Scheduling Heterogeneous Real-Time Traffic over Fading Wireless Channels

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

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

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

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

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

6. Different Delay Bounds • Deadline for client n = τn τ2=5 2 1 arrival deadline τ1=4 arrival AP deadline 3 τ3=3 arrival deadline

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

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

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

10. Sufficient Condition for Optimality • Let μn 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

11. Rate Adaptation with Different Delay Bounds • Scenario: • Rate adaptation used • Clients may have different per packet delay bounds, τn • Modified Knapsack Policy: • Find an ordered set S={m1,m2,…} to maximize total debt • A variation of knapsack problem and can be solved by DP S1 = 3 τ1=4 τ2=7 τ3=10 S2 = 5 S1 = 3 S3 = 4 S3 = 4

12. Rate Adaptation with Different Delay Bounds • Scenario: • Rate adaptation used • Clients may have different per packet delay bounds, τn • Modified Knapsack Policy: • Find an ordered set S={m1,m2,…} to maximize total debt • A variation of knapsack problem and can be solved by DP S1 = 3 τ1=4 τ2=7 τ3=10 S2 = 5 S2 = 5 S3 = 4 S3 = 4

13. Rate Adaptation with Different Delay Bounds • Scenario: • Rate adaptation used • Clients may have different per packet delay bounds, τn • Modified Knapsack Policy: • Find an ordered set S={m1,m2,…} to maximize total debt • A variation of knapsack problem and can be solved by DP S1 = 3 τ1=4 τ2=7 τ3=10 S2 = 5 S1 = 3 S2 = 5 S3 = 4

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

15. Heterogeneous Delay Bounds • Scenario: • Static channels, pn≡pn(t) • Different delay bounds for all clients, τn • Adaptive-Allocation Policy: • Let rn(t) be time debt • Estimate the # of slots needed by client n for a successful transmission, ηn • Dynamically allocate slots to maximize

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

17. Rate Adaptation: VoIP Setup • Period length = 20 ms • Two groups of clients: • 66 Group A clients and 44 Group B clients

18. Rate Adaptation: VoIP Results

19. Time-Varying Channels: VoIP Setup • Period length = 20 ms • Two groups of clients: • 57 Group A clients and 38 Group B clients

20. Time-Varying Channels: VoIP Result

21. Heterogeneous Delay Bounds: VoIP Setup • Two groups of clients: • 57 Group A clients and 38 Group B clients

22. Heterogeneous Delay Bounds: VoIP Result

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

24. Thank You

25. Rate Adaptation: MPEG Setup • Period length = 6 ms • Two groups of clients: • 6 Group A clients and 6 Group B clients

26. Rate Adaptation: MPEG Results

27. Time-Varying Channels: MPEG Setup • Period length = 6 ms • Two groups of clients: • 4 Group A clients and 4 Group B clients

28. Time-Varying Channels: MPEG Setup