Efficient Resource Allocation for Wireless Multicast

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Efficient Resource Allocation for Wireless
Multicast

• De-Nian Yang, Member, IEEE
• Ming-Syan Chen, Fellow, IEEE
• IEEE Transactions on Mobile Computing, April 2008
• speaker Yu-Hsun Chen

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Outline

• Introduction
• Problem Description
• Design of LAGRANGE Algorithm
• Protocol Design
• Experimental studies
• Conclusion

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Introduction 1

• There are a large variety of wireless
  technologies in wireless and mobile
  communications
• 3G cellulars, satellite, Wi-Fi, and Bluetooth
• The heterogeneous wireless networks combine
  various wireless networks
• Users in the heterogeneous wireless networks are
  usually covered by more than one cell to avoid
  connection drop and service disruption

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Introduction 2

• Multicast is an efficient way for one-to-many and
  many-to-many communications
• Current IP multicast routing protocol adopt the
  shortest path trees for data delivery
• The path from the root of the shortest path tree
  to each member must be the shortest path in the
  wired networks
• The routing of the shortest path is fixed
• The bandwidth consumption will not be able to
  reduced

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Introduction 3

• The shortest path tree in the heterogeneous
  wireless networks consists of two parts
• The cell and the wireless technology
• The wired links
• The routing of the shortest path tree is more
  flexible
• To reduce the bandwidth consumption
• Change the routing of the shortest path tree
• ? select different cells and wireless
  technologies for the mobile hosts

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Introduction 4
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Introduction 5

• Related issues
• Efficient mechanisms to provide seamless handover
  between different networks
• Protocol design, reliable multicast, and other
  practical issues for homogeneous wireless
  networks
• Finding a low-cost multicast tree
• Resource allocation among heterogeneous wireless
  networks has not been addressed

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Introduction 6

• Formulate the selection of the cell and the
  wireless technology for each mobile host as an
  optimization problem
• Cell and Technology Selection Problem (CTSP)
• Minimize the total bandwidth cost of the shortest
  path tree
• The designed mechanism
• Integer Linear Programming (ILP) formulation
• Distributed algorithm
• Network protocol

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Introduction 7

• Contributions of this paper
• Reduce the number of cells used in the shortest
  path tree
• The designed mechanism is flexible
• The designed mechanism is transparent to the IP
  multicast
• Support dynamic group membership

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Outline

• Introduction
• Problem Description
• Design of LAGRANGE Algorithm
• Protocol Design
• Experimental studies
• Conclusion

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Problem Description

• In the heterogeneous wireless networks
• For multicast communication
• Select the cell and the wireless technology for
  each group member to minimize the total bandwidth
  cost of the shortest path tree

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Notations
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ILP 1

• Variables

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ILP 2

• Objective function for ILP formulation
• Constraints

Minimum bandwidth
Each mobile host selects one cell
A cell is used in the shortest path tree if it
is selected by any mobile host
A link is used in the shortest path tree if it
is on the path from any selected cell to the
root of the tree
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ILP 3

• Minimum Set Cover problem is a special case of
  the CTSP problem
• Select the sets with the minimum total cost such
  that every element is covered by at least one
  selected set
• Given Main set elements 1,2,3,4,5,6,7
• subset 1 1,5,6 subset 2 1,2,4 subset 3
  2,3,4
• subset 4 3,7
• Minimum Set Cover contains the subsets 1,3,4
• CTSP is NP-hard

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Outline

• Introduction
• Problem Description
• Design of LAGRANGE Algorithm
• Protocol Design
• Experimental studies
• Conclusion

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Design of LAGRANGE Algorithm 1

• Advantages
• Can be implemented in a distributed manner
• Iteratively reduce the total bandwidth cost
• Provide a lower bound on the total bandwidth cost
  of the optimal solution to the CTSP
• The algorithm relaxes a constraint of ILP
• CTSP ? Lagrangean Relaxation Problem (LRP)

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Design of LAGRANGE Algorithm 2

• Solving steps
• Transfer CTSP into the LRP
• Decompose the LRP into multiple subproblems and
  solve each subproblem respectively
• Select the cell for each member according to the
  solutions
• Reduce the total bandwidth cost of the shortest
  path tree by iteratively updating the cost of
  each cell for each mobile host

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Decomposing and Solving the LRP 1

• Relax the second constraint ( ) in
  the ILP
• New objective function
• Lagrange multiplier the cost of cell c
  for mobile host m
• Constraints

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Decomposing and Solving the LRP 2

• Properties
• For any feasible solution to the LRP that
  contradicts the relaxed constraints (
  ), the objective value is larger
• Any feasible solution to CTSP is a feasible
  solution to the LRP
• When adopting the optimal solution to CTSP, the
  objective value of LRP the objective value
  of CTSP
• The objective value of the optimal solution to
  the LRP provides a lower bound to CTSP

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Subproblem 1

• Objective function of the subproblem 1
• Constraint
• The runtime is
• The cost for cell c is stored in each
  mobile host m

Find the cell with the minimum cost for each
mobile host m
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Subproblem 2 1

• Objective function of the subproblem 2
• Constraint

Minimize the net cost of all selected Cells in
the shortest path tree
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Subproblem 2 2

• To find the minimum net cost of the whole
  shortest path tree, we consider each link in the
  bottom-up manner
• the minimum net cost of the subtree that
  includes link and the subtree rooted at v

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Subproblem 2 3

• Theorem. The minimum net cost of the shortest
  path tree spanning all candidate cells can be
  obtained in time
• Proof.

net cost
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Subproblem 2 4

• All cells in the subtree corresponding to a link
  are not selected if net cost is not
  negative
• Each candidate cell c is selected in the second
  subproblem if the net cost of every link
  in the shortest path from c to the root of
  the tree is negative

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Finding and Improving the Solution to the CTSP 1

• The selected cells may not be feasible to CTSP
• Each mobile host is not guaranteed to be covered
  by a cell that is selected in the second
  subproblem
• Each member m in the LAGRANGE algorithm selects
  the cell c according to the cost in the
  first subproblem
• Adjust the cost iteratively with the subgradient
  algorithm and the solutions to the two
  subproblems of the LRP
• the objective function of the LRP
• The subgradient of the LRP

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Finding and Improving the Solution to the CTSP 2

• The subgradient indicates the direction of
  adjusting to find the better feasible
  solution to CTSP
• increase
• decrease
• The second subproblem tends to
• Select the cells cover more mobile hosts to save
  wireless bandwidth
• Select the cells such that the shortest path from
  the cells to the root share more common wireline
  links

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Details of the algorithm 1
assign a unit cost to each cell for each member
find the solution to the first subproblem
every cell is selected in the first subproblem
initial topology
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Details of the algorithm 2
find the solution to the second subproblem
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Details of the algorithm 3
1(-1)0
no cell is selected in the second subproblem
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Details of the algorithm 4
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Details of the algorithm 5
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Details of the algorithm 6
H3 handovers from C4 to C2 H5 moves out C4 H7
leaves the multicast group
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Details of the algorithm 7
adjustment after the mobility
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Outline

• Introduction
• Problem Description
• Design of LAGRANGE Algorithm
• Protocol Design
• Experimental studies
• Conclusion

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Protocol Design

• A distributed protocol based on the LAGRANGE
  algorithm
• Data tree the shortest path tree for data
  delivery
• Control tree to solve the second subproblem in a
  distributed manner
• Initially the control tree spans every candidate
  cell
• Incrementally prune the control tree to reduce
  the protocol overhead
• Each router and base station in the control tree
  maintains a node agent and cell agent

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State

• Each node agent stores the following states
• Multicast group address
• The address of the parent node agent in the
  control tree
• The bandwidth cost of the link with the parent
  node agent
• The address of the child agent and a Join timer
• Each cell agent stores the following states
• The bandwidth cost of the cell
• Control Flag (whether the cell is selected)
• Data Flag (whether the base station is in the
  data tree)
• The address of the mobile host
• The cost of the cell for the mobile host
  (Lagrange multiplier)
• Join timer

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Control Messages

• Join
• Mobile hosts or node agents send Join to join the
  control tree
• Join_Ack
• Confirm the Join message
• Contain the Data Flag and the cost of the cell
  for the mobile host (sent by cell agent)
• Leave
• Sent by mobile hosts, cell agents, and node
  agents
• Request, Reply, and Inform
• Update the cost of each cell in a distributed
  manner

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Operations 1

• Join a multicast group
• Mobile host sends a Join message to the cell
  agent of each cell that covers the mobile host
• Handover to a new cell
• Mobile host sends a Join message to the new cell
  and a Leave message to the original cell
• Leave the multicast group
• Mobile host sends a Leave message to cell agent

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Operations 2

• Update the cost of each cell
• Root periodically sends a Request message
• Cell agent first calculates the net cost ? Set
  Control Flag ? send Reply message
• Node agent first calculates the net cost ?
• send Reply message to parent node agent
• If net cost 0, send Inform
• message to child node agent

Inform
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Operations 3

• Prune the control tree
• Cell agent or node agent obtains a zero net cost
  for a period of time
• A node agent leaves the control tree if it
  receives a Leave message from every child agent

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Outline

• Introduction
• Problem Description
• Design of LAGRANGE Algorithm
• Protocol Design
• Experimental studies
• Conclusion

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Parameters and Metrics

• Parameters
• Group size number of mobile hosts in a multicast
  group
• Transmission range of a base station
• Bandwidth cost of each link and cell
• Metrics
• Total bandwidth cost of the data tree and the
  control tree
• Number of links and cells in the data tree and
  the control tree

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Results for Small Wireless Networks

• 25 km 25 km, 36 hexagon cells

Simulation results of small wireless
networks. (a) total bandwidth cost. (b) number of
cells in the tree.
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Results for Large Wireless Networks 1

• Georgia Tech Internetwork Topology Models, three
  wireless networks in a 50 km 50 km service area

Simulation results of large wireless networks (a)
original scenario (b) larger transmission range
The total bandwidth cost of a data tree
decreases as the transmission ranges
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Results for Large Wireless Networks 2
Simulation results of large wireless
networks. (c) (d) zero bandwidth cost for each
link.
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Transient Behavior of the LAGRANGE Algorithm
Transient behavior of the LAGRANGE algorithm with
different mobility (a) Probability 0 percent
(b) 0.1 percent (c) 0.5 percent (d) 2 percent
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Conclusion

• For reducing the total bandwidth cost of the IP
  multicast tree
• Model the selection of the cell as an
  optimization problem (ILP)
• Show the problem is NP-hard
• Design an algorithm based on Lagrangean
  relaxation
• Devise a distributed protocol
• Iteratively reduces the total bandwidth cost of
  the shortest path tree