1. 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

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

3. Background - Software Defined Network

4. Software Defined Network
Traditional Network vs Software-Defined Network
Traditional Networking
Software-Defined Networking

5. OpenFlow Protocol

6. Background - Queueing Theory

7. 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

8. 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

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

10. 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

11. System Model

12. 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

13. 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

14. 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

15. Model Design

16. Model Design (Cont’d)

17. 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

18. 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

19. 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

20. 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

21. Simulation - Environment Setup

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

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

24. Simulation - Simulation Result

25. 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

26. 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

27. 【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

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

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

30. Different Allocated BW
Arrival rate
𝜆 𝑞𝑜𝑠 = [0.1,0.9]
Fixed 𝜆 𝑑𝑎𝑡𝑎 = 𝜇 𝑑𝑎𝑡𝑎 %
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

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

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

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

34. 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

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

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

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

38. 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

39. Different Loading (Cont'd)

40. 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

41. 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

42. 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

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

44. 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

45. 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

46. 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

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

48. Conclusion

49. 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

50. Reference

51. 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 , Sep
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 , Jan
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。