DYNAMIC POWER ALLOCATION AND ROUTING FOR TIMEVARYING WIRELESS NETWORKS

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DYNAMIC POWER ALLOCATION AND ROUTING FOR
TIME-VARYING WIRELESS NETWORKS

• Michael J. Neely, Eytan Modiano and Charles
  E.Rohrs
• Presented by
• Ruogu Li
• Department of Electrical and Computer Engineering
• The Ohio State University

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CONTENTS

• Overview
• System Model and Assumptions
• Network Capacity Region
• Centralized DRPC Policy
• Proof of stability
• Enhanced DRPC Policy
• Decentralized DRPC Policy
• Conclusion
• Future work

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OVERVIEW

• We consider dynamic routing and power allocation
  for a wireless network with time-varying
  channels
• The network consists of power constrained nodes
• Transmission rates over the links are determined
  by allocated power
• Packets randomly enter the system at each node
  and wait in output queues to be transmitted to
  their destinations
• We developed a joint routing and power allocating
  policy (DRPC) that stabilizes the system and
  provides bounded average delay.

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SYSTEM MODEL AND ASSUMPTIONS

• A wireless network with nodes
• Time is slotted, channel state stays the same in
  one slot
• Multiple data stream randomly enter the
  system with source and destination
• Each node can transmit data over multiple links
  simultaneously
• Power is assigned to links
• at each node.

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SYSTEM MODEL AND ASSUMPTIONS

• Power constraint at each node
• Transmission rate on each link is determined by a
  rate-power curve , where
  is the power matrix, and is the channel
  state matrix
• Channel state represents,
• for example, attenuation
• and/or noise levels it is
• known to the controller
• at the beginning of each
• time slot

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SYSTEM MODEL AND ASSUMPTIONS

• The power curve is assumed to
  be upper semi-continuous in the power matrix
  for all states
• The power matrix , where is the
  set of acceptable power allocations.

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SYSTEM MODEL AND ASSUMPTIONS

• Each node queues data according to their
  destinations
• We classify all data flowing through the network
  as belonging to a particular commodity
  , representing the destination node for
  the data
• Define as the rate
• offered to commodity
• traffic along link

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SYSTEM MODEL AND ASSUMPTIONS

• The input process of the network are
  stationary and ergodic with rates .
• represents the incoming rate at node of
  commodity . The matrix is the
  corresponding matrix with diagonal entries equal
  to zero.
• Further assume that the second moment of
  is bounded every time slot by some finite
  maximum value regardless of past history.

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SYSTEM MODEL AND ASSUMPTIONS

• The control decision variables are
• Power allocation, choose such that
  
• Routing/Scheduling, choose such that
• The backlog of bits in node destined for node
  c is represent by (the queue length).

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NETWORK CAPACITY REGION

• A queueing system is said to be stable if the
  queue length does not blow up when time goes to
  infinity
• The network capacity region is the closure f
  the set of all rates matrices that can be
  stably supported over the network, considering
  all possible algorithms.

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NETWORK CAPACITY REGION

• Example
• The capacity region will be

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CENTRALIZED DRPC POLICY

• Dynamic Routing and Power Control (DRPC) Policy
• For all links , find commodity
  such that
• and define
• Power allocation choose a matrix
  such that
• Routing define transmission rate as follows
• , if and
• , otherwise

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CENTRALIZED DRPC POLICY

• It is inspired by the maximum differential
  backlog algorithms developed by Tassiulas and
  Ephremids
• An extension of the maximum differential backlog
  algorithm which maximize the throughput of a
  constrained network
• Thus DRPC Policy maximizes the throughput of the
  network.

Ref L. Tassiulas and A. Ephremids, Stability
properites of constrained queueing systems and
scheduling policies for maximum throughput in
multihop radio networks, IEEE trans. Autom.
Control, vol. 37, no.12, Dec 1992
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CENTRALIZED DRPC POLICY

• Stability of DRPC Policy
• Theorem Suppose an N-node wireless network has
  capacity region and rate matrix such
  that for some .
  Then, the above DPRC policy stabilize the system
  and guarantees bounded average congestion.
• Proof of Stability of DRPC Policy
• Basic idea prove the stability of the system
  using a Lyapunov function.
• A function is a Lyapunov
  candidate function if it is locally positive
  definite, i.e.
• The choice of the Lyapunov function is based on
  the problem.

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CENTRALIZED DRPC POLICY

• The proof in the paper is very complicated
• We consider a similar simpler case using the same
  approach
• Single base station sends out data to N users
• Data arrive at base station with rate
  , same assumption for the arriving
  process

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CENTRALIZED DRPC POLICY

• Constraint for the base station
  , power constraint with linear rate power
  curve, denote the set of feasible by
  
• Control variable choose
• The arrive rates satisfy ,
• where is the
  capacity region
• Policy choose

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CENTRALIZED DRPC POLICY

• Queue evolution
• Choose the Lyapunov function
• Thus the Lyapunov drift is given by

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CENTRALIZED DRPC POLICY

• Notice that
• Thus
• From the assumption of , we
  know that

second moment,
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CENTRALIZED DRPC POLICY

• Thus we get
• which is an simplified version of (21) in the
  paper
• Sum over 1 through T-1 and take
  expectation on both sides, we get
• From the non negativity of the Lyapunov function,

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CENTRALIZED DRPC POLICY

• Taking the limit of the above inequality
• Thus we proved the stability of the system under
  our policy
• Using Littles Law we can get the bound on delay
• The proof in the paper is an extension of this
  simple case.

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ENHANCED DRPC POLICY

• Potential problem of DRPC Policy
• When the network is lightly loaded, very little
  information is contained in the backlog values
• Packets may wander in the network, resulting long
  delays
• Solution
• Adding a restricted set of desirable routes
• But restricting the routes may be harmful in time
  varying channels
• Enhanced DRPC Algorithm is introduced to solve
  this problem.

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ENHANCED DRPC POLICY

• Basic idea implementing a bias in the DRPC
  Policy so that in low loading situations, nodes
  are inclined to route packets in the direction of
  their destinations
• Define
• and define as the maximizer of
  
• Power allocation and routing is done as before

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ENHANCED DRPC POLICY

• The parameters can be chosen as scaled hop
  count estimates between nodes and , so that,
  in the absence of backlog information, data is
  routed to reduce the remaining distance to the
  destination
• The values are any weights for prioritizing
  commodity service in node
• It can be shown that this enhanced DRPC Policy
  can stabilize the system for any and
  .

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DECENTRALIZED DRPC POLICY

• The DRPC Policy is a centralized control
• Hard to implement in reality
• The authors provided a simple decentralized
  approximation without proof
• Nodes have current neighbors
• The current neighbors of a node is defined as
  the set of the nodes to which node can
  currently transmit and receive.

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DECENTRALIZED DRPC POLICY

• The Decentralized DRPC Policy
• At the beginning of each time slot, nodes
  randomly decide to transmit with probability .
  All transmitting nodes send a control signal of
  power where is globally known
• Define as the set of all transmitting nodes.
  Each node measures its total resulting
  interference
  and send this quantity over a control channel to
  all neighbors
• Each transmitting user decides to transmit
  using full power to the single neighbor who
  maximizes

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CONCLUSION

• We have formulated a general power allocation
  problem for a multinode wireless network with
  time-varying channels and adaptive transmission
  rates
• The network capacity region was established
• A DRPC algorithm is developed and shown to
  stabilize the network whenever the arrival rate
  matrix is within the capacity region.

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FUTURE WORK

• The DRPC policy is based on maximum backlog
  differential algorithm which tries to maximize
  the throughput of the network, but other network
  control metrics such as minimizing the delay are
  not considered.
• In the policy, we need to find
• which is not a trivial problem. A
  straightforward exhaustive search may not work
  for large networks. Many works have been done on
  this, for example, using greedy algorithm.

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Thank you