1. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking1 / 28 Stochastic Analysis of Wireless-fair Scheduling Hwee Pink Tan and Raphael Rom Dept of Elect. Eng, Technion Israel Institute of Technology

2. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 2 / 28 Outline Introduction Wireless-Fair Scheduling Analytical Model Performance Evaluation Summary and Future Directions

3. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 3 / 28 Introduction Several Wireless Scheduling algorithms proposed recently based on fair queuing paradigm Analytical bounds inadequate to characterize scheduling performance Error-free guarantees Channel-conditioned deterministic bound Stochastic nature of wireless channel enables stochastic analysis of wireless scheduling algorithms

4. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 4 / 28 Wireless-fair Scheduling Wireless Scheduling Scenario Need for Wireless Adaptation Definition of Wireless-Fair Scheduling Lead / Lag Accounting Service Compensation Service

5. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 5 / 28 Scheduling Scenario Single Channel shared amongst N users r j = demand of user (flow) j Fixed-size time-slotted transmission Perfect Knowledge at Scheduler Queue status of user j at slot i, Q i j  {backlogged, idle} Channel state of user j at slot i, CS i j  {Good, Bad} r1r2rNr1r2rN T T Centralized Wireless Scheduler Wireless Link

6. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 6 / 28 Wireless-fair Scheduling Need for Wireless Adaptation Fair Scheduling in wired link (WiredFS) guarantees throughput, delay and fairness Direct application of WiredFS in wireless link results in degradation of Throughput and Delay guarantees ‘wasted’ slots due to channel errors Fairness guarantee time and spatial dependence of channel errors

7. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 7 / 28 Wireless-fair Scheduling Definition Wireless-Fair Scheduling WiredFS Wireless-Adaptation Service Reassigns transmission slots based on channel state Compensates for reassignment Lead / Lag Accounting Service Compensation Service

8. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 8 / 28 Wireless-fair Scheduling Lead / Lag Accounting Service Notion of Lag (Lead) A flow’s lag ( lead ) = amount of service it is entitled to ( needs to relinquish ) in the future to compensate for service lost ( gained ) in the past Lag j = Lag of flow j = - Lead of flow j

9. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 9 / 28 Wireless-fair Scheduling Lead / Lag Accounting Service Update of Lag j Lag j = Lag j + 1 when Flow j gives up an allocated slot (due to channel error) to another flow Lag j = Lag j -1 when Flow j transmits in a slot given up by another flow Effects of Bounded Lag j Tradeoff between fairness and channel efficiency

10. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 10 / 28 Wireless-fair Scheduling Compensation Service Allows lagging flows to reclaim ‘lost’ service from leading flows Defines the ‘how, when and which’ for which a flow transmits in a slot given up by another flow a flow gives up its allocated slot to allow another flow to catch up

11. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 11 / 28 Analytical Model Assumptions Definition of Analysis Intervals Definition of Symmetric Two-Flow Wireless- Fair Scheduler Scheduling Mechanism Characterization of Scheduler

12. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 12 / 28 Flow characteristics r 1 =r 2 =0.5 Independent Arrivals Equal-sized packets (tx time = T) Infinite Buffer Length Channel characteristics Similar channel conditions for f1 and f2 Analytical Model Assumptions r1r2r1r2 T T Rate- and Channel-Symmetric (Symmetric) Two-Flow Scheduling

13. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 13 / 28 Analytical Model Definition of Analysis Interval

14. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 14 / 28 Analytical Model Definition of Scheduler Notations j = flow index; i = slot index x i j = lead of flow j at the end of slot i A i = allocation in slot i  {S1,S2} Flow status Flow j is

15. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 15 / 28 Analytical Model Definition of Scheduler Wired-Fair Service Determines primary allocation policy, A i Within any performance interval, alternate slot allocation suffices Lead/Lag Accounting Service x i 1 + x i 2 = 0 Hence, sufficient to define x i = x i 1 Unbounded x i

16. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 16 / 28 Analytical Model Definition of Scheduler Compensation Service Determines secondary slot allocation policy, based on input from Lead/Lag Accounting Service Absolute transmission priority to lagging flows Allocated leading flow always relinquish transmission priority Slot ‘wasted’ only when no error-free flow exists

17. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 17 / 28 Analytical Model Implementation of Scheduler Slot allocation policy Slots are always allocated to the lagging flow if it exists; Otherwise, alternate slot allocation is employed Update of x i Flow transmits in non-allocated slot Lagging flow transmits in allocated slot

18. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 18 / 28 Analytical Model Scheduling Mechanism i Packet i of Flow 1 (F1) becomes HOL i Packet i of Flow 1(F1) departs x=0 x=0 x=0 x=-1 x=0 x=1 x=2 x=1 x=0 x=0 time 1 i Packet i of Flow 1 (F1) becomes HOL i Packet i of Flow 1(F1) departs 1 1

19. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 19 / 28 Analytical Model Characterization of Scheduler Within any performance interval, the Wireless Scheduler can be characterized as 2-D Markov Chain, {(x i,A i ), i=1,2,3,…} State variables: x i, A i Markov Points: slot intervals Simplification to 1-D Markov Chain, {y q, q=1,2,3} State variable : y q =x i q Markov Points : departure instants of packet q of flow 1, i q, q=1,2,3,…

20. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 20 / 28 Performance Evaluation Packet delay distribution, G(n) Fairness distribution, F(y) Channel Error Model Results

21. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 21 / 28 Performance Evaluation Delay distribution, G(n) Allocation S1 S2 Slot Number k k+1 k+n-1 k+n Packet q-1 departs Packet q departs y q-1 =x k-1 =x init x k+n-1 y q =x k+n =x fin Markov points Consider packet q of flow 1 that becomes HOL in slot k and departs at the end of slot n+k Markov Interval = Delay of packet q = n slots G(n) = cdf of n

22. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 22 / 28 Performance Evaluation Fairness distribution, F(y) Allocation S1 S2 Slot Number k k+1 k+n-1 k+n Packet q-1 departs Packet q departs y q-1 =x k-1 =x init x k+n-1 y q =x k+n =x fin Markov variables Markov variable, y q ≈ disparity (or ‘unfairness’) in cumulative service received by both flows F(y) = cdf of y

23. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 23 / 28 G(n) and F(y) can be computed given the channel error model Performance Evaluation Channel Error Model Good Bad p ge p eg Two-state Markov Chain Error Model p corr = p ge + p eg = 0.1 P B = {0.2,0.8} Random Error Model Uncorrelated average error rate = P E = {0.2,0.8}

24. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 24 / 28 Performance Evaluation Delay Performance p E =0.2p E =0.8 meanstdmeanstd Random Error Model2.080.805.505.17 2SMC Error Model1.933.804.8319.81 02468101214161820 10 -14 10 -12 10 -10 10 -8 10 -6 10 -4 10 -2 10 0 Delay Bound Loss Rate Delay Distribution for Symmetric Two-Flow Wireless-Fair Scheduling Random Error Model 2SMC Error Model 051015202530 10 -3 10 -2 10 10 0 Delay Bound Loss Rate Delay Distribution for Symmetric Two-Flow Wireless-Fair Scheduling Random Error Model 2SMC Error Model p E = 0.2 p E = 0.8

25. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 25 / 28 Performance Evaluation Fairness Performance p E =0.2p E =0.8 meanstdmeanstd Random Error Model0.250.562.712.79 2SMC Error Model7.658.2213.6315.98 05101520253035404550 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x=lead of flow 1 F(x) Fairness Distribution for Symmetric Two-Flow Wireless-Fair Scheduling Random Error Model 2SMC Error Model 05101520253035404550 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x=lead of flow 1 F(x) Fairness Distribution for Symmetric Two-Flow Wireless-Fair Scheduling Random Error Model 2SMC Error Model p E = 0.2 p E = 0.8

26. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 26 / 28 Summary Analytical Performance Model for Symmetric Two-Flow Wireless-Fair Scheduling By proper choice of analysis interval and time instants of observation, scheduler can be modeled as a 1-D Markov Chain Performance Evaluation Packet Delay Fairness

27. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 27 / 28 Future Directions Asymmetric Two-Flow Scheduling More general scenario Possible to approximate performance of symmetric N-flow scheduling Channel-independent Fairness Flow-dependent channel errors induce ‘unfairness’

28. 21 Mar 2002 First Israelli-Swedish Workshop on Next Generation Networking 28 / 28 References Hwee Pink Tan and Raphael Rom. Stochastic Analysis of Wireless-Fair Scheduling. Submitted to Mobicom 2002Stochastic Analysis of Wireless-Fair Scheduling Hwee Pink Tan and Raphael Rom. Performance Evaluation of Wireless-Fair Scheduling. Submitted to Globecom 2002Performance Evaluation of Wireless-Fair Scheduling Hwee Pink Tan and Raphael Rom. Stochastic Analysis of Symmetric Two-Flow Wireless-Fair Scheduling. Technical Report, Technion EE publication CITT #371, March 2002Stochastic Analysis of Symmetric Two-Flow Wireless-Fair Scheduling http://www.ee.technion.ac.il/people/hweepink