1. Cross Layer Adaptive Control for Wireless Mesh Networks (and a theory of instantaneous capacity regions) Michael J. Neely, Rahul Urgaonkar University of Southern California http://www-rcf.usc.edu/~mjneely/ *This work was supported in part by one or more of the following: NSF Digital Ocean, the DARPA IT-MANET Program ITA Workshop, San Diego, February 2007 To Appear in Ad Hoc Networks (Elsevier)

2. Network LayeringTimescale Decomposition Transport “Flow Control” Network “Routing” PHY/MAC “Resource Allocation” “Scheduling” Flow/Session Arrival and Departure Timescales Mobility Timescales Channel Fading Channel Measurement Objective: Design Algs. for Throughput and Delay Efficiency Fact: Network Performance Limits are different across different layers and timescales Example… Cross Layer Networking

3. Mobile Network at Different Timescales “Ergodic Capacity” -Thruput = O(1) -Connectivity Graph is 2-Hop (Grossglauser-Tse) “Capacity and Delay Tradeoffs” -Neely, Modiano [2003, 2005] -Shah et. al. [2004, 2006] -Toumpis, Goldsmith [2004] -Lin, Shroff [2004] -Sharma, Mazumdar, Shroff [2006]

4. Mobile Network at Different Timescales “Instantaneous Capacity” -Thruput = O(1/sqrt{N}) -Connectivity Graph for a “snapshot” in time -Thruput can be much larger if only a few sources are active at any one time!

5. Mobile Network at Different Timescales “Instantaneous Capacity” -Thruput = O(1/sqrt{N}) -Connectivity Graph for a “snapshot” in time -Thruput can be much larger if only a few sources are active at any one time!

6. Network Model --- The General Picture 3 Layers: Flow Control (Transport) Routing (Network) Resource Alloc./Sched. (MAC/PHY) *From: Resource Allocation and Cross-Layer Control in Wireless Networks by Georgiadis, Neely, Tassiulas, NOW Foundations and Trends in Networking, 2006 ownother ij Flow Control Decision Rij(t)

7. Network Model --- The General Picture 3 Layers: 1)Flow Control (Transport) 2)Routing (Network) 3)Resource Alloc./Sched. (MAC/PHY) *From: Resource Allocation and Cross-Layer Control in Wireless Networks by Georgiadis, Neely, Tassiulas, NOW Foundations and Trends in Networking, 2006 ownother

8. Network Model --- The General Picture 3 Layers: 1)Flow Control (Transport) 2)Routing (Network) 3)Resource Alloc./Sched. (MAC/PHY) *From: Resource Allocation and Cross-Layer Control in Wireless Networks by Georgiadis, Neely, Tassiulas, NOW Foundations and Trends in Networking, 2006 ownother “Data Pumping Capabilities”: (  ij (t)) = C(I(t), S(t)) Control Action (Resource Allocation/Power) Channel State Matrix I(t) in I

9. Network Model --- The Wireless Mesh Architecture with Cell Regions 0 1 2 3 4 5 6 7 8 9 Mesh Clients: -Mobile -Peak and Avg. Power Constrained (P peak, P av ) -Little/no knowledge of network topology Mesh Routers: -Stationary (1 per cell) -More powerful/knowedgeable -Facillitate Routing for Clients Assume Slotted Time t in {0, 1, 2, …} Let T(t) = Topology State of Clients on slot t (Arbitrary Mobility) Let S(t) = Channel States of Links on slot t Assume: S(t) is conditionally i.i.d. given T(t):  S (T) = Pr[S(t) = S | T(t)=T ]

10. The Instantaneous Capacity Region: 0 1 2 3 4 5 6 7 8 9 Assume Slotted Time t in {0, 1, 2, …} Let T(t) = Topology State of Clients on slot t (Arbitrary Mobility) Let S(t) = Channel States of Links on slot t Assume: S(t) is conditionally i.i.d. given T(t):  S (T) = Pr[S(t) = S | T(t)=T ] Instantaneous Capacity Region  (t) = Instantaneous Capacity Region = Ergodic Capacity Associated with a network with fixed topology state T(t) for all time (and i.i.d. channels  S (T))

11. The Instantaneous Capacity Region: 0 1 2 3 4 5 6 7 8 9 Assume Slotted Time t in {0, 1, 2, …} Let T(t) = Topology State of Clients on slot t (Arbitrary Mobility) Let S(t) = Channel States of Links on slot t Assume: S(t) is conditionally i.i.d. given T(t):  S (T) = Pr[S(t) = S | T(t)=T ] Instantaneous Capacity Region  (t) = Instantaneous Capacity Region = Ergodic Capacity Associated with a network with fixed topology state T(t) for all time (and i.i.d. channels  S (T))

12. The Instantaneous Capacity Region: 0 1 2 3 4 5 6 7 8 9 Assume Slotted Time t in {0, 1, 2, …} Let T(t) = Topology State of Clients on slot t (Arbitrary Mobility) Let S(t) = Channel States of Links on slot t Assume: S(t) is conditionally i.i.d. given T(t):  S (T) = Pr[S(t) = S | T(t)=T ] Instantaneous Capacity Region  (t) = Instantaneous Capacity Region = Ergodic Capacity Associated with a network with fixed topology state T(t) for all time (and i.i.d. channels  S (T))

13. The Instantaneous Capacity Region: 0 1 2 3 4 5 6 7 8 9 Assume Slotted Time t in {0, 1, 2, …} Let T(t) = Topology State of Clients on slot t (Arbitrary Mobility) Let S(t) = Channel States of Links on slot t Assume: S(t) is conditionally i.i.d. given T(t):  S (T) = Pr[S(t) = S | T(t)=T ] Instantaneous Capacity Region  (t) = Instantaneous Capacity Region = Ergodic Capacity Associated with a network with fixed topology state T(t) for all time (and i.i.d. channels  S (T))

14. The Instantaneous Capacity Region: 0 1 2 3 4 5 6 7 8 9 Assume Slotted Time t in {0, 1, 2, …} Let T(t) = Topology State of Clients on slot t (Arbitrary Mobility) Let S(t) = Channel States of Links on slot t Assume: S(t) is conditionally i.i.d. given T(t):  S (T) = Pr[S(t) = S | T(t)=T ] Instantaneous Capacity Region  (t) = Instantaneous Capacity Region = Ergodic Capacity Associated with a network with fixed topology state T(t) for all time (and i.i.d. channels  S (T))

15. The Instantaneous Capacity Region: 0 1 2 345 6 7 8 9 Assume Slotted Time t in {0, 1, 2, …} Let T(t) = Topology State of Clients on slot t (Arbitrary Mobility) Let S(t) = Channel States of Links on slot t Assume: S(t) is conditionally i.i.d. given T(t):  S (T) = Pr[S(t) = S | T(t)=T ] Instantaneous Capacity Region  (t) = Instantaneous Capacity Region = Ergodic Capacity Associated with a network with fixed topology state T(t) for all time (and i.i.d. channels  S (T))

16. The Instantaneous Capacity Region: 0 1 2 3 4 56 7 8 9 Assume Slotted Time t in {0, 1, 2, …} Let T(t) = Topology State of Clients on slot t (Arbitrary Mobility) Let S(t) = Channel States of Links on slot t Assume: S(t) is conditionally i.i.d. given T(t):  S (T) = Pr[S(t) = S | T(t)=T ] Instantaneous Capacity Region  (t) = Instantaneous Capacity Region = Ergodic Capacity Associated with a network with fixed topology state T(t) for all time (and i.i.d. channels  S (T))

17. Results: -Design a Cross-Layer Algorithm that optimizes throughput-utility with delay that is independent of timescales of mobility process T(t). -Use *Lyapunov Network Optimization -Algorithm Continuously Adapts *[Tassiulas, Ephremides 1992] (Backpressure, MWM) *[Georgiadis, Neely, Tassiulas F&T 2006] *[Neely, Modiano, 2003, 2005] T1 T2 T3 } (Stochastic Network Optimization)

18. Algorithm: (CLC-Mesh) 1)Utility-Based Distributed Flow Control for Stochastic Nets -g i (x) = concave utility (ex: g i (x) = log(1 + x)) -Flow Control Parameter V affects utility optimization / max buffer size tradeoff x = thruput 2)Combined Backpressure Routing/Scheduling with “Estimated” Shortest Path Routing at Mesh Routers -Mesh Router Nodes keep a running estimate of client locations (can be out of date) -Use Differential Backlog Concepts -Use a Modified Differential Backlog Weight that incorporates: (i) Shortest Path Estimate (ii) Guaranteed max buffer size  V (provides immediate avg. delay bound) -Virtual Power Queues for Avg. Power Constraints [Neely 2005]

19. Define: g*(t) = Optimal Utility Subject to Instantaneous Capacity Region Instantaneous Capacity Region  (t1) Instantaneous utility-optimal point Instantaneous Capacity Region  (t2) Instantaneous utility-optimal point Theorem: Under CLC-Mesh with flow control parameter V, we have: (a)Backlog: U i (t) <=  V for all time t (worst case buffer size in all network queues) (b)Peak and Average Power Constraints satisfied at Clients (c)

20. Define: g*(t) = Optimal Utility Subject to Instantaneous Capacity Region Instantaneous Capacity Region  (t1) Instantaneous utility-optimal point Instantaneous Capacity Region  (t2) Instantaneous utility-optimal point Theorem: Under CLC-Mesh with flow control parameter V, we have: (d) If V = infinity (no flow control) and rate vector is always interior to instantaneous capacity region (distance at most  from boundary), then achieve 100% throughput with delay that is independent of mobility timescales. (e) If V = infinity (no flow control), if mobility process is ergodic, and rate vector is inside the ergodic capacity region, then achieve 100% throughput with same algorithm, but with delay that is on the order of the “mixing times” of the mobility process. 

21. 01 2 3 4 5 6 7 8 9 Halfway through the simulation, node 0 moves (non-ergodically) from its initial location to its final location. Node 9 takes a Markov Random walk. Full throughput is maintained throughout, with noticeable delay increase (at “new equilibrium”), but which is independent of mobility timescales. 10 Mesh clients, 21 Mesh Routers in a cell-partitioned network Simulation Experiment 1 Communication pairs: 01, 2 3, …, 89

22. The achieved throughput is very close to the input rate for small values of the input rate The achieved throughput saturates at a value determined by the V parameter, being very close to the network capacity (shown as vertical asymptote) for large V Flow control using control parameter V Simulation Experiment 2

23. Effectiveness of Combined Diff. Backlog -Shortest Path Metric Simulation Experiment 3

24. Effectiveness of Combined Diff. Backlog -Shortest Path Metric Omega = weight determining degree to which shortest path estimate is used. Omega = 0 means pure differential backlog (no shortest path estimate) Full Thruput is maintained for any Omega (Omega only affects delay for low input rates) Interpretation of this slide: Simulation Experiment 3