New Insights from A Fixed Point Analysis of Single Cell IEEE 802 New Insights from A Fixed Point Analysis of Single Cell IEEE 802.11 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Chunyu Hu, University of Illinois at Urbana-Champaign Conclusion Present another way of modeling 802.11 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