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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 Study

  • 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 Study

  • 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 Study

  • 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 Study

  • 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





Centralized algorithms for is
Centralized algorithms for IS Study

  • 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









Message passing approach
Message passing approach Study

  • 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 Study

  • 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 Study

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

Contribution Study

  • 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 Study

  • 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 Study

  • 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 Study

  • 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 Study

  • 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 Study

  • 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




Admissible traffic pattern
Admissible traffic pattern Study

  • 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 Study

  • 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 Study

  • ρ=1.0

  • Conclusions

    • very little throughput degradation in irregular graphs

Conclusions Study

  • 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