1. Elec 599 Report: Modeling Media Access in Embedded Two-Flow Topologies of Multi-hop Wireless Networks Jingpu Shi Advisor: Dr. Edward Knightly Department of Electrical and Computer Engineering Rice University May 03, 2005

2. Motivation Fairness problems in Multi-hop wireless networks. Root cause: different and incomplete channel state information. Those problems have not been very well understood. All Stations are in range G. Bianchi. Performance analysis of the IEEE 802.11 distributed coordination function. IEEE Journal on Selected Areas in Communications, 18(3):535–547, March 2000. Not all stations are in radio range ? In this work, we view a network as a set of sub-graphs consisting two flows and characterize its media access.

3. Assumptions and Notations Identical transmission range and interference range. We only consider one-way flows. A link is established if two stations are in radio range. Aa is the first flow, Bb is the second flow.

4. All Possible Topologies

5. Scenario Classification Senders Connected (SC): scenarios 2-7, where senders of each flow are in radio range. Asymmetric Incomplete State (AIS), scenarios 11 and 12, where senders are disconnected, asymmetric connections between the two flows. Symmetric Incomplete State (SIS), scenario 8, 9 and 10, where senders are disconnected, symmetric connections between the two flows.

6. Scenario Likelihood Assumptions and Illustration What ’ s the probability of each scenario occurring, giving the two flows are connected? Spatial analysis, assuming the two flows are uniformly distributed in a region and border effect is negligible. Equal distance.

7. Scenario Likelihood Results for each scenario Scenario 11 dominates when distance becomes large

8. Scenario Likelihood Results for each group AIS and SIS class are highly likely to occur when distance between two hops becomes large.

9. Hop distance distribution

10. Outline Motivation Scenario identifications and their likelihood Fairness simulations Media access modeling

11. Performance Simulations With CSMA/CA protocol Observations: SC-No fairness problem. AIS-Both short-term and long-term fairness problems. SIS-Long-term fair, short-term unfair. Root cause: different information about the channel.

12. Mobility and Fairness

13. Outline Motivation Scenario identifications and their likelihood Fairness simulations Modeling media access

14. Modeling Framework View at single station Identify 4 different state idle channel channel occupied by successful transmissions channel occupied by a collision busy channel due to activity of other stations Define probabilities Probability of the four stats and throughput of the station

15. Model AIS Class: Strategies and steps Compute collision probability for the flow Aa. Compute busy probability due to other transmissions for flow Bb Use decoupling technique Assume flow Bb never collides. Flow Aa never defers.

16. Model AIS Class Results With RTS/CTS Without RTS/CTS

17. Model SIS Class Sample topology and modeling strategy We analyze short-term unfairness. Main difficulty: the two transmitting nodes are tightly correlated. A Markov chain model using bi-dimensional state description.

18. Model SIS Class: Strategies and steps We represent the system state as pair (S A, S B ), where S A and S B denote the backoff stage of Sender A and B respectively. Transition probability of the Markov chain. r i is the probability that a station transmits after one slot in backoff stage i. f is the duration of the first packets (RTS or DATA) transmitted. After solving the Markov chain, we can compute the transition time from state (m, 0) to (0,m), where m is the maximum backoff stage.

19. Model SIS Class Results (cont.) (C1) RTS/CTS access, m = 6, CW max = 1024. (C2) RTS/CTS access, m = 8, CW max = infinity. (C3) Basic access, m = 3, CW max = 1024. (C4) Basic access, m = 6, CW max = 1024.

20. Thanks! Questions or Comments ?