學生：杜筱菡 指導教授：柯開維 教授 日期：2017/6/22 軟體定義網路具重傳效應之數學建模與驗證 Performance Modelling Considering Retransmission and Verification for a Software Defined Network 學生：杜筱菡 指導教授：柯開維 教授 日期：2017/6/22

Outline Background System Model Simulation Conclusion Reference Software Defined Network Queueing Theory System Model Simulation Environment Setup Simulation Result Conclusion Reference

Background - Software Defined Network

Software Defined Network Traditional Network vs Software-Defined Network Traditional Networking Software-Defined Networking

OpenFlow Protocol

Background - Queueing Theory

Queueing Theory Input Process System Structure Output Process Arrival pattern Input Process System capacity Number of service channels Number of service stages System Structure Service pattern Queue discipline Output Process

Poisson process Counting process {𝑁 𝑡 ,𝑡≥0} 𝑁 𝑡 denotes the number of arrivals up to time 𝑡 Independent increments Stationary increments Poisson process is a counting process Poisson process Exponential arrival pattern with arrival rate 𝜆 𝑝 𝑁 𝑡+𝑠 −𝑁 𝑠 =𝑛 = 𝑒 −𝜆𝑡 (𝜆𝑡) 𝑛 𝑛! , 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑠,𝑡>0

M/M/1 Poisson arrival with rate 𝜆 Exponential service time with mean 1 𝜇

Open Jackson Network Arrival/Depart according to a Poisson process 𝐾：Number of nodes in the network 𝜆：Total arrival rate of single node 𝛾：Arrival rate from external source 𝑞 𝑖,𝑗 ：The probability that customer from node 𝑖 go to node 𝑗 Traffic equation： 𝜆 𝑖 = 𝛾 𝑖 + 𝑗=1 𝐾 𝜆 𝑗 𝑞 𝑗,𝑖

System Model

Parameter Customer Arrival rate of (edge / core) switch 𝑖 Bit Arrival rate of (edge / core) switch 𝑖 Total arrival rate Λ 𝑖 External source 𝜆 𝑖 Service rate of switch 𝑖 𝜇 𝑖 =𝜇 Link capacity

Parameter (Cont’d) Arrival rate of controller Λ 𝑐 From switch with probability 𝑞=0.04[1] Service rate of controller 𝜇 𝑐 For a message ,mean processing time of around 0.2ms[2] Retransmission probability of switch 𝑖 𝑃 𝑖,𝑟𝑒𝑡𝑟𝑎𝑛𝑠 = 𝑃 𝑖,𝑙𝑜𝑠𝑠 + 𝑃 𝑖,𝑒𝑟𝑟𝑜𝑟 Percentage of traffic to each other between switches 𝜂= 𝜂 𝑖𝑗 𝑁×𝑁 [1] K. Mahmood, A. Chilwan, O. Østerbø and M. Jarschel, Modelling of OpenFlow-based software-defined networks: the multiple node case, 2015 [2]C. Metter, S. Gebert, S. Lange, T. Zinner, P. Tran-Gia and M. Jarschel, Investigating the impact of network topology on the processing times of SDN controllers, 2015

Parameter (Cont’d) Type of flow 𝑀 Bandwidth allocation of switch 𝑖 𝛼 = 𝛼 1 𝛼 2 𝛼 3 𝛼 4 High priority QoS flow Low priority QoS flow Elephant data flow Mice data flow

Model Design

Model Design (Cont’d)

Model Description Total arrival rate of edge switch 𝑖 Λ 𝑖 = 𝜆 𝑖 + Λ 𝑖 𝑃 𝑖,𝑟𝑒𝑡𝑟𝑎𝑛𝑠 + 𝑗=1 𝑁 𝜂 𝑗 𝑖 (1− 𝑃 𝑖,𝑟𝑒𝑡𝑟𝑎𝑛𝑠 ) Λ 𝑖 Total arrival rate of core switch 𝑖 Λ 𝑖 = Λ 𝑖 𝑃 𝑖,𝑟𝑒𝑡𝑟𝑎𝑛𝑠 + 𝑗=1 𝑁 𝜂 𝑗 𝑖 (1− 𝑃 𝑖,𝑟𝑒𝑡𝑟𝑎𝑛𝑠 ) Λ 𝑖 Switching probability 𝜂 𝑖 𝑗 = 1 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛 𝑖 𝑗 ≠0 ,for all j where 0≤j<N , j≠i 來自主機的流量λ、從其他邊緣交換器 Λ (𝑒𝑑𝑔𝑒) 與核心交換器的流量 Λ (𝑐𝑜𝑟𝑒) 以及重傳的流量 Λ 𝑖 𝑒𝑑𝑔𝑒 𝑃 𝑖,𝑟𝑒𝑡𝑟𝑎𝑛𝑠 𝑒𝑑𝑔𝑒

Model Description (Cont’d) Arrival rate of controller Λ 𝑐 =𝑞 𝑖=1 𝑁 𝑒𝑑𝑔𝑒 𝜆 𝑖 Service rate of type M in switch 𝑖 𝜇 𝑖,𝑀 = 𝛼 𝑀 𝜇 𝑖

Performance Metrics Obtained the value by the M/M/1 model Expectation of sojourn time in switch 𝑖 𝐸 𝑇 𝑖 = 1 𝜇 𝑖 − Λ 𝑖 Expectation of sojourn time in controller 𝐸 𝑇 𝑐 = 1 𝜇 𝑐 − Λ 𝑐 Server utilization in switch 𝑖 𝜌= Λ 𝑖 𝜇 𝑖

Performance Metrics (Cont’d) System time 𝑆𝑇= 𝑇 𝑖 , 𝑤𝑖𝑡ℎ 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 (1−𝑞) 𝑇 𝑖 + 𝑇 𝑐 + 𝑇′ 𝑖 , 𝑤𝑖𝑡ℎ 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑞 Expectation of system time 𝐸 𝑆𝑇 = 1−𝑞 𝐸 𝑇 𝑖 +𝑞 𝐸 𝑇 𝑖 +𝐸 𝑇 𝑐 +𝐸 𝑇 ′ 𝑖 = 1+𝑞 E 𝑇 𝑖 +𝑞𝐸 𝑇 𝑐

Simulation - Environment Setup

Environment Setup Network emulator：Mininet Controller：Ryu Link capacity = 100Mbits/s (85Mbits/s) Switch：3 Queues

Environment Setup (Cont’d) Flow Definition Qos flow and Data flow QoS Flow Tool：iperf Protocol：UDP Data Flow Tool：wget Protocol：TCP

Simulation - Simulation Result

Simulation Result Performance Indicators Theoretical value Flow Completion Time(FCT) Path Load Theoretical value 𝐹𝐶𝑇 = 𝐸[𝑆𝑇] × 𝐹𝑖𝑙𝑒 𝑠𝑖𝑧𝑒 𝑃𝑎𝑡ℎ 𝐿𝑜𝑎𝑑= 𝜌 # 𝑜𝑓 𝑝𝑎𝑡ℎ , 𝜌= Λ 𝜇 Do average of 10 times simulation

Simulation Result (Cont'd) 【Data flow】 versus 【QoS flow + data flow】 Different allocated BW Scenario 1 Type of input traffic Different retransmission probability Different loading Scenario 2 Loading and retransmission probability Different file size Mix different file size Scenario 3 File size

【Data Flow】versus【QoS Flow + Data Flow】 Arrival rate 𝜆=[0.1,0.9] Service rate μ= 85Mbits/s for each link 𝜇 𝑄𝑜𝑆 = 𝛼 𝑄𝑜𝑆 × 𝜇=30% × 85 = 25.5𝑀𝑏𝑖𝑡𝑠/𝑠 𝜇 𝑑𝑎𝑡𝑎 = 𝛼 𝑑𝑎𝑡𝑎 × 𝜇=70% × 85 = 59.5𝑀𝑏𝑖𝑡𝑠/𝑠 File size = 100MB Retransmission probability 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 = 0

【Data Flow】versus【QoS Flow + Data Flow】 (Cont'd)

【Data Flow】versus【QoS Flow + Data Flow】 (Cont'd)

Different Allocated BW Arrival rate 𝜆 𝑞𝑜𝑠 = [0.1,0.9] Fixed 𝜆 𝑑𝑎𝑡𝑎 = 𝜇 𝑑𝑎𝑡𝑎 + 10% Different bandwidth limitation of queue 𝛼 𝑄𝑜𝑆 = 30%, 𝛼 𝑑𝑎𝑡𝑎 = 70% 𝛼 𝑄𝑜𝑆 = 50%, 𝛼 𝑑𝑎𝑡𝑎 = 50% 𝛼 𝑄𝑜𝑆 = 70%, 𝛼 𝑑𝑎𝑡𝑎 = 30% Retransmission probability 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 = 0 File size = 100MB

Different Allocated BW (Cont'd) 𝛼 𝑄𝑜𝑆 =30%, 𝛼 𝑑𝑎𝑡𝑎 =70%

Different Allocated BW (Cont'd) 𝛼 𝑄𝑜𝑆 =50%, 𝛼 𝑑𝑎𝑡𝑎 =50%

Different Allocated BW (Cont'd) 𝛼 𝑄𝑜𝑆 =70%, 𝛼 𝑑𝑎𝑡𝑎 =30%

Different Retransmission Probability Arrival rate 𝜆=[0.1,0.9] Service rate μ= 85Mbits/s for each link 𝜇 𝑄𝑜𝑆 = 𝛼 𝑄𝑜𝑆 × 𝜇=30% × 85 = 25.5𝑀𝑏𝑖𝑡𝑠/𝑠 𝜇 𝑑𝑎𝑡𝑎 = 𝛼 𝑑𝑎𝑡𝑎 × 𝜇=70% × 85 = 59.5𝑀𝑏𝑖𝑡𝑠/𝑠 File size = 100MB

Different Retransmission Probability (Cont'd) Pretrans = 0 Pretrans = 0.01 Pretrans = 0.02 Pretrans = 0.03

Different Retransmission Probability (Cont'd) Pretrans = 0.04 Pretrans = 0.05 Pretrans = 0.06 Pretrans = 0.07

Different Retransmission Probability (Cont'd) Pretrans = 0.08 Pretrans = 0.09 Pretrans = 0.1

Different Loading Light load ：𝜆= 0.1,0.3 =0.2 Middle load：𝜆= 0.4,0.6 =0.5 Heavy load：𝜆= 0.7,0.9 =0.8 Retransmission probability 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 = 0,0.1 Service rate μ= 85Mbits/s for each link 𝜇 𝑄𝑜𝑆 = 𝛼 𝑄𝑜𝑆 × 𝜇=30% × 85 = 25.5𝑀𝑏𝑖𝑡𝑠/𝑠 𝜇 𝑑𝑎𝑡𝑎 = 𝛼 𝑑𝑎𝑡𝑎 × 𝜇=70% × 85 = 59.5𝑀𝑏𝑖𝑡𝑠/𝑠 File size = 100MB

Different Loading (Cont'd)

Matching Retransmission Probability 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 =0 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 =0.05 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 =0.07 Arrival rate 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Corresponding retransmission probability 0.05 0.07

Matching Retransmission Probability (Cont'd) 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 =0 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 =0.05 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 =0.07 Arrival rate 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Corresponding retransmission probability 0.05 0.07

Different File Size Matching retransmission probability 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 100MB 200MB Arrival rate 𝜆=[0.1,0.9] Service rate μ= 85Mbits/s for each link 𝜇 𝑄𝑜𝑆 = 𝛼 𝑄𝑜𝑆 × 𝜇=30% × 85 = 25.5𝑀𝑏𝑖𝑡𝑠/𝑠 𝜇 𝑑𝑎𝑡𝑎 = 𝛼 𝑑𝑎𝑡𝑎 × 𝜇=70% × 85 = 59.5𝑀𝑏𝑖𝑡𝑠/𝑠

Different File Size (Cont'd) FCT with File size 100MB FCT with File size 200MB

Different File Size (Cont'd) Matching retransmission probability 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 =0 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 =0.05 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 =0.07 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 =0 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 =0.05 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 =0.07 FCT with File size 100MB FCT with File size 200MB

Mix Different File Size 2 different file size of files transfer simultaneously 𝐹𝐶𝑇= 𝐸 𝑆𝑇 1 ×100𝑀𝐵 𝐸 𝑆𝑇 1 ×100𝑀𝐵+𝐸 𝑆𝑇 2 ×100𝑀𝐵 Flow completion time with 95% CI (Confidence interval) 95% CI 𝑜𝑓 F𝐶𝑇= 𝑋 ±1.96∗ 𝜎 𝑛 100MB 200MB 100MB 200MB

Mix Different File Size (Cont'd) Arrival rate λ= [0.1,0.9] Service rate μ= 85Mbits/s for each link 𝜇 𝑄𝑜𝑆 = 𝛼 𝑄𝑜𝑆 × 𝜇=30% × 85 = 25.5𝑀𝑏𝑖𝑡𝑠/𝑠 𝜇 𝑑𝑎𝑡𝑎 = 𝛼 𝑑𝑎𝑡𝑎 × 𝜇=70% × 85 = 59.5𝑀𝑏𝑖𝑡𝑠/𝑠 Matching retransmission probability 𝑃 𝑟𝑒𝑡𝑟𝑎𝑛𝑠 File size 100MB and 200MB

Mix Different File Size (Cont'd) FCT with File size 100MB FCT with File size 200MB

Conclusion

Finish List 已完成 建模 數據 初稿第二、三章 未完成 初稿撰寫與修改

Reference

Reference Donald Gross, John F. Shortie, James M. Thompson, Carl M. Harris, Fundamentals of Queueing Theory, 4th edition. Hoboken, New Jersey, U.S. state: John Wiley & Sons, Inc., 2008. K. Mahmood, A. Chilwan, O. Østerbø and M. Jarschel, “Modelling of OpenFlow-based software-defined networks: the multiple node case,” IET Networks, vol. 4, no. 5, pp. 278-284, Sep. 2015. D. Kreutz, F. M. V. Ramos, P. E. Veríssimo, C. E. Rothenberg, S. Azodolmolky and S. Uhlig, "Software-Defined Networking: A Comprehensive Survey," Proceedings of the IEEE, vol. 103, no. 1, pp. 14-76, Jan. 2015. 張朕瑀(2016)。軟體定義網路之自適性流量工程設計。碩士論文，國 立臺北科技大學資訊工程，台北。