1. Message-Passing for Wireless Scheduling: an Experimental Study Paolo Giaccone (Politecnico di Torino) Devavrat Shah (MIT) ICCCN 2010 – Zurich August 2 nd, 2010

2. 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 R T 2

3. System model and notation packet duration is fixed and time is slotted i is the node x i =1 if node is transmitting, 0 if not X=[x i ] is the transmission vector N(i) is the set of neighboring nodes at a distance < R T from node i, i.e. the set of nodes that may eventually interfere a interference-free X must be 3

4. 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 4

5. 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 w i of a node i is the number of enqueued packets 5 10 5 5

6. 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 6 1 10 9 9 1 9 9

7. 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 7

8. 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 8

9. Message Passing for MWIS 9 Derived by Sanghavi, Shah, Willsky, IEEE Transactions in Information Theory, 2009

10. Computational tree interpretation 10 1 1 2 2 5 5 3 3 4 4

11. 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 11

12. Memory exploit “continuity” in the system state – queue evolution is limited: |w i (t+1)-w i (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 12

13. Message averaging observation: message may oscillate idea: to average message values with a weighted moving average filtering – – filter constant: α=1  no filtering 13

14. 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 1.each node wakes at some random time 2.it updates the outgoing messages based the messages received so far 3.its sends the new updated messages to all its neighbors 14

15. Simulation results given – interference graph – traffic pattern the simulator estimates – throughput – packet delay – packet loss for the whole network and for each node 15

16. Noisy grid as interference graph random geometric graph 1.place N nodes on a perfect grid 2.add some noise to the position (η parameter) η=0 corresponds to a perfect grid η very large corresponds to a bidimensional Poisson process 3.all the nodes with distance < R T are connected 16 η=0.0η=0.5η=1.0

17. Admissible traffic pattern given G, finding the admissibility rate region is NP-hard r i 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 17

18. 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 18

19. Noisy grid ρ=1.0 Conclusions – very little throughput degradation in irregular graphs 19

20. 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 w i graph structure -> messages depend on the graph 20