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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

(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 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…


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!


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


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


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


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 ]


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 ]


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 ]


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 ]


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 ]


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 ]


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 ]


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 ]


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)


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]


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)


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.


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.


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


Simulation Experiment 3

Effectiveness of Combined Diff. Backlog -Shortest Path Metric


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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