1. Scheduling Heterogeneous Real- Time Traffic over Fading Wireless Channels I-Hong Hou P.R. Kumar University of Illinois, Urbana-Champaign 1/24

2. Background: Wireless Networks  There will be increasing use of wireless networks for serving traffic with QoS constraints: Example: VoIP, Video Streaming, Real-time Monitoring, Networked Control, etc.  Client requirements include Specified traffic patterns Delay bounds Timely throughput bounds 2 /24

3. Previous Work and Challenges  Prior work [Hou et al] [Hou and Kumar]: Clients have hard throughput requirements Static but unreliable wireless channels All clients require the same delay bounds Optimal packet scheduling policies are proposed  Q: How to deal with more complicated scenarios? Rate adaptation may be applied Channel qualities can be time-varying Clients may require different delay bounds  This work extends the model in prior work and proposes a guideline for these scenarios 3 /24

4. Client-Server Model  A system with N wireless clients and one AP  Time is slotted  AP schedules all transmissions AP 1 2 3 4 /24

5. More General Traffic Model  Group time slots into periods with T time slots  Clients may generate packets at the beginning of each period AP 1 2 3 {1,.,3} {.,2,.}{1,2,3} {1,.,3} {.,2,.} {1,2,3} T 5 /24

6. Different Delay Bounds  Deadline for client n = τ n AP 1 2 3 τ 1 =4 arrival deadline τ 3 =3 deadlinearrival τ 2 =5 deadlinearrival 6 /24

7. Without Rate Adaptation  Transmission takes 1 time slot  Transmissions succeeds with probability p c,n Channel Model  Channel changes from period to period  Channels are static within a period  System may or may not support rate adaptation 7 /24 With Rate Adaptation  Transmission takes s c,n time slots under channel c  Transmissions are error-free

8. Timely Throughput Requirements  Timely throughput =  Client n requires timely throughput q n  Q: How to design a scheduling policy to fulfill requirements of all feasible sets of clients? Feasibility optimal scheduling policy 8 /24

9. Pseudo-debt  Delivery debt: deficiency of timely throughput  Time debt: deficiency of time spent on a client  Pseudo-debt r n (t) quantifies the behavior of client n up to time t The set of clients is fulfilled  converges to 0 in probability 9 /24

10. Sufficient Condition for Optimality  Let μ n be the reduction on debt for client n  Theorem:  A policy that maximizes for each period is feasibility optimal.  Analogous to Max-Weight scheduling in wireline networks 10 /24

11. Rate Adaptation with Different Delay Bounds  Scenario: Rate adaptation used Clients may have different per packet delay bounds, τ n  Modified Knapsack Policy: Find an ordered set S={m 1,m 2, … } to maximize total debt A variation of knapsack problem and can be solved by DP 11 /24 τ 1 =4τ 2 =7τ 3 =10 S 1 = 3 S 2 = 5 S 3 = 4 S 1 = 3S 3 = 4

12. Rate Adaptation with Different Delay Bounds  Scenario: Rate adaptation used Clients may have different per packet delay bounds, τ n  Modified Knapsack Policy: Find an ordered set S={m 1,m 2, … } to maximize total debt A variation of knapsack problem and can be solved by DP 12 /24 S 3 = 4S 2 = 5 τ 1 =4τ 2 =7τ 3 =10 S 1 = 3 S 2 = 5 S 3 = 4

13. Rate Adaptation with Different Delay Bounds  Scenario: Rate adaptation used Clients may have different per packet delay bounds, τ n  Modified Knapsack Policy: Find an ordered set S={m 1,m 2, … } to maximize total debt A variation of knapsack problem and can be solved by DP 13 /24 S 2 = 5S 1 = 3 τ 1 =4τ 2 =7τ 3 =10 S 1 = 3 S 2 = 5 S 3 = 4

14. Time-Varying Channels  Scenario: Same delay bounds for all clients, τ≡τ n Time-varying channels, p n (t) Applicable to Gilbert-Elliot fading Model  Joint Debt-Channel Policy: Let r n (t) be delivery debt Clients with larger r n (t) p n (t) get higher priorities  Theorem: The Joint Debt-Channel policy is feasibility optimal 14 /24

15. Heterogeneous Delay Bounds  Scenario: Static channels, p n ≡p n (t) Different delay bounds for all clients, τ n  Adaptive-Allocation Policy: Let r n (t) be time debt Estimate the # of slots needed by client n for a successful transmission, η n Dynamically allocate slots to maximize 15 /24

16. Evaluation Methodology  Evaluate four policies: Proposed policies for each scenario PCF with randomly assigned priorities (random) Two policies proposed by [Hou, Borkar, and Kumar]  Time debt first policy  Weighted-delivery debt first policy  Metric: Total delivery debt 16 /24

17. Rate Adaptation: VoIP Setup  Period length = 20 ms  Two groups of clients:  66 Group A clients and 44 Group B clients Group AGroup B One packet every 60 msOne packet every 40 ms 21.3 kb/s traffic32 kb/s traffic require 19.2 kb/s timely throughput require 22.4 kb/s timely throughput Starting times evenly spaced Data rates alternate between 11 Mb/s and 5.5 Mb/s 17 /24

18. Rate Adaptation: VoIP Results 18 /24

19. Time-Varying Channels: VoIP Setup  Period length = 20 ms  Two groups of clients:  57 Group A clients and 38 Group B clients Group AGroup B One packet every 60 msOne packet every 40 ms 21.3 kb/s traffic32 kb/s traffic require 19.2 kb/s timely throughput require 22.4 kb/s timely throughput Starting times evenly spaced Channel evolves based on Gilbert-Elliot model 19 /24

20. Time-Varying Channels: VoIP Result 20 /24

21. Heterogeneous Delay Bounds: VoIP Setup  Two groups of clients:  57 Group A clients and 38 Group B clients Group AGroup B One packet every 60 msOne packet every 40 ms 21.3 kb/s traffic32 kb/s traffic require 19.2 kb/s timely throughput require 22.4 kb/s timely throughput Delay bound = 20 msDelay bound = 13 ms Starting times evenly spaced Average channel reliabilities between 80% and 96% 21 /24

22. Heterogeneous Delay Bounds: VoIP Result 22 /24

23. Conclusion  Extend previous model for more complicated scenarios With or without rate adaptation Time-varying channels Heterogeneous delay bounds  Identify a sufficient condition for optimal scheduling policies  Design policies for several cases Time-varying channels, heterogeneous delay bounds with rate adaptation Time-varying channels without rate adaptation Heterogeneous delay bounds without rate adaptation 23 /24

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25. Rate Adaptation: MPEG Setup  Period length = 6 ms  Two groups of clients:  6 Group A clients and 6 Group B clients Group AGroup B 1700 kb/s traffic1360 kb/s traffic require 1530 kb/s timely throughput require 816 kb/s timely throughput Data rates alternate between 54 Mb/s and 24 Mb/s 25

26. Rate Adaptation: MPEG Results 26

27. Time-Varying Channels: MPEG Setup  Period length = 6 ms  Two groups of clients:  4 Group A clients and 4 Group B clients Group AGroup B 1700 kb/s traffic1360 kb/s traffic require 1530 kb/s timely throughput require 816 kb/s timely throughput Average channel reliabilities between 80% and 89% 27

28. Time-Varying Channels: MPEG Setup 28