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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
0
1
2
3
4
5
6
78
9
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:
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
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
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.
0 1
2
3
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5
6
78
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 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