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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

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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

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### 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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### 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

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### 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

• 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