GAGAN RAJ GUPTA, PURDUE

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Delay-Efficient Control of Wireless Networks

• GAGAN RAJ GUPTA, PURDUE
• NESS B. SHROFF, OSU

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Thesis WorkControl Policies for Networks

• Wireless networks (Ad-hoc , Mesh networks etc.)
• Link Scheduling
• Flow Scheduling
• Congestion Control
• Delay-efficient scheduling for IQ switches.
• Results apply to constrained queuing systems.

Input-Queued Switch
Ad-hoc wireless network
Wireless mesh network
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Motivation

• Maximizing throughput while keeping queues
  stable.
• Well understood (Tassiulas and Ephremedes.)
• Stability is a first-order property
• Very-long time-scale allocation
• We need to understand delay performance!
• Provide QoS for applications.
• Eg. Online meetings talk, share data.
• Network dimensioning
• How to choose capacity of links, buffer sizes
  etc.?
• Networked Control with sensors.
• Data should reach in time to generate proper
  feedback.

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Challenges in delay analysis

• Complex network interactions
• Correlations within the flow
• Link interference
• Statistical multiplexing
• Flow scheduling
• Varying channel states
• Heterogeneous links
• General arrival process

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Limited Work on Delay Analysis in Wireless
Networks

• Fluid Limits
• Stability Dai and Prabhakar00
• Heavy traffic Stolyar04
• Difficult to compare policies
• Does not yield estimates of delay (expectation,
  distribution)
• Large Deviations analysis of buffer overflows
• Single-hop networks Venkatramanan and Lin07
• Difficult to estimate actual overflow
  probability.
• Method of Lyapunov Drifts
• Upper bounds on delay performance of MWM
  Neely07
• Improved bounds Gupta and Shroff08
• GMWM better than any Randomized Scheduling policy
• Doesnt capture statistical multiplexing caused
  due to interference

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System Model

• STANDARD MODEL
• Multiple s-d pairs
• Fixed Routes
• Set based link interference
• Eg K-hop interference
• All links within K hops
• Fixed size packets
• Heterogeneous links
• Channel Variability
• ON Full Capacity
• OFF Zero

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Scheduled Link
Feasible Schedule
Interference Set
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System Model

• STANDARD MODEL
• Set based link interference
• Eg K-hop interference
• All links within K hops
• Fixed size packets
• Heterogeneous links
• Channel Variability
• ON Full Capacity
• OFF Zero

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Fundamental Bounds on Delay Performance

• A novel methodology to establish fundamental
  lower bound on delay using the resource
  constraints
• Algorithm to compute bottlenecks in the system.
• Analyze the queuing upstream of these bottlenecks
  
• Reduction to a single queue system.
• Most of the queuing takes place upstream of these
  bottlenecks.
• Use Littles law to bound delays.

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(K, X)- Bottleneck

• Definition A set of links X such that no more
  than K of them can be scheduled simultaneously.
• Examples

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(1, X)-Bottlenecks
(2, X)-Bottleneck
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Queue Grouping
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Reduction
Server ON when at least one of the links is ON
(11)AI(t)
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(1, X)-Bottleneck
Q(t)
( 1)AII(t)
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AI(t)
Single server queue
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Stochastic Coupling
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• No assumption on the arrival process!

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Server ON when at least one of the links is ON
AII(t)
AIII(t)
2AIII(t)
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Summary of the Reduction Technique

• Stochastic Bound on the queues upstream of a
  (K,X)-bottleneck.
• Captures the essential elements of a wireless
  network
• Interference constraints (Bottlenecks)
• Statistical Multiplexing (Single server with
  multiple flows)
• Channel variability (Server ON/OFF process)
• Allows for general arrival processes.
• Advancement from product-form networks.
• Technique applicable also to wired networks.
• Obtain lower bounds on expected packet delay
• Expectation is a linear operator
• Single server queue can be analyzed for a large
  class of arrival processes

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Simulation Results (Tandem-1)
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Bottleneck
Min. Delay of hops

• 9 node tandem network with unit capacity links
• Node-exclusive (1-hop) interference model
• Heavy-tailed (Zipf) traffic
• Optimal Policy derived by
• Tassiulas Tass93
• Lower Bound coincides numerically
• with the optimal policy.
• Back-Pressure policy (with small
• alpha) comes close to optimal.

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Simulation Results (Tandem-2)
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Bottleneck
Min Delay of hops

• 9 node tandem network with different capacity
  links
• 2-hop interference model
• Heavy-tailed (Zipf) traffic
• Optimal Policy not known!
• Back-Pressure performs poorly.
• Designed a new policy that is
• close to lower bound and hence
• nearly optimal!

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Representative topologies
Dumbbell
Tree
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Representative topologies
8-Cycle

• Shows importance of (K,X)-Bottlenecks for Kgt1
• Both types of bottlenecks are important for
  analysis
• Technique general enough to handle multiple flows

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Simulations (Multiple bottlenecks)

• Tree Network
• Single-hop traffic
• Random Load
• Heterogeneous links
• Varying channel states
• Bernoulli (ON/OFF)
• 2-hop interference
• Tighter Upper Bound

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Flow crossing multiple bottlenecks?
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D(t)
D(t)
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AI(t)
2AIII(t)
III
AII(t)
AIII(t)
Control Policy Inject packets D(t) to minimize
delay. The optimal policy for Tandem queue
injects packets when the corresponding queue is
empty.
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Switch Scheduling (with S. Sanghavi)

• Node (Bottleneck) based Scheduling
• Schedule enough heavy nodes.
• Evacuation Time
• Time to drain out the packets from the system.
• Characterize new class of online policies that
  are
• Evacuation Time Optimal (Given any initial
  configuration.)
• Throughput Optimal (For any admissible load.)
• Complexity smaller than MWM (for switches)
• Empirical delay performance slightly better than
  MWM.
• Novel proof techniques!

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Thanks!

• Why is the delay performance hard to analyze?
• Reduction technique Lower Bounds
• Holds for a large class of arrival processes
• Capture the essential elements of the wireless
  network
• Accurate for tandem networks
• Design control policies that are delay-efficient
• Simpler and efficient schedulers for switches

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References

• Tassiulas and Ephremedes92 Stability
  properties of constrained
• queueing systems and scheduling policies for
  maximum throughput in multihop radio networks.
  IEEE Trans. Aut. Contr
• Dai and Prabhakar00 The throughput of data
  switches with and without speedup, INFOCOM.
• Stolyar04 Maxweight scheduling in a
  generalized switch State space collapse and
  workload minimization in heavy traffic. Annals of
  Applied
• Probability.
• Venkataramanan and Lin 07 Structural
  properties of ldp for queuelength based wireless
  scheduling algorithms, Allerton.
• Neely05, Neely06 Order optimal delay for
  opportunistic scheduling in multiuser wireless
  uplinks and downlinks, Allerton
• Gupta and Shroff08 Scheduling policies with
  queue length guarantees in resource constrained
  systems, SIGMETRICS
• Gupta and Shroff09a Delay Analysis for
  Multi-hop Wireless Networks, INFOCOM
• Gupta and Shroff09b Node Weighted Scheduling,
  SIGMETRICS

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MWM policy

• Given the weights on each link, compute the
  matching (non-interfering set of links) with
  maximum weight.

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Back-Pressure Policy (fixed routing)

• Has two components
• Flow scheduling
• For each link, choose the flow with maximum
  back-pressure.
• Back-pressure of link (i,j)
• Link scheduling
• With the above assignment of weights, schedule
  the Max Weight Matching.