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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/. ITA Workshop, San Diego, February 2007 To Appear in Ad Hoc Networks (Elsevier).

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Cross Layer Adaptive Control for Wireless Mesh Networks

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Cross layer adaptive control for wireless mesh networks

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/

ITA Workshop, San Diego, February 2007

To Appear in Ad Hoc Networks (Elsevier)

*This work was supported in part by one or more of the following:

NSF Digital Ocean , the DARPA IT-MANET Program


Cross layer adaptive control for wireless mesh networks

Cross Layer Networking

Network Layering

Timescale Decomposition

Transport

“Flow Control”

Flow/Session Arrival and

Departure Timescales

Network

“Routing”

Mobility Timescales

PHY/MAC

“Resource Allocation”

“Scheduling”

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 adaptive control for wireless mesh networks

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]


Cross layer adaptive control for wireless mesh networks

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!


Cross layer adaptive control for wireless mesh networks

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!


Cross layer adaptive control for wireless mesh networks

lij

Network Model --- The General Picture

Flow Control

Decision Rij(t)

own

other

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


Cross layer adaptive control for wireless mesh networks

Network Model --- The General Picture

own

other

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


Cross layer adaptive control for wireless mesh networks

Network Model --- The General Picture

own

other

“Data Pumping Capabilities”:

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

Control Action

(Resource

Allocation/Power)

Channel

State

Matrix

3 Layers:

Flow Control (Transport)

Routing (Network)

Resource Alloc./Sched. (MAC/PHY)

I(t) in I

*From: Resource Allocation and Cross-Layer Control in Wireless Networks by

Georgiadis, Neely, Tassiulas, NOW Foundations and Trends in Networking, 2006


Cross layer adaptive control for wireless mesh networks

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

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

1

2

8

7

4

0

6

3

5

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):

pS(T) = Pr[S(t) = S | T(t)=T ]


Cross layer adaptive control for wireless mesh networks

Instantaneous Capacity

Region

The Instantaneous Capacity Region:

1

2

8

7

4

0

6

3

5

L(t) = Instantaneous Capacity Region

= Ergodic Capacity Associated with a

network with fixed topology state T(t)

for all time (and i.i.d. channels pS(T))

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):

pS(T) = Pr[S(t) = S | T(t)=T ]


Cross layer adaptive control for wireless mesh networks

Instantaneous Capacity

Region

The Instantaneous Capacity Region:

1

2

8

7

4

0

6

3

5

L(t) = Instantaneous Capacity Region

= Ergodic Capacity Associated with a

network with fixed topology state T(t)

for all time (and i.i.d. channels pS(T))

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):

pS(T) = Pr[S(t) = S | T(t)=T ]


Cross layer adaptive control for wireless mesh networks

Instantaneous Capacity

Region

The Instantaneous Capacity Region:

1

2

8

7

4

0

6

3

5

L(t) = Instantaneous Capacity Region

= Ergodic Capacity Associated with a

network with fixed topology state T(t)

for all time (and i.i.d. channels pS(T))

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):

pS(T) = Pr[S(t) = S | T(t)=T ]


Cross layer adaptive control for wireless mesh networks

Instantaneous Capacity

Region

The Instantaneous Capacity Region:

1

2

8

7

4

0

6

3

5

L(t) = Instantaneous Capacity Region

= Ergodic Capacity Associated with a

network with fixed topology state T(t)

for all time (and i.i.d. channels pS(T))

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):

pS(T) = Pr[S(t) = S | T(t)=T ]


Cross layer adaptive control for wireless mesh networks

Instantaneous Capacity

Region

The Instantaneous Capacity Region:

2

1

8

7

0

6

4

3

5

L(t) = Instantaneous Capacity Region

= Ergodic Capacity Associated with a

network with fixed topology state T(t)

for all time (and i.i.d. channels pS(T))

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):

pS(T) = Pr[S(t) = S | T(t)=T ]


Cross layer adaptive control for wireless mesh networks

Instantaneous Capacity

Region

The Instantaneous Capacity Region:

2

1

8

7

0

6

4

3

5

L(t) = Instantaneous Capacity Region

= Ergodic Capacity Associated with a

network with fixed topology state T(t)

for all time (and i.i.d. channels pS(T))

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):

pS(T) = Pr[S(t) = S | T(t)=T ]


Cross layer adaptive control for wireless mesh networks

Instantaneous Capacity

Region

The Instantaneous Capacity Region:

2

1

8

7

0

4

3

6

5

L(t) = Instantaneous Capacity Region

= Ergodic Capacity Associated with a

network with fixed topology state T(t)

for all time (and i.i.d. channels pS(T))

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):

pS(T) = Pr[S(t) = S | T(t)=T ]


Cross layer adaptive control for wireless mesh networks

Results:

-Design a Cross-Layer Algorithm that optimizes

throughput-utility with delay that is independent of timescales

of mobility processT(t).

-Use *Lyapunov Network Optimization

-Algorithm Continuously Adapts

*[Tassiulas, Ephremides 1992] (Backpressure, MWM)

*[Georgiadis, Neely, Tassiulas F&T 2006]

*[Neely, Modiano, 2003, 2005]

T2

T1

T3

}

(Stochastic Network

Optimization)


Cross layer adaptive control for wireless mesh networks

Algorithm: (CLC-Mesh)

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

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 hV

(provides immediate avg. delay bound)

-Virtual Power Queues for Avg. Power Constraints [Neely 2005]


Cross layer adaptive control for wireless mesh networks

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

Instantaneous Capacity

Region L(t1)

Instantaneous Capacity

Region L(t2)

Instantaneous

utility-optimal point

Instantaneous

utility-optimal point

Theorem: Under CLC-Mesh with flow control parameter V, we have:

Backlog: Ui(t) <= hV for all time t (worst case buffer size in all network queues)

Peak and Average Power Constraints satisfied at Clients

(c)


Cross layer adaptive control for wireless mesh networks

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

Instantaneous Capacity

Region L(t1)

Instantaneous Capacity

Region L(t2)

Instantaneous

utility-optimal point

Instantaneous

utility-optimal point

e

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 e 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.


Cross layer adaptive control for wireless mesh networks

Simulation Experiment 1

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

Communication pairs:

01, 2 3, …, 89

0

1

2

8

7

4

6

3

5

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.


Cross layer adaptive control for wireless mesh networks

Simulation Experiment 2

Flow control using control parameter V

  • 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


Cross layer adaptive control for wireless mesh networks

Simulation Experiment 3

Effectiveness of Combined Diff. Backlog -Shortest Path Metric


Cross layer adaptive control for wireless mesh networks

Simulation Experiment 3

Effectiveness of Combined Diff. Backlog -Shortest Path Metric

Interpretation of this slide:

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)


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