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!
Network Model --- The General Picture
lij
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:
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
Network Model --- The General Picture
own
other
“Data Pumping Capabilities”:
(mij(t)) = C(I(t), S(t))
3 Layers:
1) Flow Control (Transport)
2) Routing (Network)
3) Resource Alloc./Sched. (MAC/PHY)
Control Action
(Resource
Allocation/Power)
Channel
State
Matrix
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
1
2
8
7
0
4
6
3
9
5
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 t
Assume: S(t) is conditionally i.i.d. given T(t):
pS(T) = Pr[S(t) = S | T(t)=T ]
The Instantaneous Capacity Region:
Instantaneous Capacity
Region
1
2
8
7
0
4
6
3
9
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))
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 ]
The Instantaneous Capacity Region:
Instantaneous Capacity
Region
1
2
8
7
4
0
6
3
9
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))
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 ]
The Instantaneous Capacity Region:
Instantaneous Capacity
Region
1
2
8
7
4
0
6
3
9
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))
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 ]
The Instantaneous Capacity Region:
Instantaneous Capacity
Region
1
2
8
7
0
4
6
3
9
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))
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 ]
The Instantaneous Capacity Region:
Instantaneous Capacity
Region
2
1
8
7
0
4
6
3
5
9
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))
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 ]
The Instantaneous Capacity Region:
Instantaneous Capacity
Region
2
1
8
7
0
6
4
3
5
9
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))
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 ]
The Instantaneous Capacity Region:
Instantaneous Capacity
Region
2
1
8
7
0
4
3
6
9
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))
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 process T(t).
-Use *Lyapunov Network Optimization
-Algorithm Continuously Adapts
T2
T1
T3
*[Tassiulas, Ephremides 1992]
*[Georgiadis, Neely, Tassiulas F&T 2006]
*[Neely, Modiano, 2003, 2005]
}
(Backpressure, MWM)
(Stochastic Network
Optimization)
Algorithm: (CLC-Mesh)
1) Utility-Based Distributed Flow Control for Stochastic Nets
x = thruput
-gi(x) = concave utility (ex: gi(x) = log(1 + x))
-Flow Control Parameter V affects
utility optimization / max buffer size tradeoff
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 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:
(a) Backlog: Ui(t) <= hV 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 L(t1)
Instantaneous Capacity
Region L(t2)
Instantaneous
utility-optimal point
e
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 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
0
Communication pairs:
0
1, 2
3, …, 8
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.
9
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)