Cross Layer Adaptive Control for Wireless Mesh Networks

(and a theory of instantaneous capacity regions)

Michael J. Neely , Rahul UrgaonkarUniversity 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 2007To Appear in Ad Hoc Networks (Elsevier)

Network Layering Timescale Decomposition

Transport“Flow Control”

Network“Routing”

PHY/MAC“Resource Allocation”

“Scheduling”

Flow/Session Arrival and Departure Timescales

Mobility Timescales

Channel FadingChannel Measurement

Objective: Design Algs. for Throughput and Delay Efficiency

Fact: Network Performance Limits are different across different layers and timescales

Example…

Cross Layer Networking

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]

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!

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!

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

own other

ij

Flow ControlDecision Rij(t)

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

own other

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

own other

“Data Pumping Capabilities”:

(ij(t)) = C(I(t), S(t))

Control Action(Resource Allocation/Power)

ChannelState Matrix

I(t) in I

Network Model --- The Wireless Mesh Architecture with Cell Regions

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Mesh Clients:-Mobile-Peak and Avg. Power Constrained (Ppeak, Pav)-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 tAssume: S(t) is conditionally i.i.d. given T(t): S(T) = Pr[S(t) = S | T(t)=T ]

The Instantaneous Capacity Region:

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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 tAssume: 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))

The Instantaneous Capacity Region:

0

1

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78

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 tAssume: 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))

The Instantaneous Capacity Region:

0

1

2

3

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6

78

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 tAssume: 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))

The Instantaneous Capacity Region:

0

1

2

3

4

5

6

78

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 tAssume: 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))

The Instantaneous Capacity Region:

0

1 2

3

4

5

6

78

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 tAssume: 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))

The Instantaneous Capacity Region:

0

1 2

34 5

6

78

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 tAssume: 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))

The Instantaneous Capacity Region:

0

1 2

3

4

56

78

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 tAssume: 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))

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)

Algorithm: (CLC-Mesh)

1) Utility-Based Distributed Flow Control for Stochastic Nets

-gi(x) = concave utility (ex: gi(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]

Define: g*(t) = Optimal Utility Subject to Instantaneous Capacity Region

Instantaneous Capacity Region (t1)

Instantaneousutility-optimal point

Instantaneous Capacity Region (t2)

Instantaneous utility-optimal point

Theorem: Under CLC-Mesh with flow control parameter V, we have: (a) Backlog: Ui(t) <= V for all time t (worst case buffer size in all network queues)(b) Peak and Average Power Constraints satisfied at Clients

(c)

Define: g*(t) = Optimal Utility Subject to Instantaneous Capacity Region

Instantaneous Capacity Region (t1)

Instantaneousutility-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.

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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 delayincrease (at “new equilibrium”), but which is independent of mobilitytimescales.

10 Mesh clients, 21 Mesh Routers in a cell-partitioned network

Simulation Experiment 1Communication pairs:0 1, 2 3, …, 8 9

• 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

Effectiveness of Combined Diff. Backlog -Shortest Path Metric

Simulation Experiment 3

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