path between each pair of network nodes based on links weights which can be configured manually or set by default according to a predefined standard [10]. Then, the traffic is sent toward the destination through the computed shortest path. Even though these protocols are very useful, they suffer from a lack of flexibility. In conventional dynamic routing protocols that follow shortest path algorithms, if there are several shortest paths with the same cost, only one of them will be selected to host the traffic. To make these protocols more flexible, network operators use Equal-Cost Multi-Path (ECMP). When multiple shortest paths between a pair of nodes exist, ECMP spreads traffic evenly among the
8 CHAPTER2. BACKGROUND
paths [11]. As an example, Figure 2.1 presents a topology where there are two equal-cost paths between R1 and R5. Through ECMP, R1 could split the traffic evenly between two paths. Being supported in OSPF and IS-IS [12], ECMP is used in conjunction with dynamic routing protocols for traffic distribution in many intra-domain networks.
Figure 2.1: Sample of ECMP routing.
However, traditional IP networks even with ECMP are still not sufficiently sophisticated to prevent congestion within the network and they are oblivious to the traffic demands and traffic patterns. One way to solve this problem is to over-provision the network bandwidth resources; However, this solution is not economically efficient and may lead to a waste of resources. Another solution is to apply for TE solutions.
2.1. TRAFFICENGINEERING 9
business model. Thus, each network may have different optimization objectives for performance improvement.
Figure 2.2: Routing based on shortest path algorithms (a) and traffic engineering solutions (b).
There are different approaches to TE [5]. In the following, we explain two of these approaches:
• TE with ECMP in IP networks - Traffic engineering has been proposed due to the limitations of traditional routing protocols; However, it was shown during the past researches that the routing of demands over traditional shortest-path network infrastructure can be controlled by playing with different routing parameters and metrics such as link weights. Consequently, an operator may set the weights according to either the distance between adjacent nodes or requirements set with the aim of avoiding link overutilization. Fortz and Thorup [14], [15], [16], [17] proposed the first TE solution for IP networks. Their solution tries to mitigate the probability of having overutilized links by tuning OSPF weights in response to the demands and split the demands among the paths with the same cost using ECMP. They showed that the problem of finding the global optimal settings of the OSPF link weights for a set of demands in an arbitrary network is NP-hard. Subsequently, they defined a local search heuristic and a link criticality function to discover the set of link weights. Based on the measured set of demands, they tuned the weights in order to favor ECMP and minimize the sum of link costs. They found that their results were very close to global optimal routing.
10 CHAPTER2. BACKGROUND
labels for forwarding packets through the network and classifies packets into different classes [19], [20]. MPLS capable routers are called Label Switching Routers (LSR). They exchange the labels to set up a path between nodes and they look at the label instead of the IP address of the destination for making forwarding decisions. In MPLS, the path between an ingress LSR and an egress LSR is known as a label switched path (LSP). These paths are programmed based on a set of requirements, objectives, and operator policies and may not follow traditional shortest path calculation. LSP setup process is performed before sending any data. In order to propagate the labels between adjacent LSRs during the setup process, the Label Distribution Protocol (LDP) [21] is used. As soon as the setup process is complete, data will be sent toward the egress LSR through the explicit LSP configured by the ingress LSR.
TE tools tend to compute paths or determine traffic distribution rates among available paths in the most effective way. Based on the view of the traffic demands, these tools can be categorized into two classes:
1. Oblivious TE - TE tools do not have any information about traffic demands. The process of path computation and splitting ratio calculation is conducted offline. Oblivious TE tools make routing decisions over a set of expected traffic scenarios. The disadvantage of these tools is that the routing and splitting ratios are static. Therefore, oblivious TE tools do not necessarily achieve optimal performance [22].
2. Demand-aware TE - TE tools are aware of traffic demands and make decisions based on the traffic information. Routing decisions or traffic distribution rates may dynamically change during the time. These tools repeat the optimization process to cover the traffic fluctuations and to possibly compute new routes and rates. In all the demand-aware TE tools, the traffic distribution rates dynamically adapt based on the demands [16]; However, some tools follow static routing and the paths do not change during the optimization process. One of the examples of such tools is SMORE [23]. Since paths were obliviously computed in SMORE, it was also called semi-oblivious TE. In this thesis, the TE environment that we employ for the experiments is similar to a semi-oblivious TE tool.
2.2
Traffic Engineering Systems
2.3. LINK CRITICALITY FUNCTION 11
mechanisms, and policies and they are on top of the network infrastructure. As input, they take information about the properties of the network and the operator’s performance goals in the form of an objective function. Then, they compute a network configuration (i.e., a fractional allocation of the demands onto the physical paths) that optimizes the objective function value [5]. Figure 2.3
presents a generic view of a traffic engineering system. TE systems can use different objective functions according to the operator’s policy. One objective is to minimize the maximum link utilization while another objective function may aim for minimizing the sum of the link costs computed by a link criticality function.
Figure 2.3: Generic view of TE system.
To find the appropriate network configuration, TE systems use a heuristic algorithm (e.g., Tabu search or Greedy algorithm) alongside the objective function to explore among possible network configurations. The objective function and heuristic are in-built into the protocols (e.g., MPLS autobandwidth) or given to the system by network operators. Also, TE systems may employ an LP solver which can compute the optimal configuration. Depending on the solution, TE system may need different parameters as inputs to perform the network optimization. For example, if a TE solution is demand-aware, then the system needs to know the set of the demands for flow between the nodes. Also, in semi-oblivious TE, the TE system needs the pre-computed paths to return the appropriate traffic distribution rates as the updated configuration.
This thesis focuses on minimizing the sum of the link costs as one of the popular objective functions used by TE systems. We aim to provide new link criticality function(s) for computing the cost of each link in the network which can lead TE systems to improve the network performance.
2.3
Link Criticality Function
12 CHAPTER2. BACKGROUND
the link capacity. These functions may be defined differently depending on traffic characteristics and other aspects of the networks. Being used to compute each link cost, link criticality functions are beneficial for TE systems that intend to minimize the sum of the link costs:
Φ =
∑
a∈linksΦa a∈ links (2.1)
Objective function −→ min Φ (2.2) Link criticality functions may have one or several critical points. These points are used to model the impact of increasing link utilization on the link performance. Based on the definition of link criticality function, the impact on the link performance can be either severe or gentle when the link utilization goes over a criticality point. For example, in one link criticality function, passing over 50% of link utilization is less critical than passing over 80% of link utilization. Therefore, criticality function is more aggressive around 80% utilization (see Figure2.4). Being more aggressive means that the criticality function has more tendency to keep the link utilization below the critical point. To define a good criticality function, it is very important to set accurate critical point(s) and to determine the impact on the link performance when the link utilization passes over the point(s).
Figure 2.4: An example of a link criticality function.
2.3. LINK CRITICALITY FUNCTION 13
2.3.1
Fortz Link Criticality Function
Fortz and Thorup [14], [17] provided a traffic engineering system to optimize routing solutions in OSPF/IP networks. In their approach, they used a piecewise linear convex function as the link criticality function in order to optimize their objective function, i.e., minimizing the sum of the link costs. As shown in Figure
2.5, this criticality function is continuous and it is defined as follows:
Φa(x) = x 0 ≤ x < 13 3x −23 13≤ x < 23 10x −163 23≤ x < 109 70x −1783 109 ≤ x < 1 500x −14683 1 ≤ x < 1110 5000x −163183 1110 ≤ x a∈ links (2.3)
This criticality function is very popular and it has been used in many studies such as [16], [24], [25], [26]. In this project, we refer to this function as the Fortz function. The Fortz function includes multiple critical points which modify the impact of the link utilization on the performance cost in the network; However, the authors did not explain how they determined the critical points and different gradients of the formula.
Figure 2.5: Fortz function.
14 CHAPTER2. BACKGROUND
of all the links is 10Mbps. There is only one bursty traffic flow from n1 to n2. When traffic is bursty it means that the traffic rate is unstable. Depending on how bursty the traffic is, a link may start losing packets even if the mean traffic rate is lower than the link capacity. In this case, we say that the link entered the bursty zone. In the example, l1 and l2 are respectively the load on the first path and the second path from n1to n2. The mean traffic rate is 15Mbps and the bursty zone is defined as 0.75 which means a link is prone to lose packets if its utilization exceeds 75%. Figure2.6shows that if the TE system uses Fortz function for the network optimization process, the utilization of the link between n1 and n2 exceeds 75%. In this particular example, a desirable optimization solution balances the load between the paths to prevent all the links from entering the bursty zone.
Figure 2.6: Drawback of Fortz function.
In this thesis, we use Fortz function as the benchmark to evaluate the effectiveness of the link criticality functions that we define in Chapter3. We aim to introduce a new link criticality function which results in the desired traffic distribution.
2.4
Traffic Estimation
2.5. TRAFFICGENERATIONMODEL AND CHARACTERISTICS 15
network. Each element in the demand matrix represents the amount of the aggregated traffic flows sent from node i to node j on average. Since we intend to work on the simulated environment, we need to follow a model that generates the demand matrices that reflect real-world traffic patterns.
2.4.1
Gravity Model
The gravity model [28] is a simple yet popular model for estimating traffic matrices. The general definition of the gravity model is that the amount of vehicle traffic from one city to another city is proportional to the product of the population of cities divided by the distance between cities. In the context of PSN networks, the definition is slightly different. There are several ways to generate a traffic matrix depending on operators [29]. In this thesis, each element of traffic matrix produced by gravity model represents the amount of traffic from node i to node j which is proportional to the product of the degree of the nodes divided by the distance between them:
Tri j= Gcoe f f× (Ni× Nj) Di j
(2.4) In Formula 2.4, Tri j represents the amount of traffic in bits per second sent between node i and j, Niand Njare respectively the degree of the node i and node j, and Di j is the distance between two nodes which is based on the transmission and propagation delay of the links in the shortest path between the nodes. Gcoe f f is a normalization constant which we call it gravity coefficient. Since tracing real traffic in many networks is challenging [30], many recent works such as [31], [32], [22] used gravity model for traffic matrix generation.
After the traffic estimation process, it is necessary to define a model to generate the estimated traffic matrix. In the next section, traffic modeling is clarified and a method for generating real Internet traffic is introduced.
16 CHAPTER2. BACKGROUND
unrealistic but it is very simple to use for calculation and analysis due to the fixed value of the traffic rate. On the other hand, bursty traffic has an unstable rate and it is more difficult to analyze. A burst is a large amount of data sent from one node to another in a short period of time. Real traffic tends to be bursty (e.g., request for a web service or a file). Therefore, a realistic traffic generation model should model burstiness.
Early traffic generation models were based on probability distribution such as Poisson distribution. There are many works such as [33] that used Poisson models for generating traffic; However, Poisson models were not adequate since they could not model sudden bursts in traffic [34]. Being memoryless, Poisson models are not able to satisfy real Internet traffic properties (e.g., self-similarity). As real traffic is self-similar [35], a realistic traffic model needs to support a large time-scale analysis. Self-similarity means that the characteristic of traffic such as burstiness is the same at different time scales. An option for modeling Internet traffic is Pareto distribution. A Pareto distribution may not represent self-similarity perfectly, yet it is better than Poisson distribution as it covers heavy tails and it can be used to model Internet traffic in a short period. Pareto distribution was originally proposed to model the income distribution among people. It followed the trend that most of the wealth in the world is distributed among a few numbers of people. [36].
The degree of self-similarity is described by the Hurst parameter (0 ≤ H ≤ 1). The Hurst parameter denotes whether a self-similar process is Long-Range Dependent (LRD). If a process is LRD, then the process has a long memory and follows the same pattern with different time scales. In other words, the decay rate of the dependency between two points is very slow when increasing the time interval [37]. If the Hurst parameter gets closer to 1, the process model can support longer memory and it is more self-similar.
The discovery of the self-similarity nature of Internet traffic led to designing different Internet traffic models such as SWING [38] and Poisson Pareto Burst Process (PPBP) [39]. In this thesis, the PPBP model is used for modeling and generating traffic due to its simplicity and accuracy.
2.5.1
Poisson Pareto Burst Process
2.6. DISCRETE-EVENTNETWORKSIMULATOR 17
1. A function for following the number of active bursts at time t (nt). 2. A function for generating packets at a constant bit-rate r.
In the PPBP model, the arrival of the bursts is followed by Poisson distribution with the rate λp. The length of each burst is based on Pareto distribution with mean Ton. Also, this model uses the Hurst parameter, H, for determining the degree of self-similarity. In order to generate LRD traffic, H must be between 0.5 and 1. In the PPBP model, the average number of active bursts can be computed based on Little’s law [41]:
E[n] = λp× Ton (2.5)
2.6
Discrete-event Network Simulator
In order to simulate a network environment for analysis and evaluation, we use discrete-event simulation. In the context of computer networks, discrete-event simulation is the process of examining the behavior and performance of a network system [42]. This would help network providers to predict how networks will respond to various changes and react in critical scenarios.
A discrete-event simulation models the system as a consecutive series of well-defined events and movement from one event to the next event occurs over time. OMNeT++ [43], ns-3 network simulator [44], and openWNS [45] are different examples of discrete-event network simulators. In this thesis, ns-3 is used for network simulation. In the following subsection, a brief introduction to this simulator is provided.
2.6.1
The ns-3 Network Simulator
Ns-3 is an open-source discrete-event, packet-level network simulator which is written in C++. Ns-3 is a new version of ns-2 but it is not backward-compatible since ns-2 APIs are not supported by ns-3 [44]. In the ns-3 network simulator, different software libraries are provided which are supposed to work together. Network users can write a program in C++ or Python in order to combine different ns-3 libraries and create a networking scenario. Also, scripting using C++ and Python is supported by ns-3.
18 CHAPTER2. BACKGROUND
this thesis, we only follow the P2P model for communication between network nodes. P2P model is a very simple model that uses P2P channels for establishing a connection between a pair of nodes. A P2P channel between two nodes can be viewed as a full-duplex link.
Comparing with other discrete-event network simulators, ns-3 has several advantages. Ns-3 follows modularity design and allows programmers to write modular libraries. Also, a network programmer has the capability of generating pcap files. These files are used for collecting information on packets and they can be examined by software tools such as Wireshark. In addition, ns-3 can deliver very good computation time and memory usage in comparison with other simulators such as OMNeT++ [46].
2.7
Related Work
This thesis targets the objective function of TE systems. Over the years, there have been different objective functions used in research papers. Two of the most popular objective functions are the minimization of maximum link utilization and minimization of the sum of link costs.
Minimization of Max Link Utilization - One of the common objective functions is minimizing the maximum link utilization (MLU). The utilization of a link is defined as the load on the link vs. the link capacity (utilization =capacityload ). This objective function tends to control and keep MLU of the network below 100%. As long as MLU is below 100%, there is no congested link in the network. MLU minimization is considered as a convex function and solved using an LP solver such as CPLEX [47]. This objective function has been very useful and used in many recent research papers [32], [22], [48]. A drawback of this objective function is that it only targets the maximum link utilization and aims to minimize it. Therefore, it does not care about balancing the load for the other links.
Minimization of Sum of Link Costs - This thesis mainly focuses on this objective function that tends to minimize the link costs computed by a link criticality function. As mentioned in Subsection 2.3.1, one of the popular link criticality functions defined by Fortz and Thorup, is a Convex Piecewise Linear function; However, this function is old and the authors did not explain how they find and compute the gradients and the critical points in their link criticality function. We use this function as the benchmark for the evaluation of our defined link criticality functions.
2.7. RELATEDWORK 19
network. When a source node sends a packet toward a destination node, the packet goes through several network devices and may get buffered. Therefore, it suffers from several queueing delays imposed by different network devices. Queueing delay is the time that a packet needs to wait in the queue before being transmitted to the wire. Based on M/M/1 model [49], the average queueing delay on a link a is as follows:
ta= 1 Ca− la
a∈ links (2.6)
In Formula2.6, Ca and larepresent the capacity of link a and the load on link a, respectively. This formula is called mean link delay; However, since optimizing the delay for the paths with higher traffic load delivers better performance, a new link criticality function is defined [50]:
la× ta= la Ca− la −→ Φa(x) = x 1 − x (2.7)
Chapter 3
Definition of Link Criticality
Functions
In PSNs, congestion may cause packet loss. During congestion, bottleneck links become overutilized and packets start being buffered in a queue. When the device buffer is full, there is no space for new arriving packets and consequently, the device drops them. One way to avoid or mitigate the probability of having congestion is to keep all the links in the network below 100% of utilization. Thus, we decided to define the critical point as the moment a link reaches full utilization (x = 1). In this project, a link that goes over the criticality point is called a critical link. When one link becomes overutilized and its buffer is full (steady-state), packet loss occurs linearly by increasing the traffic rate. This intuition led us to define the first criticality function of the thesis, the Rectified Linear Unit (ReLU).
3.1
Rectified Linear Unit (ReLU)
Rectified Linear Unit (ReLU) is a linear function that returns the positive part of the argument. This function is mostly used in the context of artificial neural networks [52]. In this project, ReLU function was defined as follows:
Φa(x) = (
Cnorm× (x − 1) if x ≥ 1.
0 otherwise. a∈ links (3.1) In Formula 3.1, x and Cnorm respectively represent link utilization and normalization constant. In this thesis, we arbitrarily set Cnorm to the minimum link capacity of the network. Hence, Φa(x) indicates the cost of link a based on its utilization. The formula, depicted in Figure 3.1, shows that there is no penalty as long as a link has available space. But, as soon as it gets into the overutilization area, the cost increases linearly. A clear drawback of ReLU is
3.2. LEAKY RECTIFIEDLINEAR UNIT(LEAKYRELU) 21
that it does not differentiate among underutilized links. For example, there is no difference between an empty link and a nearly full link in ReLU. This is problematic when traffic is bursty or if network operators care about traffic delays. Therefore, we extend Relu with the following two functions: 1) LeakyReLU, and 2) Softplus.
Figure 3.1: ReLU function.
3.2
Leaky Rectified Linear Unit (LeakyReLU)
The LeakyReLU function is equal to the ReLU function but also contains a leaky part. LeakyReLU allows us to add a very small, non-zero gradient to ReLU when links are underutilized (see Figure3.2). Consequently, increasing the link utilization will increase the cost of the link, even if the link is underutilized. In practice, it means that the cost of an empty link is less than the cost of a half-full link during the computation of the sum of the link costs.
22 CHAPTER 3. DEFINITION OFLINK CRITICALITY FUNCTIONS
We define LeakyReLU as follows: Φa(x) =
(
Cnorm× (x − 1) if x ≥ 1. Rleaky×Cnorm× (x − 1) otherwise.
a∈ links (3.2) Rleakydetermines the very small gradient of the leaky part and how effective it can be around the critical point. In this thesis, we set Rleaky to 0.01 since it is a very small gradient comparing to the gradient of the ReLU part.
3.3
Softplus
Softplus is a ReLU function which is smooth around the critical point. It is also called SmoothReLU. To get to Softplus, the derivative of ReLU is needed:
dΦa(x) dx =
(
Cnorm if x ≥ 1.
0 otherwise. a∈ links (3.3) Formula3.3represents a unit step function. As one can see in Figure 3.3, one of the smooth approximation of unit step function is Sigmoid function:
dΦa(x)
dx = Cnorm×
eβ (x−1)
1 + eβ (x−1) a∈ links (3.4)
Figure 3.3: Smooth approximation of unit step function.
In the Sigmoid function, β is the limit of the slope of the function at the critical point. The Softplus function is the integral of the Sigmoid function:
3.4. LINK CAPACITYINJECTION INTOFUNCTIONS 23
Figure 3.4: Softplus with three different β values.
3.4
Link Capacity Injection into Functions
Up to this point, we have defined two functions as criticality functions: LeakyReLU and Softplus. We use these functions regardless of the link capacity. Therefore, in the case of having two links with equal residual capacity, the cost of the smaller link is lower. For example, if there are two links, one empty 1Gbps link (x = 0) and one 10Gbps link filled to 80% (x = 0.8), then the first link will be favored even though there is double free space in the second link. Hence, we aim to understand whether favoring the placement of the flows on the link with higher absolute capacity would lead to better traffic distributions.
Conjecture- Injecting information about link capacity into criticality functions outperforms LeakyReLU and Softplus. The new information helps the criticality functions to reflect current link status and distinguish between two links with different capacity filled at the same rate.
LeakyReLU and Softplus are derived from ReLU. Thus, we add link capacity information into ReLU and recalculate LeakyReLU and Softplus again. We defined ReLU with capacity information as follows:
24 CHAPTER 3. DEFINITION OFLINK CRITICALITY FUNCTIONS
In Formula3.6, Ca is the capacity of the link a. Consequently, as the cost of the link a, Φa(x) indicates the amount of the traffic that exceeds the capacity of the link a. By adding the leaky part to the new ReLU function, LeakyReLU with capacity is derived as follows:
Φa(x) = (
Ca× (x − 1) if x ≥ 1. Rleaky×Ca× (x − 1) otherwise.
a∈ links (3.7)
We named new LeakyReLU as LeakyCap. Figure 3.5 illustrates LeakyCap functions for two links with a capacity of 1Gbps and 2Gbps respectively. The cost of the 2Gbps link filled with traffic at 50% is equal to the cost of the 1Gbps link when it is empty. Also, in case of overutilization for both links, if x1Gbps= x2Gbps and both links have the same buffer size, then more packets will be lost in traffic that goes through 2Gbps link.
Figure 3.5: LeakyCap for 1Gbps and 2Gbps links
3.5. THEORETICAL ANALYSIS OFCRITICALITY FUNCTIONS 25
We named the new defined Softplus function as SoftCap. Figure 3.6 shows SoftCap functions with the same β for two different links, a and b, where link bhas the capacity two times greater than link a. Hence, the costs for empty link a and half-filled link b are identical.
Figure 3.6: SoftCap for two links with different capacities (C and 2C) In the next section, we theoretically examine the behavior of the aforesaid criticality functions in simple networks with two and three links.
26 CHAPTER 3. DEFINITION OFLINK CRITICALITY FUNCTIONS
In this thesis, we have used a wide number of β values in each experiment and reported the best values. Chapter6provides interesting findings about the best β for different scenarios.
For better understanding the behavior of LeakyReLU and LeakyCap, we provide the network shown in Figure3.7. In this network, there are two paths between nodes n1 and n2. The first and second paths respectively contain M and N links where M ≤ N. There are four constraints in this network:
1. The shorter path has a fewer or equal number of links. Therefore, if M 6= N, then the first path is the shorter path.
2. The links that belong to one path have the same capacity. Hence, the capacity of the links in the first and second paths are respectively C1 and C2.
3. If the amount of traffic sent from n1 to n2 is Tr and the loads on the paths are respectively l1and l2, then Tr = l1+ l2.
4. The utilization of every link in the network is lower than 1.
Figure 3.7: Network with two paths between n1 and n2
LeakyCap - According to the constraints, we can calculate the cost of the network using LeakyCap as follows:
Path1Cost : Φ1=
∑
Φa1(x) = M × Rleaky×C1× (x1− 1)= M × Rleaky× (l1−C1)
3.5. THEORETICAL ANALYSIS OFCRITICALITY FUNCTIONS 27
Path2Cost: Φ2=
∑
Φa2(x) = N × Rleaky×C2× (x2− 1)= N × Rleaky× (l2−C2) = N × Rleaky× (Tr − l1−C2)
(3.10)
Total Cost: Φ = Φ1+ Φ2= Rleaky× M × (l1−C1) + N × (Tr − l1−C2) = Rleaky×
M− Nl1+ N(Tr −C2) − MC1
(3.11)
Cost Minimization: min Φ = min M − Nl1 (3.12) Based on Formula3.11, to minimize the total cost, it is required to only minimize M− Nl1 since the second term of the equation is constant. Hence, LeakyCap tends to maximize l1 if M < N. In the case that M = N, it does not matter how we distribute the traffic between the paths since the total cost does not change. As mentioned before, LeakyCap distributes the traffic between two paths evenly due to fair-balancing. Note that moving over the criticality point affects Formula 3.9 and 3.10 due to the gradients. Thus, Formula 3.12 is valid only if both x1, x2 ≤ 1.0 at the same time. The gradient of LeakyCap is set to Rleaky (0.01 in this thesis) when the links are underutilized and otherwise it is set to 1. If a link utilization exceeds the critical point of LeakyCap (x = 1), we need to use a new gradient (removing Rleaky) for computing the cost of the link. LeakyReLU - Computing the cost of the network using LeakyReLU is very similar to LeakyCap. The only difference is that we replaced Cawith Cnorm: Path1Cost: Φ1=
∑
Φa1(x) = M ×Cnorm× (x1− 1)= M ×Cnorm× ( l1 c1− 1)
(3.13)
Path2Cost: Φ2=
∑
Φa2(x) = N ×Cnorm× (x2− 1)= N ×Cnorm× ( l2 C2− 1) = N ×Cnorm× ( Tr− l1 C2 − 1) (3.14)
Total Cost: Φ = Φ1+ Φ2= Cnorm×
28 CHAPTER 3. DEFINITION OFLINK CRITICALITY FUNCTIONS
Cost Minimization: min Φ = min MC2− NC1l1 (3.16) Based on Formula3.16, minimizing the cost depends on the capacity of the links in addition to the number of links. If MC2 > NC1, then l1 must get minimized (l1= 0) and all the traffic is sent through the second path. MC2 = NC1 makes the formula zero and causes equal distribution. In case that MC2< NC1, l1 must be maximized. Therefore, all of the traffic goes through the first path. Same as what mentioned for LeakyCap, passing over the critical point in LeakyReLU affects Formula3.13and3.14due to different gradients in the criticality function. Different gradients can lead to a different linear formula to minimize.
Fortz - The cost computation in Fortz is similar to LeakyReLU and it also tends to follow Formula 3.16 to minimize the total cost; However, since Fortz contains multiple critical points, the derivative of the Fortz function is modified accordingly before the link gets fully utilized. Therefore, a gradual increase in traffic rate can cause the criticality function to redirect the new extra traffic to the other path several times. The traffic redirection when using Fortz in addition to the behavior of LeakyCap and LeakyReLU are illustrated in the following examples. To analyze these functions, we used two topologies. In each topology, there are two paths between ingress and egress nodes and the goal of criticality functions is to distribute the traffic between two paths to minimize the objective function.
3.5.1
Two Paths with the Same Number of Links
In this example, we examine a network with two nodes and two links (see Figure
3.5. THEORETICAL ANALYSIS OFCRITICALITY FUNCTIONS 29
Figure 3.8: Network with 2 nodes and 2 paths with same number of links
LeakyReLU - When the number of links is equal, LeakyReLU is affected only by link capacity. Therefore, it decides to send all the traffic toward the second path which has a higher bandwidth until the link becomes fully utilized. Then, the function moves the new incoming traffic to the first path. When the link of the first path reaches its critical point, the function redirects the traffic to the second path.
3.5. THEORETICAL ANALYSIS OFCRITICALITY FUNCTIONS 31
the behavior of all three criticality functions with different amounts of traffic. Each sample network shows the amount of traffic which has been injected into the network (red arrow) and the utilization of each link caused by the injected traffic.
Figure 3.9: The behavior of linear criticality functions against the different amount of traffic in a simple network discussed in Subsection 3.5.1: (a) LeakyCap, (b) LeakyReLU, (c) Fortz
3.5.2
Two Paths with Different Number of Links
32 CHAPTER 3. DEFINITION OFLINK CRITICALITY FUNCTIONS
scenarios, we selected two examples: uniform and non-uniform simple network with two nodes and three links (see Figure3.10). In the following subsections, we examine both examples for LeakyCap, LeakyReLU, and Fortz functions.
Figure 3.10: Two triangle networks: (a) uniform, (b) non-uniform.
3.5.2.1 Uniform Network
In a uniform network, all the links have the same capacity. The example provides two paths between two nodes with one and two links respectively as first and second paths. The capacity of the links is 1Mbps and there is only one traffic flow from n1 to n2. Same as before, the traffic rate steadily increases. In this example, the linear criticality functions behave as follows:
LeakyCap - The first path has fewer links than the second path (M < N). Thus, LeakyCap sends all the traffic through the first path. When the link gets to full utilization, the function redirects the new incoming traffic to the second path. After the links in the second path become full, LeakyCap redirects further incoming traffic to the first path again.
LeakyReLU - Since the network is uniform, LeakyReLU exactly has the same behavior as LeakyCap.
3.5. THEORETICAL ANALYSIS OFCRITICALITY FUNCTIONS 33
Figure 3.11: The behavior of linear criticality functions against the different amount of traffic in a simple uniform network with three links discussed in Subsection3.5.2.1: (a) LeakyCap, (b) LeakyReLU, (c) Fortz
3.5.2.2 Non-uniform Network
34 CHAPTER 3. DEFINITION OFLINK CRITICALITY FUNCTIONS
Figure 3.12: The behavior of linear criticality functions against the different amount of traffic in a simple non-uniform network with three links discussed in Subsection3.5.2.2: (a) LeakyCap, (b) LeakyReLU, (c) Fortz
LeakyCap - If one path has fewer links than the other path, LeakyCap always prefers the path with fewer links since sending the traffic through more links decreases the total available bandwidth of the network for future demands. Hence, LeakyCap does not care about the capacity difference and exactly follows the same pattern as the uniform network.
3.5. THEORETICAL ANALYSIS OFCRITICALITY FUNCTIONS 35
between first and second paths is significant (MC2− NC1 > 0). Therefore, LeakyReLU starts filling the second path up to the critical point. Then, it moves new incoming traffic to the first path.
Chapter 4
Methodology
This chapter provides an overview of the research methodology used in this project. In Section 4.1, we describe the research process. Section 4.2 and 4.3
explain how we collect data and conduct measurements throughout the project. In Section4.4, we clarify the scenarios designed for the project. Section4.5presents the experimental design of the thesis. In Section4.6, we explain the reliability and validity of the collected data.
4.1
Research Process
To proceed with this project, we take various steps which are listed in Figure4.1. First, we conducted several studies on several traffic engineering solutions using different objective functions. After enough background research, we realized that many traffic engineering systems tended to minimize the sum of link costs as an objective function and they used Fortz function as the link criticality function. The next step was to look for better link criticality functions. As a result, we defined four link criticality functions for objective functions of traffic engineering systems. The main goal of these functions was to improve the performance of packet-switched networks (PSN) in terms of packet loss. We also selected Fortz function to compare it with the criticality functions.
After defining the criticality functions, we prepared the environment for experiments and evaluation. We implemented a path-based network similar to the semi-oblivious TE solution with two pre-computed link-disjoint paths between each pair of nodes. Also, we installed several traffic generators on each node as applications to produce constant and bursty traffic. Additionally, we developed a library for criticality measurements and modeling the entire network. The traffic engineering system of the environment received the network topology,
