ThroughputDelay Tradeoff in Wireless Networks

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Throughput-Delay Trade-off in Wireless Networks

• A. El Gamal, J. Mammen, B. Prabhakar, D. Shah
  
• EE360 Presentation
• Vahideh Hosseinikhah
• May 14th, 2004

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Outline

• Introduction to Wireless networks
• Previous Work
• Overview of main results
• T-D trade-off for fixed networks
• T-D trade-off for mobile networks
• Conclusion

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Wireless Networks

• There are n wireless nodes capable of
  transmitting and receiving from each other
• Topology is not completely known and is
  continuously changing in mobile networks
• Transmitting nodes create interference for other
  nodes
• Successful transmission requires low interference
• Questions
• How does the throughput of the network scale with
  n?
• How does the associated delay scale with n?
• What is the throughput-delay trade-off?

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Notations

• f(n) O(g(n)) means that there exists a constant
  c and integer N such that f(n) cg(n) for nN.
• f(n) T(g(n)) means that f(n) O(g(n)) and g(n)
  O(f(n))
• f(n) o(g(n)) means that limn?8f(n)/g(n) 0
• f(n) ?(g(n)) means that g(n) o(f(n))
• whp means with probability 1-1/n
• Throughput Definition
• Throughput ? is said to be feasible if every node
  can send data at a rate of ? bits per second to
  its chosen destination
• T(n) is defined as the maximum feasible
  throughput whp

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Delay definition

• Delay is the time it takes for a packet to reach
  its destination after it leaves the source
• Queuing delay at the source is not considered
• D(n) is obtained by averaging over all packets,
  all Source-Destination (S-D) pairs, and all
  random network configurations.
• In fixed networks, it is proportional to the
  number of intermediate relay
  nodes
• In mobile networks, in addition to number of hops
  it depends on the velocity of nodes
• Packet size scales as T(n) so that the
  transmission delay is always constant and D(n)
  captures the dynamics of the network/scheme

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Previous Work

• Fixed Random Network Gupta and Kumar IT00
• Network and successful transmission models were
  described in Mohammads presentation
• For this fixed random network
• T(n) T(1/vnlogn) under protocol model
• Mobile Network Model Grossglauser and Tse01
• Each of the n nodes move on a unit sphere
• The movement of each node is independent with a
  uniform stationary and ergodic distribution on
  the unit sphere
• For this mobile network
• T(n) T(1)
• Delay and T-D trade-off were not addressed
  

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Main results of this paper

• Optimal T-D trade-off in fixed networks (segment
  PQ)
• Delay in mobile networks when T(n) T(1) (point
  R)
• An optimal scheme for T-D trade-off in mobile
  networks
• (segment PR)

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System Model

• n nodes are distributed in a unit torus uniformly
  at random
• Each node is capable of transmitting at W bits
  per second
• Relaxed protocol model
• Transmission from node i to node j is
  successful if for any other simultaneously
  transmitting node k,
• Xk - Xj (1?) Xi - Xj

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Scheme 1 T-D trade-off in fixed Networks

• The torus is divided into square cells each of
  area a(n)
• Transmission scheme
• at most one node can transmit in a cell
• the receiver node is in the same or an adjacent
  cell

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Scheme 1, Contd

• Under the Relaxed Protocol Model,
• The number of cells that can interfere with an
  active cell is bounded by a constant c
• it is possible to have a schedule where each cell
  becomes active every (1c) time slots
• Packets are sent from S to D along adjacent cells
  falling on the straight line connecting S to D
• When a cell becomes active, it transmits a single
  packet for each of the S-D lines passing through
  it

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Scheme 1, Contd

• Throughput depends on the number of S-D lines
  passing through any cell which is
• Delay is the number of hops, which is
• Theorem 1 For a(n) 2logn/n
• Theorem 2 Let the average delay be bounded above
  by D(n). Then the achievable throughput, T(n),
  for any scheme scales as O(D(n)/n)
• Scheme 1 is optimal
• Theorem 2 corresponds to segment PQ

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Scheme 2 T(n) T(1) for Mobile Networks

• Mobile Random Network Model
• Each node moves independently in unit torus with
  a uniform, stationary and ergodic distribution
• Scheme 2
• Each packet is relayed at most once
• The unit square is divided into n square cells,
  each of area 1/n
• In an active cell, the transmission is always
  between two nodes within the same cell
• In an active cell, if two or more nodes are
  present a node i is chosen at random
• Each time slot is divided into two sub-slots A
  and B
• sub-slot A i acts as a source and sends its own
  packet to a randomly chosen node j in the same
  cell or its destination
• sub-slot B i acts as a relay and sends packet
  destined for randomly chosen node k in the same
  cell

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Scheme 2, Contd

• In steady state each node has a packet for every
  other S-D pairs
• Each cell is active for constant fraction of
  time, so T(1) is possible per cell
• In any time slot, c .26 fraction of the cells
  contain two or more nodes
• The overall network throughput is T(n)
• Since each packet is relayed once, the net
  throughput remains T(n)
• Because of symmetry, this is equally divided
  among S-D pairs
• Theorem 3 the throughput using scheme 2 is T(n)
  T(1)

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Scheme 2, Contd

• Delay
• Additional assumption each node moves according
  to an independent Brownian motion
• Let v(n) be the velocity of the nodes
• v(n) is assumed to scale down with n
• Theorem4 For scheme 2, the average delay is
• If , we obtain
  (point R)

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Scheme 3T-D trade-off for Mobile Networks

• Scheme 3(a) is for T(n) O(1/vnlogn)
• The torus is divided into square cells each of
  area a(n)
• Same as scheme 1, each cell becomes active every
  1c time-slots
• A source S sends its packet directly to its
  destination D if D is in a neighboring cell.
  Otherwise, it randomly chooses a relay node R in
  an adjacent cell on the S-D line at the time of
  transmission
• When the cell containing R is active, R transmits
  the packet directly to D, if D is in a
  neighboring cell. Otherwise, it relays the packet
  again to a randomly chosen node in an adjacent
  cell on the straight line connecting it to D
• This process continues until the packet reaches
  the destination
• Theorem 5scheme 3(a) achieves the following T-D
  trade-off for

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Scheme 3, Contd

• Scheme 3(b) is for T(n) ?(1/vnlogn)
• and T(n)O(1/logn)
• All transmissions are done only inside a cell
• Source S delivers its packet to a random mobile
  relay R in the same cell via multi-hops along
  sub-cells
• Mobility of R and D is used to get packet into
  the same cell as D
• R transmits packet to D via multi-hops along
  sub-cells in the same cell

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Scheme 3, Contd

• Theorem 6scheme 3(b) achieves the following T-D
  trade-off for
• If v(n) vlogn/n, then D(n) T(nT(n))
• Theorem 7scheme 3 obtains the optimal T-D
  trade-off for mobile networks

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Conclusion

• Delay was defined and computed for schemes
  providing the optimal T-D trade-off
• The optimal T-D trade-off for fixed/mobile random
  networks was obtained by varying
• The number of hops
• Transmission range
• The degree to which node mobility was used
• It was shown that Gupta-Kumar and
  Grossglauser-Tse schemes are optimal