Transcript Throughput Scaling in Wideband Sensory Relay Networks

The Value of State Awareness in A Changing World:
Tackling Dynamics in Wireless Networks and Smart Grids
Junshan Zhang
School of ECEE, Arizona State University
http://informationnet.asu.edu
1
A Growing Mobile World

“Broadband's take-up has repeatedly been jumpstarted by must-have
applications. Napster drove the shift from dialup to wired broadband. Now
Apple's iPhone is playing the same role in triggering explosive growth in the
wireless Web. Unless we miss our guess, this dynamic is about to rudely
change the subject from net neutrality to a shortage of wireless capacity to
meet enthusiastic consumer demand …”
[ “The Coming Mobile Meltdown,” Wall Street Journal, 10/14/2009]
2
State-of the-Art of Power Grid

“If Alexander Graham Bell were somehow transported to the 21st century,
he would not begin to recognize the components of modern telephony –
cell phones, texting, cell towers, PDAs, etc; while Thomas Edison, one of
the grid’s key early architects, would be totally familiar with the grid.''
[ “Final report on smart grid," Dept of Energy Report, Dec. 2008]
3
Smart Grid in the Making
The many meanings of “smart”:
 Generation: renewable energy integration …
 Transmission: enhanced situational awareness …
 Distribution: demand response, automatic control…
 End-user: smart metering, smart appliances…

Multi-scale dynamics in mobile communications
and in mega-scale power grids.
5
Mobile Commuications


Many signs of explosive growth of wireless traffic:
voice/email, web browsing, audio/video streaming
Unique challenges in wireless communications:

Channel fading occurs on multi-timescales;
Time-varying topology due to mobility;
Interference varies on multi-timescales;

……


6
Multi-scale Information Dynamics

Multi-scale network dynamics: channel-level, link-level, pathlevel, user-level …
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Multi-scale Power System Dynamics and
Operation Functions
8
Multi-scale Nature of Wind Uncertainty
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Part I: The Value of State Awareness for
Tackling Dynamics in Wireless Networks
Q) How can we design state-aware transmissions in multi-scale dynamics?
o Network/channel states are changing continuously;
o Sensing/probing is needed to estimate/track states for state-aware
network management.
State-aware scheduling: DOS (Distributed opportunistic scheduling)
Opportunistic
state-aware




DOS
DOS
DOS
DOS
under noiseless probing [Mobihoc 2007, IT 2009]
under noisy probing: reactive vs. proactive [ToN 2010]
for cooperative networking [JSAC 2011]
under delay constraint [Infocom 2010]
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System Model

Model: contention-based ad-hoc network
A
D
E
C
F
B

Two stages of probing: I) contention; II) channel estimation

Challenges: Links have no knowledge of others’ states; even their


own states are unknown before probing.
 Q) Which link to schedule based on local information, and how?
Approach: distributed exploitation and exploration
Focus: fundamental tradeoffs between probing and throughput gain.

Distributed Opportunistic scheduling under noiseless probing
(i.e., CSMA-type contention in Stage I and perfect channel
estimation in Stage II)
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I) Noiseless Probing
Suppose after contention, the successful link has
poor channel, and has two options:

Continue data transmission;

Or, alternatively, let this link give up this
opportunity, and all links re-contend.


Intuition: At additional cost, further probing can
lead to data transmission with better channel
conditions.
In this way, multiuser diversity and time
diversity can be exploited in a distributed and
opportunistic manner.
D
A
E
C
B
F
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Tradeoff between Probing and Throughput Gain
Channel coherence
time
Probing time



s(n) denote the successful link in n-th round of probing.
Clearly, there is a tradeoff between throughput gain from better
channel conditions and the cost for further probing.
Using optimal stopping theory, we characterize this tradeoff for
distributed scheduling.
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Technical Conditions
Throughout Maximization via Maximizing Rate of Return
Threshold Structure of Optimal Scheduling Policy
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
Distributed Opportunistic scheduling under noisy probing:
Reactive versus Proactive Scheduling
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II) Noisy Probing:
Probing with Imperfect Rate Estimation
•
•
•
In the above, channel state information (CSI) is assumed to be
perfectly known after probing.
In practical scenarios, channel conditions are often estimated using
noisy observations, and CSI is imperfect.
Consider channel-aware distributed scheduling with noisy rate
estimation.
MMSE Estimation of the channel rate:
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Noisy Probing




Major differences between noisy/perfect probing:

The rate, after probing, is not perfectly known.

The stopping rule in noisy case is defined over filtration generated by
noisy observations
Can show that structure of optimal scheduling remains same, except that
the rate is replaced with its conditional expectation.
Reactive strategy: (linear) rate backoff
Proactive strategy: next
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Proactive Strategy with Noisy Probing



Further probing may be helpful to improve the quality
of rate estimation and hence the throughput.
Particularly interested in the wideband low SNR
regime, i.e.,
and
Potential
significant improvement of rate estimation due to
further probing in wideband regime. [Verdu’ IT2002]
Trade-off between enhanced rate gain due to
improved estimate and further probing cost.
Proactive approach: DOS with two-level probing;
Underlying theory: optimal stopping theory with incomplete information
[Stadje’ 97].
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Proactive Strategy: DOS with Two-Level Probing
Q: Is it worthwhile for the successful link to “refine” rate estimation,
with an additional cost? How much can we bargain?
- Gain: more accurate rate estimate;
- Cost: time overhead
The answer is yes or no; there is a grey area where additional
probing will help.
Channel condition is good
Channel condition is bad
refinement is not helpful,
defer and re-contend
?
refinement is relatively
meager, transmit immediately
at the current rate
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DOS with Two-Level Probing:
Structural results
Optimality Conditions:
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DOS with Two-Level Probing:
Strategy A
C
I
S(n)
1st level probing
?
Possibilities
Rate R(1)
R(1)
Give up and
re-contend
C I
2nd Level Probing
Refined rate R(2)
Transmit at R(1)
?
Possibilities
T
R(2)
Give up and re-contend
Transmit at R(2)
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DOS with Two-Level Probing:
Strategy B
C
I
S(n)
?
1-st level probing
Rate R(1)
Possibilities
Give up and
re-contend
Transmit at R(1)
T
Details: [Infocom’09]
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Numerical Example
- performance gap is
significant in the low-SNR
regime.
- As
increases, the
performance gap narrows
down
-The overhead due to extra
probing offsets its gain in
mitigating estimation errors
- The “gray area” collapses.
As a result, Strategy A
degenerates to Strategy B
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
Distributed scheduling for cooperative networking
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State Awareness & Cooperative Networking


Our initial steps started in 2001/2002 and studied 1) Capacity bounds of
MIMO relay channel; 2) Power allocation in wireless relay networks; 3) Scaling
laws of Wideband sensory relay networks
Two of our IT papers received about 800 citations: B. Wang, JZ & Host
Madsen (IT 05); Host-Madsen & JZ (IT 05). [Google scholar]
• High traffic volume
• Need cooperative
networking
III) Distributed Scheduling for Cooperative Networking:
To Relay or Not to Relay?
collision! re-contend
no collision : to relay ?
no collision and ‘good’
channel: transmit
no collision but ‘bad’ channel :
re-contend
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DOS with Dedicated Relay Node
trade-off: higher rate vs. overhead for probing relay and
establishing coopertive relaying
re-contend
re-contend
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DOS without Dedicated Relay Node
...
...
tradeoff: (node diversity + higher rate) vs. (probing
overhead + cost of relay)
re-contend
re-contend
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
Distributed scheduling under delay constraints
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DOS under Network-wide Delay Constraint
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Relaxation and Duality
34
From Primal to Dual to Dual’s Dual
“Hidden convexity”
(Lyapunov Theorem)
Details: [Infocom’10]
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Part II: The Value of Situation Awareness:
Tackling Dynamics in Smart Grid



Transmission: PMU data processing for dynamic contingency
analysis [He-JZ-Vittal (preprint)]
CPS inter-networking architecture: robustness vs. allocation of
interconnecting edges [Yagan-Qian-JZ-Cochran 2011]
Wind generation integration: modeling and fortcast of wind
generation; multi-scale scheduling and dispatch
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Situation Awareness in Smart Grid



Multi-scale dynamics of power grid:

Supply uncertainty: deep penetration of renewable energy (wind, solar …)

Demand uncertainty: load variation, distributed generations …
Traditional SCADA systems

Measurements taken every few seconds; state estimation every few mins.

Lack “real-time” situational awareness; may fail to prevent large-scale
blackouts (e.g., 2003 northeast blackout)
Emerging wide-area monitoring system (WAMS)

PMU sampling frequency (30~60/s), synchronized by GPS time-stamps

Useful for state estimation, fault diagnosis, and contingency analysis
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Synchronized Measurements of Phasor Measurement Units
Location 2
Location 1
• Synchronizing pulses obtained
from GPS satellites.
• Phase angular difference between
the two can be determined.
Example: June 2005 Houston Blackout
Phasor Angle Jumping and Frequency Spikes
Frequency “spikes”
as Phase Angle
jumps to 76⁰
Normal Phase angle 30⁰
5:10 PM
Diff
120⁰
Frequency Collapse
5:16 PM (T-0 min)
Frequency becomes
Unstable and Phase
Angle difference
Exceeds 120⁰
Contingency Analysis
Contingency analysis: “What-if” a hypothetical accidental event occurs, e.g.,
outage of lines or generators; determines if state trajectories are in insecure
regions, and if yes, take preventive/corrective actions.

Two important approaches (both assuming a given set of contingencies)

Nonlinear system analysis [Chiang’95, Chiang’99]

Decision tree [Sun-Vittal’07,Diao-Vittal’09]
Dynamic contingency analysis:

Goal: Incorporate
new contingencies and adapt to new
measurements; distributed implementation.

Challenges:


Large contingency list; thousands of states and many more data;
Exact analysis is non-attainable since large-scale power systems
are highly nonlinear; numerical study is challenging due to
computational burden.
Decision Tree for Contingency Analysis


Decision tree: a tree structure that maps observation X  ( X1, X 2 , X p )
to a predicted value Yˆ
 Yˆ is binary for classification (continuous for regression tree )

At each internal node, compare an attribute X i to a threshold, and
generate two branches

Each binary string points to a region and a predicted value per leaf
Decision tree learning: Select the attribute and its threshold for each internal
node, so as to minimize prediction error, e.g., for classification tree using Gini
Index ,
1

 1 1


1
1
1
min min 
1
1

1

1
1

1








Yn  m
Yn  m
Yn  m
Yn m 
Xi
ti
N
N
N
N
m 0
L Xn AL
L Xn AL
R Xn AR

 m 0 R Xn AR


For regression tree:
1
min min
Xi
ti
NL

Xn AL
Yn  YˆL

2
1

NR

Xn AR
Yn  YˆR
where, A L is the region corresponding to left branch of A,
number of samples in A L , and Yˆ  N1  Y .
L
L Xn AL
n
NL

2
is
Example: DT Learning for Contingency Analysis

A classification tree trained with
given historic data to find secure
(insecure) regions in attribute space

Learned DT applied to real-time
PMU data for contingency
analysis
Pre-processing and Post-processing for
DT-based Dynamic Contingency Analysis



In existing approaches:
 DT is rebuilt to incorporate new contingencies; high complexity for
updating a DT; centralized.
 DT with a large number of correlated attributes is prone to overfitting.
Treelets based preprocessing [Lee08]:
Data mining & learning tools are used for dimension reduction to transform
attributes into a lower dimensional space; new attributes as linear
combinations of original ones
Multi-classifier boosting (MCBoost) as post-processing [Kim08]:
 Each classifier corresponds to a subset of contingencies.
 Each classifier is obtained by boosting a few simple DTs, easy to update
in online applications.
 Combine multiple classifiers to obtain final decision.
Examples: Boosting simple DTs


Use the SRP database
Single DT: 35 internal nodes, largest simple DT: 7 internal nodes;
complexity is much lower
Examples: Incorporation of New Contingency
Convergence performance: the 6th contingency (CT183) is
incorporated into a 5-classifier analyzer, via updates with
incremental observations for CT183
.
Robust CPS inter-networking architecture:
Allocating Interconnecting Links against
Cascading Failures
47
CPS - Two Interacting Networks
cross-networks support
physical system
(e.g. power grid)
cyber network
(e.g. Internet)
Networked systems: modern world consists of an intricate web of
Interconnected infrastructure systems.
Interdependence: Operation of one network depends heavily on the
functioning of the other network
Vulnerability to cascading failures: node failures in one network may
trigger a cascade of failures in both networks, and overall damage on
cyber-physical systems can be catastrophic since the affected area is
much greater than that affected in a single network alone.
48
Robust Inter-networking Architecture:
An Interconnecting Edge Allocation View
Q) How to improve robustness against cascading failures,
under constraint of average inter-edges per node
 Allocation without intra-degree information
 Random vs. Uniform allocation
 Unidirectional edges vs. bi-directional edges
 Allocation with intra-degree information
 Preferential allocation
 Ranking based allocation
 Approach: compute ultimate fractions of functioning giant
components, and critical threshold pc; the lower pc the
more robust
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Robustness of Different Allocation Strategies
1
random & uni-directional
random & bi-directional
uniform & uni-directional
uniform & bi-directional
0.9
0.8
Lower pc indicates the
higher robustness
Pc
0.7
0.6
0.5
0.4
0.3
0.2
2
3
4
5
6
k
7
8
9
10
 Two Erdos-Renyi networks with average intra-degree fixed at 4
 The pc varies over different average inter-degree k
 As expected, the uniform & bi-directional allocation leads to the lowest pc
under various conditions
2015/7/17
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Allocation with Intra-degree Information
 Preferential allocation
 Intuition: Important nodes have more support
 Probabilistically allocate the inter-degree proportional to intradegree
 Ranking based allocation
 Rank nodes based on their intra-degrees; and partition nodes into groups
 Deterministically allocate more inter-edges to groups with higher intradegrees
 Analysis is fairly difficult; evaluate the performance by simulations.
 By exploiting intra-degree information, both strategies outperform the
allocations without topology information
2015/7/17
55
Conclusions





Multi-scale dynamics is ubiquitous in complex networks, e.g., in mobile
communications and in mega-scale power grids.
Tackling dynamics in mobile communications: distributed opportunistic
scheduling for a variety of models.
Tackling dynamics in smart grids: PMU data processing for contingency
analysis, and robust CPS architecture design.
(We have also looked into fault diagnosis based on Markov random field
model of PMU data; multi-scale scheduling and control for wind generation
integration.)
Many open research problems need “marriage” of expertise in
power system, renewable energy, communication, control,
computing, …
Need multi-disciplinary research!
56