1. New Insights from A Fixed Point Analysis of Single Cell IEEE 802
New Insights from A Fixed Point Analysis of Single Cell IEEE WLANs
IEEE INFOCOM 2005
Authors: A. Kumar, E. Altman, D. Miorandi and M. Goyal
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

2. Chunyu Hu, University of Illinois at Urbana-Champaign
Outline
Fixed point equation
Derivation
Analysis
A case study: TCP-controlled file transfer
Assumptions
Evaluation
Conclusion
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

3. Chunyu Hu, University of Illinois at Urbana-Champaign
Outline
Fixed point equation
Derivation
Analysis
A case study: TCP-controlled file transfer
Assumptions
Evaluation
Conclusion
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

4. Derivation – Model the Exponential Backoff Procedure
Notations
k:= backoff stage
K+1 := transmission retry limit
bk := the mean backoff time (in slots) at the k-th attempt for a packet. 0 <= k <= K
 := Prob[an attempt made by a node fails due to collision]
G:= G() the attempt rate/probability of a node
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

5. Chunyu Hu, University of Illinois at Urbana-Champaign
Express G in terms of 
R: total number of attempts for transmitting a packet
X: total number of backoff slots for transmitting a packet
Given the collision probability , the attempt probability G is:
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

6. Chunyu Hu, University of Illinois at Urbana-Champaign
Express  in terms of G
With the independent access assumption, the collision probability of an attempt is
Alternatively, using the expression in the paper,
Where,  (),   G(), and n is the total number of active nodes.
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

7. Chunyu Hu, University of Illinois at Urbana-Champaign
Fixed Point Equation
Give the (conditional) collision probability , the attempt probability is
Given the attempt probability, the (conditional) collision probability is
The equilibrium point is defined by the solution of the so-called fixed point equation:
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

8. Chunyu Hu, University of Illinois at Urbana-Champaign
Outline
Fixed point equation
Derivation
Analysis
A case study: TCP-controlled file transfer
Assumptions
Evaluation
Conclusion
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

9. Existence of Fixed Point
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

10. Existence of Fixed Point (Cont’d)
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

11. Solution to the Equation
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

12. Limit of Fixed Point as n  
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

13. Chunyu Hu, University of Illinois at Urbana-Champaign
Throughput as n  
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

14. Chunyu Hu, University of Illinois at Urbana-Champaign
Outline
Fixed point equation
Derivation
Analysis
A case study: TCP-controlled file transfer
Assumptions
Evaluation
Conclusion
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

15. A Case Study: TCP-Controlled File Transfer
Assumptions
Infinitely long file transfer
No packet loss (either because of bit errors or buffer loss)
The WLAN is the bottleneck
All the device queues are saturated
These assumptions simplify the problem as modeling a saturated single-hop network, therefore
Can apply the previous results directly, by defining several new variables in order to bridge the two scenarios.
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

16. Chunyu Hu, University of Illinois at Urbana-Champaign
Evaluation
FPA
ns2
Ad hoc networks, with n pairs of nodes, one sending a file to the other
11Mbps, Wmax = 20 pkts, Lmax = 1KB, no delayed ACKs.
Aggregate throughput over all the n transfers is shown
Error less than 6%
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

17. Chunyu Hu, University of Illinois at Urbana-Champaign
Outline
Fixed point equation
Derivation
Analysis
A case study: TCP-controlled file transfer
Assumptions
Evaluation
Conclusion
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign

18. Chunyu Hu, University of Illinois at Urbana-Champaign
Conclusion
Present another way of modeling MAC
Differ from existed work in deriving attempt probability
Analyze the equilibrium state (fixed point)
Show the saturation analysis can be directly applied to certain scenarios
E.g. the TCP-controlled file transfer
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign