1. On the Exploitation of CDF based Wireless Scheduling Udi Ben-Porat Tel-Aviv University, Israel Anat Bremler-Barr IDC Herzliya, Israel Hanoch Levy ETH Zurich, Switzerland

2. Wireless Scheduling Model:  Players: Base Station (scheduler) and Clients  Time is divided to separate time slots  At each time slot, data is sent to one user only  Clients have variable channel rate (capacity)  The scheduler assigns a client for transmission based on the reported channel rates of the users 2 Cisco talk - April 2009 Scheduler’s goals:  Good overall throughput performance of the system  Fairness among users (avoid starvation)

3. CDF Scheduler - Example Cisco talk - April 2009 3 Bob Rate ~ Uniform(0,100) Base station Priority by CDF value 60 kbps Alice Rate ~ Uniform(0,50) DATA Priority: V=0.9 (90% of the time Alice has worse channel than now) Priority: V=0.6 (60% of the time Bob has worse channel than now) 45 kbps Scheduler’s goals:  Good overall throughput performance of the system  Fairness among users (avoid starvation)

4. Cumulative Distribution Function (CDF) Scheduling R – Channel rate of a user Point (x,y): y =F R (x)= Prob(R<x) Every time slot he reports his rate – r i His Priority value: V=F R (r i ) The CDF scheduler picks the user with the highest Priority value 4 REMON talk - Feb. 2009 CDF Graph 0 100 1010 Channel Rate (kbps) CDF value (in [0,1]) 70 kbps 0.7 25 kbps 0.9

5. CDF Scheduler - Characteristics CDF maintains time-share fairness:  All users get the same amount of time slots  Each user has equal chance to “win” a timeslot regardless of his channel rate distribution Our work – the vulnerability of CDF:  One user alone can’t fool the system  Coordinated selfish users destabilize FAIRNESS  Bigger time-share on the expense of others  Malicious users degrade the system even more 5 Cisco talk - April 2009

6. CDF Scheduler - Example Two users with different distributions:  Bob – Uniform(0, 100)  Alice – Uniform(0, 50) Cisco talk - April 2009 6 Time slot:123456 Bob Rate - r708010904030 Priority - V(r)0.70.80.10.90.40.3 Alice Rate - r30452010355 Priority - V(r)0.60.90.40.20.70.1

7. Our work – CDF Scheduler Exploits One user alone can’t fool the system Coordinated users can destabilize FAIRNESS.  Gain more time slots on the account of others Malicious users get e-1 (~ 170%) of what other users get (when both regular and mal. Are in equal numbers and should get equal time share) 7 Cisco talk - April 2009

8. Proved: No one-user-strategy Theorem: One user with no knowledge on the others cannot benefit throughput or time slots by reporting fake channel rates. Intuition:  No point pretending he has other channel rate distribution – every user gets equal time share regardless of his channel rate distribution.  No point reporting exaggerated rate which he can’t physically utilize (if he wins the time slot)  Reporting fake low rates only decreases his throughput (CDF follows time fairness, not throughput) 8 Cisco talk - April 2009

9. Coordinated Group Strategy Formally:  Group of users are cooperating to gain bigger time share  Each user shares with the group the CDF value of his channel rate (for the next time slot) Strategy:  Only the user with the maximal CDF value in the group reports his real channel rate (r i )  All others report fake channel rate r=0 9 Cisco talk - April 2009

10. Coordinated Group Strategy Such behavior influence the CDF functions that the scheduler learns about the users in the group This results in higher priority values given to the members of the group -> more bandwidth on the expense of others 10 Cisco talk - April 2009

11. Why Report Zero? Example  R = Bob’s real rate; R’= what Bob actually reports  Scenario A: Bob always report his real rate (R=R’) Bob’s CDF: P(R’ < x) = P(R < x)  Scenario B: Reports 0 every EVEN time slot In the ODD time slots - he reports his real rate Q: P(R’ < x) = ? A: P(this time slot is ODD)* P(R < x) + P(this time slot is EVEN) Bob’s CDF: P(R’ < x) = ½ + ½ P(R < x) 11 Cisco talk - April 2009

12. Coordinated Group Strategy Bob decides to report 0 every even timeslot V - real CDF value function V’ – The function according to his reports Cisco talk - April 2009 12 1 0.5 0 Channel Rate (kbps) CDF value 0 100 40 kbps 0.4 0.7 V’ = 0.5+0.5V

13. Why Report Zero? 13 Cisco talk - April 2009 The new CDF of the reported channel rates as seen by the scheduler is given by: V k =0.5+0.5*(F Rk (r)) 2 Generally with n users: V k = (n-1)/n+(1/n)*(F Rk (r)) n 2 Coordinating Users – CDF Increase

14. Coordinated Group Strategy Why coordinate with others?  When reporting zero the user loses the time slot for sure  Coordination allows the user to report zero in time slots that he has no chance to win anyway  User can only Benefit from coordination with others Cisco talk - April 2009 14 1010 Channel Rate (kbps) CDF value 0 100

15. Without Coordination Cisco talk - April 2009 15 Alice Uniform(0,100) Base station Priority by CDF value Bob Uniform(0,100) Mary Uniform(0,100) 27 kbps 50 kbps 31 kbps V = 0.31V = 0.27V = 0.5 DATA

16. Coordination Strategy - Example Bob and Mary decide to cooperate in order to increase the priority values they get. Every time slot one of them reports his real channel rate while the other reports zero channel rate. The one who reports his real channel rate is the one who is expected to be assigned with better priority value than the other 16 Cisco talk - April 2009

17. Coordination Strategy 17 Alice Uniform(0,100) Base station Priority by CDF value Bob Uniform(0,100) Mary Uniform(0,100) F = 0.31 F = 0.27 0 kbps 50 kbps 31 kbps

18. Base station Priority by CDF value Coordination Strategy 18 Cisco talk - April 2009 31 kbps 0.55 0.31 Mary Uniform(0,100) 31 kbps

19. Coordination Strategy Cisco talk - April 2009 19 Alice Uniform(0,100) Base station Priority by CDF value Bob Uniform(0,100) Mary Uniform(0,100) F = 0.31 F = 0.27 0 kbps 50 kbps 31 kbps V = 0.55V = 0V = 0.5 DATA

20. Coordination Strategy Example Cisco talk - April 2009 20 Time slot:12345678910 Alice Rate - r5061154821376032676 Priority - V(r).50.61.15.48.21.37.60.03.26.76 Bob Real Rate:27806426754729875541 Reported rate:08064267502987041 Priority - V(r)0.820.53.780.54.880.58 Mary Real Rate:3140771375894388132 Reported rate:310770758900810 Priority - V(r)550.800.78.9000.830 Time slots Alice lost due to the coordination of Bob and Mary.

21. CDF Exploits - Results Y-axis is the additional time share (in percents) that a coordinated user gains when he takes part in a coordinated group of size L (X-Axis). Participating in a coordinated group of 11 users is the most beneficial and increases the time share of the user by 28%. 21 Cisco talk - April 2009 Time Share Benefit (%)

22. CDF Exploits - Results The previous results are for time share benefit These results are independent of the channel rate distributions of the users (coordinated and regulars) Throughput benefit is strongly connected to the time share benefit but depends on the channel rate distribution 22 Cisco talk - April 2009

23. CDF Scheduler– Discrete model Limited set of possible channel rates: {r 1 < r 2 < …< r M } The only difference:  The way priority values are assigned Algorithm:  User k reports channel rate - r i  Assigned with random priority value: V ~ Uniform(F k (r i-1 ), F k (r i )) 23 Cisco talk - April 2009

24. Discrete model - Example Cisco talk - April 2009 24 Alice r1r1 r2r2 r3r3 Probability Rates 0.25 0.5 r3r3 r2r2 r1r1 1.00 0.75 0.25 0 CDF Alice

25. CDF Scheduler - Example Cisco talk - April 2009 25 Base station Priority by CDF value Priority value: V=0.6 r2r2 0.75 0.25 r3r3 r1r1 1.00 0 Alice r2r2 0.6

26. CDF Scheduler– Discrete model Discrete CDF Scheduler:  Priority value for every user is still V~Uniform(0,1)  Therefore, preserves time-share fairness Coordinated group strategy:  Users share the range of their priority value  Users with no chance to win, report min. rate (r 1 )  Sometimes more than one user in the group may report his real rate  Benefit less than in the continuous model 26 Cisco talk - April 2009

27. CDF Scheduler– Discrete model Coordinated group strategy - Results: 27 Cisco talk - April 2009 Time Share Benefit (%) Throughput Benefit (%) Group Size (out of 30)

28. Discrete model - Malicious users Malicious users  Don’t care about their time/throughput share  Malicious strategy -> greater system degradation Malicious users strategy:  Every user chooses his “favorite rate” - R  Always only one user (in his turn) reports his R  All other users report other rate lower than their R Hard to detect – normal pattern of reported rates 28 Cisco talk - April 2009

29. Discrete model - Malicious users Malicious strategy - Example  10 malicious users  Each user: Report r 3 10% of the time (in his turn) Reports r 1 or r 2 90% of the time  In his turn, the user gets priority in [0.9,1]  Therefore, every time slot there’s a malicious user with priority value in [0.9,1] 29 Cisco talk - April 2009 0.90 r1r1 1.00 0 Malicious User r2r2 r3r3

30. CDF Scheduler - Example Cisco talk - April 2009 30 Base station Priority by CDF value 0.90 r3r3 1.00 0 Bad #1 0.90 r1r1 1.00 0 Bad #2 0.90 r1r1 1.00 0 Bad #3 Bad #1: V=0.95 r2r2 0.75 0.25 r2r2 r2r2 r2r2 r1r1 r3r3 r3r3 r3r3 r1r1 1.00 0 Alice His turn Alice: V=0.51

31. CDF Scheduler - Example Cisco talk - April 2009 31 Base station Priority by CDF value 0.90 1.00 0 Bad #1 0.90 1.00 0 Bad #2 0.90 r1r1 1.00 0 Bad #3 Bad #2: V=0.91 0.75 0.25 r2r2 r3r3 r3r3 r2r2 r3r3 r1r1 r2r2 r2r2 r1r1 r3r3 r1r1 1.00 0 Alice His turn Alice: V=0.78

32. Malicious VS. Coordinated Users Coordinated users’ goal: more bandwidth Malicious users’ goal: harm the others Malicious users get e-1 (~ 170%) of what other users get (when both regular and mal. are in equal numbers and should get equal time share) Cisco talk - April 2009 32 System Loss (%)

33. Future Work Development of basic scheduling algorithms resilient to extreme conditions in next generation cellular networks. 33 Cisco talk - April 2009

34. Questions? 34 Cisco talk - April 2009