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Message-Passing for Wireless Scheduling: an Experimental Study. Paolo Giaccone (Politecnico di Torino) Devavrat Shah (MIT) ICCCN 2010 – Zurich August 2 nd , 2010. Scheduling in wireless networks. schedule simultaneous transmissions to avoid interference among neighboring nodes

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message passing for wireless scheduling an experimental study

Message-Passing for Wireless Scheduling: an Experimental Study

Paolo Giaccone (Politecnico di Torino)

Devavrat Shah (MIT)

ICCCN 2010 – Zurich

August 2nd, 2010

scheduling in wireless networks
Scheduling in wireless networks
  • schedule simultaneous transmissions
    • to avoid interference among neighboring nodes
    • needs coordination across the communication medium
  • simplified interference model
    • a transmission is successful if none of its neighbors are transmitting
    • neighbors defined simply by the transmission range RT
system model and notation
System model and notation
  • packet duration is fixed and time is slotted
  • i is the node
  • xi=1 if node is transmitting, 0 if not
  • X=[xi] is the transmission vector
  • N(i) is the set of neighboring nodes at a distance < RT from node i, i.e. the set of nodes that may eventually interfere
  • a interference-free X must be
interference graph
Interference graph
  • G=(V,E)
    • V is the set of nodes
    • edge
  • an independent set (IS) on G corresponds to a subset of nodes that can transmit simultaneously without interference
optimal scheduler
Optimal scheduler
  • Optimal scheduling
    • for generic constrained resource allocation problem
      • Tassiulas and Ephremides, IEEE Trans. Automatic Control, 1992
    • to maximize throughput, compute the maximum weight independent set (MWIS) at each timeslot
      • weight wi of a node i is the number of enqueued packets

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5

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centralized algorithms for is
Centralized algorithms for IS
  • IS is NP-complete
  • greedy approximations
  • Rnd-IS: S is a random permutation of nodes
  • MaxW-IS: S is a sequence of nodes in decreasing order of weights

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10

9

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1

message passing approach
Message passing approach
  • derived from belief propagation to perform inference on graphical models, such as Bayesian networks and Markov random fields
    • successfully employed in many fields: physics, computer vision, statistics, coding (Viterbi algorithm), generic combinatorial optimization
  • amenable to parallel implementation
    • network protocols are based on message passing algorithms
message passing
Message passing
  • update phase
    • each node sends a message to the neighbors based on the received messages
    • is the message from node i to j at iteration n
  • estimate phase
    • each node takes a local decision
message passing for mwis
Message Passing for MWIS

Derived by Sanghavi, Shah, Willsky, IEEE Transactions in Information Theory, 2009

contribution
Contribution
  • for a generic graph with loops, messages may not converge, leading to unfeasible solutions
  • to improve converge we propose
    • use of memory
    • message averaging
  • we investigate their effects on the performance
memory
Memory
  • exploit “continuity” in the system state
    • queue evolution is limited: |wi(t+1)-wi(t)|≤1
    • Property: |MWIS(t+1)-MWIS(t)|≤ N
    • MWIS(t) is also a good candidate for time t+1
  • idea: keep the most recent messages from the previous timeslot as the initial value
    • leads to reduced convergence time
message averaging
Message averaging
  • observation: message may oscillate
  • idea: to average message values with a weighted moving average filtering
    • filter constant: α=1  no filtering
asynchronous update
Asynchronous update
  • Earlier pseudocode of MP-IS assumes that all the nodes update synchronously their messages in parallel at each iteration
    • this assumption is not needed
  • We assume uncoordinated, asynchronous update
    • each node wakes at some random time
    • it updates the outgoing messages based the messages received so far
    • its sends the new updated messages to all its neighbors
simulation results
Simulation results
  • given
    • interference graph
    • traffic pattern
  • the simulator estimates
    • throughput
    • packet delay
    • packet loss

for the whole network and for each node

noisy grid as interference graph
Noisy grid as interference graph
  • random geometric graph
    • place N nodes on a perfect grid
    • add some noise to the position (η parameter)
      • η=0 corresponds to a perfect grid
      • η very large corresponds to a bidimensional Poisson process
    • all the nodes with distance < RT are connected

η=0.0

η=0.5

η=1.0

admissible traffic pattern
Admissible traffic pattern
  • given G, finding the admissibility rate region is NP-hard
  • ri is the normalized arrival rate at node i
  • ρ is the load factor
    • ρ=1 is such that Rnd-IS will obtain 100% throughput
  • K is a traffic parameter
    • K=1  unbalanced traffic
    • large K  balanced traffic
perfect grid
Perfect grid
  • N=100 nodes
  • ρ=1.35
  • Conclusions
    • memory boosts performance of MP-IS
    • one iteration is enough for MP-IS to be optimal
noisy grid
Noisy grid
  • ρ=1.0
  • Conclusions
    • very little throughput degradation in irregular graphs
conclusions
Conclusions
  • MP-IS with just 1 iteration + memory + averaging performs comparable with centralized algorithms
    • similar result for Tree-Reweighted Message Passing algorithm
  • promising approach for the limited protocol overhead
    • belief propagation is taking care of
      • longer queues -> messages are proportional to wi
      • graph structure -> messages depend on the graph
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