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Message-Passing for Wireless Scheduling: an Experimental Study

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### 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

- 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

- 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

- 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 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

10

5

5

10

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

10

10

9

9

9

9

1

1

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

- 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

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

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

- 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

- observation: message may oscillate
- idea: to average message values with a weighted moving average filtering
- filter constant: α=1 no filtering

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

- 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

- 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

- 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

- 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

- ρ=1.0
- Conclusions
- very little throughput degradation in irregular graphs

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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