1. A New Approach for Accurate Modelling of Medium Access Control (MAC) Protocols Presenter: Moshe Zukerman ARC Centre for Ultra Broadband Information Networks EEE Dept., The University of Melbourne Presented at EE Dept., City University of Hong Kong, 11 April, 2002 Credit: Chuan Foh (EEE, Melbourne)

2. 1.The big picture 2.Classical performance models 3.Ethernet 4.IEEE 802.3 5.How can we get performance statistics for a complicated protocol 6.Breaking the problem into two: Saturation and SSQ fed by correlated SRD Markovian traffic 7.Numerical results OUTLINE

3. The Big Picture

4. Traffic Modelling Queueing Theory Performance Evaluation Simulations and Fast Simulations Numerical Solutions Formulae in Closed Form Traffic Measurements Link and Network Design and Dimensioning Traffic Prediction

5. Research in Performance Evaluation 1.Exact analytical results (models) 2.Exact numerical results (models) 3.Approximations 4.Simulations (slow and fast) 5.Experiments 6.Testbeds 7.Deployment and measurements 8.Typically, 4-7 validate 1-3.

6. Classical Performance Models Poisson Traffic Model Many simplified assumptions on System/protocol operation Inaccurate results

7. We want Realistic Traffic Model No simplified assumptions on System/protocol operation Accurate results

8. Example 1: Ethernet The Ethernet MAC protocol: (1) Carrier Sensed Multiple Access with Collision Detection (CSMA/CD) (2) The Binary Exponential Backoff (BEB) Algorithm

9. Ethernet D time FG The Big Bang of E, F & G E CDEFG CDEFG time

10. Detailed Analysis CSMA/CD BEB collided packets LAN traffic Served packets Ethernet -or - IEEE 802.3

11. Classical Performance Models retransmission offered load G LAN traffic Served packets BEB collided packets 1-persistent CSMA/CD  Poisson Poisson 

12. Example 2: IEEE 802.11 The IEEE 802.11 MAC protocol: (1) Carrier Sensed Multiple Access with Collision Avoidance (CSMA/CA) (2) The Binary Exponential Backoff (BEB) Algorithm

14. Detailed Analysis CSMA/CA BEB collided packets LAN traffic Served packets IEEE 802.11

15. Simplified Performance Models fixed window retransmission offered load G LAN traffic Served packets BEB collided packets CSMA/CA Bernoulli or Poisson 

16. How do we do it?

17. Well, we know how to get: Queueing performance of state dependent Markovian Single Server Queue (SSQ) Performance results without simplified assumptions on System/protocol operation when system is saturated

18. so, we break the hard problem into two separate easy problems: Queueing performance of a state dependent Markovian SSQ Performance evaluation of the System/protocol operation when system is saturated

19. From saturation analysis without simplified assumptions on system/protocol operation, we can get: The service rate, given that there are n saturated stations in the system. Then using state dependent Markov Chain analysis, we get: The performance results we are after

20. State dependent single Server queue Markovian SRD arrival process State dependent ( n ) service For each n solve MAC under saturation n stations

21. What statistical traffic models we have considered?

22. Source Traffic Arrival Model time Data frame Phase type distributed transmission time Phase type distributed transmission time Exp. distributed gaps Data frame = Packet Train of packets

23. Source Traffic Arrival Model time A new data frame is generated, it is scheduled for transmission immediately The data frame is transmitted successfully at this point of time After an idle period, another new data frame is generated. It is scheduled for transmission immediately Exponentially distributed

24. Another Traffic Model considered: Markov Modulated Poisson Process (MMPP) The number of active stations increases based on MMPP And decreases based on the MAC service process

25. Now let’s use the simpler problem under saturation to model the service rate

26. Saturation Traffic n stations arrivaldeparture

27. Service Process E 8 will be chosen

28. Why we think it will work?

29. Why E 8 is good enough? Let X  exp(  ), E [X] = 1/  X 8  E 8, X 32  E 32 both with mean 1/ , Var [X] = 1/  2 Var [X 8 ] =8/(8  ) 2 =1/(8  2 ) Var [X 32 ] = 32/(32  ) 2 =1/(32  2 ) Var [X 32 ] = (1/4)Var [X 8 ] = (1/32)Var [X] 2  [X 32 ] =  [X 8 ], 2.82  [X 8 ] =  [X]

30. Why E 8 is good enough (cont.)? Q:mean queue size  :utilization  S :SD of the service time distribution S:mean service time From M/G/1 mean queue size result:

31. Why E 8 is good enough (cont.)? Det.X 32 X8X8 X SD/Mean0(1/32) (1/2) = 0.176 (1/8) (1/2) = 0.353 1 When the SD/mean is small (as for X 32 ), doubling it does not significantly affect queueing performance for small . However, when it is already doubled, multiplying it further by 2.82, affects performance.

32. How accurate are we?

33. Mean delay under different payload sizes: simulation vs. analysis

34. Solid lines: dual fixed data frames Dotted lines: fixed size data frames Mean delay under different date frame distributions: simulation vs. analysis

35. Mean delay under different train arrival processes: simulation vs. analysis Mean train size = 24576 bits

36. Delay performance: IEEE 802.11

37. Delay Performance: 802.11

38. Delay Performance: IEEE 802.3

39. How inaccurate are classical performance models?

40. A Comparison

41. Lam’s results overestimate the performance. Our results indicate that the Ethernet protocol will be unstable at 30% for a=0.1 and 75% at a=0.01. Lam’s predictions (Computer Network 4, 1980) are much higher in the two cases. a = the signal propagation delay normalized to the data frame transmission time between any pair of stations. We assume a star network and the distance between any station and the hub (active or passive) is fixed. D/b1= the mean transmission delay normalized to the data frame transmission time. Traffic: Lam’s=Ours=Poisson traffic Data frame size distribution: Lam’s=Ours=fixed Retransmission algorithm: Lam’s=An adaptive retransmission algorithm; Ours=BEB

42. Accurate MAC performance results under statistical traffic can be achieved by breaking up the original problem into two simpler easier problems: (1) SSQ (2) MAC under saturation Conclusion: