MURI Tools for the A nalysis and D esign of C omplex Multi-Scale N etworks

1. MURI Tools for the Analysis and Design of Complex Multi-Scale Networks Review September 9, 2009 Protocols for Wireless Networks ADCN Libin Jiang, Jiwoong Lee and Jean Walrand Department of EECS University of California at Berkeley

2. Outline ADCN • Three topics: • CSMA Algorithms • Basic Idea; Example 1; Example 2; Example 3 • Future Work • Algorithms for Stochastic Processing Networks (SPN) • Cooperation with Incomplete Information 2/15

3. 1. CSMA Algorithms: Basic Idea ADCN Instead of Maximum Weight, use gradient algorithm to improve the schedule. The backpressure is the gradient with respect to the aggressiveness of a link: If the backpressure increases, the link should be more aggressive. This is the gradient of the distance between the stationary distribution of the independent sets and the distribution that supports the arrival rates. 2/15

4. 1. CSMA Algorithms: Example 1 ADCN Wireless Backpressure (Jiang-Walrand): Distributed protocols for scheduling, routing, and congestion control in ad hoc networks. THEOREM: Converges to optimal control with suitable step sizes. Extends to routing and to collisions in general ad hoc network. 2/15

5. 1. CSMA Algorithms: Example 2 ADCN 2/15

6. 1. CSMA Algorithms: Example 3 ADCN • Goal • Maximize U(x) • x = rate delivered to A and B • Assume all 9 links interfere • How? • scheduling: who transmits when • network coding • congestion control: x

7. 1. CSMA Algorithms: Example 3 ADCN X Y Z = X + Y Z Z • Solution • HOL coding • sum of BP • rate control at input

8. 1. CSMA Algorithms: Example 3 ADCN Scheduling: 9 6 L 5 7 Link L: exponential waiting time with rate = exp of αr(L)[ (9 – 5)+ + (6 – 7)+]

9. 1. CSMA Algorithms: Example 3 ADCN • A “flow” is maintained for each destination in each session. • Network coding performed among flows in the samemulticast session Multipath routing allowed Two-way interference

10. 1. CSMA: Future Work ADCN • Combine with Srikant’s shadow queues and per-hop penalty • Combine LQF and CSMA • Combine throughput/delay 11/15

11. 2. Stochastic Processing Networks ADCN • General situation: tasks require parts and resources to produce new parts • Examples: Military mission, assembly plant, service network, hospital, ... • Goal: Schedule tasks and ordering of parts to maximize the utility of the production

12. 2. SPN: Example ADCN

13. 2. SPN: Basic Problem ADCN Task A requires a part from queue 1 Task B requires a part from all queues Task C requires a part from queue 3 Time 0 Time 1- Time 2- Time 1

14. 2. SPN: Basic Problem ADCN Task A requires a part from queue 1 Task B requires a part from all queues Task C requires a part from queue 3 Time 2 Time 3- Maximum Backpressure Scheduling is not stable.

15. 2. SPN: Basic Problem ADCN Task A requires a part from queue 1 Task B requires a part from all queues Task C requires a part from queue 3 Time 1: Do not serve Time 0 Time 2- Modified scheduling is stable.

16. 2. SPN: Basic Problem ADCN Under a reasonable assumption on the arrival processes, one should be able to stabilize the network. For instance, assume that the arrival rates are in the convex hull of the service vectors. Moreover, assume that the distance between the arrivals and their averages in [0, t] is bounded. Then some scheme should stabilize the system. The goal is to find a scheme that automatically adjusts the schedule.

17. 2. SPN: Basic Problem ADCN Scheme: Deficit Maximum Weight. 1) “Augment State” with virtual backlog. 2) Schedule according to virtual backlog which may be negative, thus scheduling a “null activity”. Schedule with maximum weight. 3) Prove that the difference between actual and virtual is bounded. Thus, waste a finite amount of time.Extends to utility maximization.

18. 2. SPN: Basic Problem ADCN qi = virtual backlog at queue i. Qi = actual backlog at queue i. Repeats forever

19. 2. SPN: DMW: Deficit MaximumWeight ADCN • Actual queues Q(t), virtual queues q(t) • Allow q(t) to be negative • Queue dynamics • If Qk “underflows”, then activate a “null SA” and use “fictitious parts” • “Deficit” Activation of SA’s decided by MW

20. 2. SPN: DMW (Main properties) ADCN • Prop. 1: If q(t) is bounded, then both Q(t) and D(t) are bounded. Only a finite number of null SA’s occur long-term throughput not affected. • Prop. 2: If the arrival process is smooth enough, then q(t) is bounded • For example, there exists T>0 so that (t=0, T, 2T, 3T…) is in the interior of the capacity region (uniformly) • Mild condition • More random arrivals • System is still “rate-stable”, although Q(t) may slowly drift to infinity • Can force Q(t) to be stable, at a cost of the throughput • Tradeoff between queue lengths and throughput

21. 2. SPN: DMW +congestioncontrol ADCN • Congestion control Throughput: Flow 1: 0.4998 Flow 2: 0.4998 Close to the theoretical optimum 0.5, 0.5

22. 3. Cooperation with Incomplete Information ADCN • General motivation: Robust protocols • Initial idea: a protocol that achieves maxmin • Problem: Nodes want to help, but their information is incomplete. • Model? What type of result? 12/15

23. INCOMPLETE INFORMATION IN NETWORKS Relay network (Lee-Walrand): Sensitivity of optimal protocols w.r.t. lack of knowledge in network. FACT: Under conservative max-min algorithm, throughput may not converge. Optimal protocol: Limited updates.

24. Summary ADCN 1. CSMA Algorithms: Distributed control of wireless ad hoc networks; maximize utility 2. SPN: Deficit Maximum Weight: Stabilize SPN 3. Search for robust protocols.