Congestion Control to Reduce Latency in Sensor Networks for Real-Time Applications

1. Congestion Control to Reduce Latency in Sensor Networks for Real-Time Applications Presented by Phoebus Chen EE228A – Communication Networks

2. Outline • Motivation: Sensor Network Surveillance • Background: Congestion Control • Difficulties with Addressing Latency • Design Guidelines for Latency Congestion Control Policies EE228A – Communication Networks

3. Sensor Networks for Real-Time Surveillance • Event Detection • bursty traffic • varying importance of data for estimation • can operate with incomplete data • Low Latency • routing • selective packet delivery • congestion control EE228A – Communication Networks

4. Sample Surveillance Scenario • Multiple targets on linear trajectories • One centralized estimator per cell Ultimate scenario: Pursuit-Evasion Games with mobile robots EE228A – Communication Networks

5. Study focused on design of network congestion control • Wireless, multi-hop channel • Fixed routing • Multiple sources, one sink Sensing and Data Aggregation (source) Sensing and Data Aggregation (network) Estimation (sink) EE228A – Communication Networks (source)

6. Performance Metric: Estimator • Linear System Dynamics • driven by a white noise process • Simple linear measurement model • Estimation via Kalman Filter • Check performance under different traffic patterns EE228A – Communication Networks

7. Background on Congestion Control [1] [2] • Flow model • Network Optimization Problem [1] R. Srikant, The Mathematics of Internet Congestion Control, ser. Systems & Control: Foundations & Applications. Birkhauser Boston, 2004. [2] F. P. Kelly, A. K. Maulloo, and D. K. H. Tan, “Rate control for communication networks: shadow prices, proportional fairness and stability,” Journal of the Operational Research Society, vol. 49, no. 3, pp. 237–252, March 1998. EE228A – Communication Networks

8. Various User Utility Functions • Weighted Proportional Fairness • Minimum Potential Delay • Max-Min Fair • General Utility Function [3] • For max-min fairness [3] J. Mo and J. Walrand, “Fair end-to-end window-based congestion control,” IEEE/ACM Transactions on Networking, vol. 8, no. 5, pp. 556– 567, Oct 2000. EE228A – Communication Networks

9. Primal Algorithm and Controller • Primal Algorithm (Lyapunov Function) • Flow Controller • kr(xr) > 0 is a non-decreasing, continuous function • Assume prices react instantaneously EE228A – Communication Networks

10. Dual Algorithm and Controller • Dual Algorithm • Price Controller • hl(pl) > 0 is a non-decreasing continuous function • Assume flows react instantaneously EE228A – Communication Networks

11. Primal-Dual Algorithms and other variants • Can combine primal and dual controllers, and prove via a Lyapunov function that the algorithm is globally, asymptotically stable • Other variants exist • Calculate prices using a weighted average of the flow at a link over time • Setting prices based on fullness of a virtual queue (Adaptive Virtual Queue, or AVQ) • Prices are marking probabilities of packets EE228A – Communication Networks

12. Examples of Congestion Control Analysis • Convergence Rate • Linearize about equilibrium • Look at smallest eigenvalue of dynamics matrix • Time-delay Stability Analysis • Linearize about equilibrium • Look at transfer function in the frequency domain and apply Nyquist stability criterion • Stochastic Stability • Linearize about equilibrium • Look at Brownian motion perturbations, check induced covariance of fluctuations EE228A – Communication Networks

13. Applying TCP/IP congestion control to wireless sensor networks • Does not account for wireless networks with: • interference from neighboring paths • physical channel errors • Hard to address both, first pass is to treat as constant error disturbance like [4] [5] [4] M. Chen, A. Abate, and S. Sastry, “New congestion control schemes over wireless networks: stability analysis,” in Proceedings of the 16th IFAC World Congress, 2005. [5] A. Abate, M. Chen, and S. Sastry, “New congestion control schemes over wireless networks: delay sensitivity analysis and simulations,” in Proceedings of the 16th IFAC World Congress, 2005. EE228A – Communication Networks

14. Properties of Utility and Pricing Functions • Assumptions on Ur(xr),  r • is a non-decreasing, continuously differentiable, strictly concave function • Ur(xr)  - as xr 0 • Assumptions on prices pl()  l • is a non-decreasing, continuous function such that EE228A – Communication Networks

15. Incorporating Latency into Utility • Assign a utility to each packet • Sigmoidal function for differentiability EE228A – Communication Networks

16. Incorporating Latency into Utility (2) • Integrate delay utility of each packet with flow • non-decreasing, continuously differentiable, strictly concave (assuming additional flow only come with greater delay) • May not be able to meet constraint Ur(xr)  - as xr 0 EE228A – Communication Networks

17. Flow Rate vs. Delay and Packet Drop Rate Congestion at merge points In routing tree • Delay is a function of • queuing delay • Congestion • Errors from wireless channel • CSMA contention • transmission delay (number of hops) • Do not have a good/simple model of CSMA contention at the MAC layer • Without knowing we have a hard time knowing for our optimization problem EE228A – Communication Networks

18. Hope? Congestion control policies as an optimization solver with a black box • Some optimization solvers only needs a black box • Make delay part of objective function • Know general trend D = g(x), delay increases with more flow • Treat channel contention, lossy wireless link, inteference, as noise Congestion Black Box D D = g({xr}) D {xr} Delay Noise Lossy Communication Channel Source Nodes Relay Nodes pl pl EE228A – Communication Networks

19. Design Guidelines for Packet Drop Policy • May want to use a LIFO queue on a node, to get latest packets delivered (least delay) • Fairness for packets from different merging routes suggests round robin service over many queues • May want to prioritize based on time to last delivered packet • Need to design policy on when to purge LIFO queues, and how many LIFO queues • Parameters of policy set by messages from sink • Given vehicle dynamics, sink can determine how many targets it can track well EE228A – Communication Networks

20. Design Guidelines for Congestion Feedback Policy • Since low network bandwidth, may not want end-to-end acknowledgement • Sparse end-to-end acknowledgement means cannot adapt to network changes as quickly • Types of Information • Queue lengths • Number of hops to congestion point • Delay on packets delivered • Interfering nodes may want to share information about their respective flow rates and packet delays EE228A – Communication Networks

21. Design Guidelines for Rate Adaptation Policy • Slow start phase? • May want evenly spaced samples for Kalman Filter • If within delay constraints, may want to queue packets to accommodate channel fluctuations • How to decode multiple congestion indicators from relay nodes (queue length, delay, number of hops)? EE228A – Communication Networks

22. Future Work • Fix a model for simulating the network • Design a congestion control scheme via heuristics, and simulate • If I can get a mathematical model, analyze its stability and convergence EE228A – Communication Networks

23. Extra Slides EE228A – Communication Networks

24. Definition of Max-Min Fair EE228A – Communication Networks

25. What pursuers really see EE228A – Communication Networks

26. Sensor net increases visibility EE228A – Communication Networks