Introduction Multirate Multicast Multirate multicast: non-uniform receiving rates. 100 M bps 10 M bps 100 M bps 500 K bps

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1 Stochastic Optimal Multirate Multicast in Socially Selfish Wireless Networks Hongxing Li 1, Chuan Wu 1, Zongpeng Li 2, Wei Huang 1, and Francis C.M. Lau 1 1 The University of Hong Kong, Hong Kong 2 University of Calgary, Canada Mar. 27, 2012

2 Introduction Multirate Multicast Multirate multicast: non-uniform receiving rates. 100 M bps 10 M bps 100 M bps 500 K bps

3 Introduction Multirate Multicast Multirate multicast: non-uniform receiving rates. Example: media streaming, High-bandwidth receiver high quality streaming; Low-bandwidth receiver low but acceptable quality streaming. 100 M bps 100 M bps 500 K bps 10 M bps

4 Introduction Multirate Multicast Multirate multicast: non-uniform receiving rates. Example: media streaming, High-bandwidth receiver high quality streaming; Low-bandwidth receiver low but acceptable quality streaming. Layer 2 Layer M bps Layer M bps Layer K bps Layer 2 Layer 1 10 M bps Typical implementation: Multi-Resolution Coding (MRC), e.g., H.264/SVC and MPEG-4 Divide the data flow into layers; Base layer: most important and basic information; received by each destination; Enhancement layers: incremental details for better quality; optionally obtained; Allocate different number of layers to different receivers.

5 Introduction Multirate Multicast Multirate multicast: non-uniform receiving rates. Example: media streaming, High-bandwidth receiver high quality streaming; Low-bandwidth receiver low but acceptable quality streaming. Layer 2 Layer M bps Layer M bps Layer K bps Layer 2 Layer 1 10 M bps Typical implementation: Multi-Resolution Coding (MRC), e.g., H.264/SVC and MPEG-4 Divide the data flow into layers; Base layer: most important and basic information; received by each destination; Enhancement layers: incremental details for better quality; optionally obtained; Useful only if all lower layers correctly received! Allocate different number of layers to different receivers.

6 Introduction Stochastic Wireless Networks Stochastic wireless network: user mobility and channel fading.

7 Introduction Stochastic Wireless Networks Stochastic wireless network: user mobility and channel fading. R1 S R1 S D1 D1 R2 D2 D2 R2 Figure: User mobility dynamic topology dynamic routing.

8 Introduction Stochastic Wireless Networks Stochastic wireless network: user mobility and channel fading. R1 S R1 S D1 D1 R2 D2 D2 R2 Figure: User mobility dynamic topology dynamic routing. Figure: Channel fading dynamic link capacity dynamic capacity allocation.

9 Introduction Stochastic Wireless Networks Stochastic wireless network: user mobility and channel fading. R1 S R1 S D1 D1 R2 D2 D2 R2 Figure: User mobility dynamic topology dynamic routing. Figure: Channel fading dynamic link capacity dynamic capacity allocation. Dynamic throughput dynamic rate control (number of layers and data rate on each layer).

10 Introduction Social Selfishness Network users in the real world:

11 Introduction Social Selfishness Network users in the real world: Social relationships: social tie between relay node i and destination d, ρ id [0, 1], ρ id =1 strongest tie; ρ id =0 no tie;

12 Introduction Social Selfishness Network users in the real world: Social relationships: social tie between relay node i and destination d, ρ id [0, 1], ρ id =1 strongest tie; ρ id =0 no tie; Socially selfish: A user prefers helping others (in data relay) with stronger social ties; Unit cost for relaying one packet towards d: ξ(ρ id ), Non-increasing cost function on ρ id ;

13 Introduction Social Selfishness Network users in the real world: Social relationships: social tie between relay node i and destination d, ρ id [0, 1], ρ id =1 strongest tie; ρ id =0 no tie; Socially selfish: A user prefers helping others (in data relay) with stronger social ties; Unit cost for relaying one packet towards d: ξ(ρ id ), Non-increasing cost function on ρ id ; New challenge to protocol design: R 1 R 1 S 5 5 D S 5 X D R 2 Figure: Routing without social selfishness: S to R 1 to D. Figure: Routing with social selfishness: S to R 2 to D. R 2

14 Introduction Utility maximization problem Network model Single multicast session; General mobility model: ergodic process; General channel fading model: ergodic process; General interference model: interference relation set.

15 Introduction Utility maximization problem Network model Single multicast session; General mobility model: ergodic process; General channel fading model: ergodic process; General interference model: interference relation set. E.g., (a, b) I a and b are mutual interfering.

16 Introduction Utility maximization problem Essential questions: At source: calibrate the number of layers and the data rate on each layer towards each receiver; At each relay: make packet forwarding decisions; in each time slot, such that the overall net utility of time-averaged throughput is maximized over time?

17 Introduction Utility maximization problem Essential questions: At source: calibrate the number of layers and the data rate on each layer towards each receiver; At each relay: make packet forwarding decisions; in each time slot, such that the overall net utility of time-averaged throughput is maximized over time? Current literature: Known receiving rates at the destinations; And/or, given routing table of the layers. Our solution: an online algorithm with none of above assumptions.

18 Techniques Lyapunov optimization framework Proposed by Dr. Neely from USC; Online algorithm for time-averaged utility optimization; Strategically make decision in each time slot based on network status.

19 Techniques Lyapunov optimization framework Proposed by Dr. Neely from USC; Online algorithm for time-averaged utility optimization; Strategically make decision in each time slot based on network status. This work: decide rate control, routing and capacity allocation in each time slot based on Network topology; Channel capacity; Lengthes of packet queues and virtual queues.

20 Techniques Random linear network coding How? Why? Divide long flow on each layer into consecutive generations; Encode packets in the same generation. Increase diversity of packets each packet equivalently useful; Reduce coding complexity. r 3 (t) dk r 2 (t) dk r 1 (t) dk Q dk 3 s (t) Q dk 2 s (t) Q dk 1 s (t) Figure: The progress of sending the layer flow at source: an example.

21 Techniques Random linear network coding How? Why? Divide long flow on each layer into consecutive generations; Encode packets in the same generation. Increase diversity of packets each packet equivalently useful; Reduce coding complexity. r 3 (t) dk r 2 (t) dk r 1 (t) dk Q dk 3 s (t) Q dk 2 s (t) Q dk 1 s (t) Figure: The progress of sending the layer flow at source: an example. Rate control r dkl (t): data admission of generation k on layer l towards destination d.

22 Techniques Wireless transmission: broadcast 1J 12J dkl 13J dkl 14J dkl Figure: Example: hyperarc. Figure: Example: virtual flows.

23 Techniques Wireless transmission: broadcast 1J 12J dkl 13J dkl 14J dkl Figure: Example: hyperarc. Capacity allocation { α ij (t): 1 h ij is scheduled α ij (t) = 0 Otherwise Figure: Example: virtual flows. Routing µ dkl ijj (t): packets of generation k on layer l to node j over hyperarc h ij towards destination d.

24 Algorithm design Queues Packet queue at each node Q dkl i (t): packets queue on node i of generation k on layer l towards destination d, Incoming rate at slot t: If i is source: data admission r dkl (t) and packets routed from other nodes, e.g., µ dkl uij (t); dkl uij dkl ijj dkl ijj dkl If i not source: packets routed from other nodes, e.g., µ dkl uij (t); uij dkl ijj dkl ijj dkl Outgoing rate at slot t: packets routed to other nodes, e.g., µ dkl ijj (t).

25 Algorithm design Queues Virtual queues at source Y dkl (t): if the utility functions U l ( ), l [1,L], are non-linear, Incoming rate in slot t: γ dkl (t) [0,R]; Outgoing rate in slot t: r dkl (t); dkl dkl dkl Remark: Y dkl (t) is stable γ dkl r dkl U l ( γ dkl ) U l ( r dkl )

26 Algorithm design Queues Virtual queues at source (Cont.) G dkl (t): Incoming rate in slot t: r dkl +(t) with l + = l +1; Outgoing rate in slot t: r dkl (t); dkl+ dkl dkl Remark: G dkl (t) is stable r dkl + r dkl average end-to-end rate of layer l no less than that of layer l +1

27 Algorithm design Queues Virtual queues at source (Cont.) G dkl (t): Incoming rate in slot t: r dkl +(t) with l + = l +1; Outgoing rate in slot t: r dkl (t); dkl+ dkl dkl Remark: G dkl (t) is stable r dkl + r dkl average end-to-end rate of layer l no less than that of layer l +1MRC constraint!

28 Algorithm design Dynamic Algorithm With Lyapunov optimization framework, we get three optimization problems: Optimization only with auxiliary variable; Optimization only with rate control variable; Optimization only with routing and capacity allocation variables.

29 Algorithm design Dynamic Algorithm Rate control: auxiliary variable Remarks: γ dkl (t) = max{min{u 1 l ( Y dkl(t) ),R}, 0}, V Y dkl (t): the amount of packets ready for admission; Large Y dkl (t) too many non-admitted packets small γ dkl (t);

30 Algorithm design Dynamic Algorithm Rate control: data rate variable min{p dkl (t),r} if Y dkl (t)+1 {l<l} G dkl (t) r dkl (t) = >Q dkl s (t)+1 {l>1} G dkl (t), 0 otherwise Remarks: Y dkl (t): the amount of packet ready for admission; G dkl (t): extra packets received on layer l than layer l +1; Q dkl s (t): packets for delivery to the network;

31 Algorithm design Dynamic Algorithm Rate control: data rate variable min{p dkl (t),r} if Y dkl (t)+1 {l<l} G dkl (t) r dkl (t) = >Q dkl s (t)+1 {l>1} G dkl (t), 0 otherwise Remarks: Y dkl (t): the amount of packet ready for admission; G dkl (t): extra packets received on layer l than layer l +1; Q dkl s (t): packets for delivery to the network; Enough packet for admission and satisfaction of MRC constraint while low congestion data admission at maximum rate;

32 Algorithm design Dynamic Algorithm Joint routing and capacity allocation Capacity allocation: max α ij (t) W ij (t), h ij H(t) s.t. Interference Constraints. Weight W ij (t): multiplication of Hyperarc capacity; Maximum differential packet queue length minus social cost, over all combinations of Generation k; Layer l; Destination set D ij.

33 Algorithm design Dynamic Algorithm Joint routing and capacity allocation Capacity allocation: max α ij (t) W ij (t), h ij H(t) s.t. Interference Constraints. Weight W ij (t): multiplication of Hyperarc capacity; Maximum differential packet queue length minus social cost, over all combinations of Generation k; Layer l; Destination set D ij. Routing: µ dkl ijj(t) = { α ij (t) c ij (t) if (d, k, l, j) =arg max{w ij (t)}. 0 otherwise.

34 Algorithm design Dynamic Algorithm Joint routing and capacity allocation Capacity allocation: max α ij (t) W ij (t), h ij H(t) s.t. Interference Constraints. Weight W ij (t): multiplication of Hyperarc capacity; Maximum differential packet queue length minus social cost, over all combinations of Generation k; Layer l; Destination set D ij. Routing: µ dkl ijj(t) = { α ij (t) c ij (t) if (d, k, l, j) =arg max{w ij (t)}. 0 otherwise. Remarks: preference to Hyperarc with larger capacity; Flow with larger differential packet queue length. Destination with smaller social cost or larger social tie.

35 Algorithm design Dynamic Algorithm Distributed implementation for capacity allocation Greedily schedule the hyperarc h ij with, Largest weight W ij (t) among all its interfering hyperarcs; Largest weight W ij (t) among all its local hyperarcs, e.g., h iz (t) with Z J.

36 Performance analysis Theoretical results Utility optimality and network stability Constant gap to the offline optimum: Net utility by our online algorithm Offline optimum B/V, B is a constant; V is a configurable parameter; All queues are stable, i.e., stable network.

37 Performance analysis Empirical results Three types of social tie distributions 1) Uniform Distribution of Social Ties (UST): uniformly randomly assigned between (0, 1]. 2) Clustered Distribution of Social Ties 1 (CST1): normalized distribution of contact frequencies between two nodes from a trace. Low social tie among most nodes; Only a few nodes have strong social ties with others. 3) Clustered Distribution of Social Ties 2 (CST2): complementary of CST1 High social tie among most nodes; Only a few nodes have low social ties with others.

38 Performance analysis Empirical results Total Net Utility Centralized UST Centralized CST1 1.5 Centralized CST2 1 Distributed UST 0.5 Distributed CST1 Distributed CST Max link capacity between two nodes (c max ) (a) a 50-node network Total Net Utility 8 6 Centralized UST 4 Centralized CST1 Centralized CST2 2 Distributed UST Distributed CST1 Distributed CST Max link capacity between two nodes (c max ) (b) a 100-node network Figure: Centralized vs. distributed algorithm on total net utility.

39 Performance analysis Empirical results Average utility per destination UST CST1 CST Average social tie strength Average utility per destination UST CST1 CST Average social tie strength (a) a 50-node network (b) a 100-node network Figure: Impact of different social tie strengths. Observation: Obvious social preference under UST and CST1 distributions; No differentiated utility gain under CST2 distribution;

40 Performance analysis Empirical results Average utility per destination UST CST1 CST Average social tie strength Average utility per destination UST CST1 CST Average social tie strength (a) a 50-node network (b) a 100-node network Figure: Impact of different social tie strengths. Observation: Obvious social preference under UST and CST1 distributions; No differentiated utility gain under CST2 distribution; Reason: Free-riding in CST2.

41 Conclusion Contribution: First effort on optimal multirate multicast in stochastic wireless networks with user mobility and channel fading; Investigation on the impact of social selfishness on multicast; Cross-layer design achieving overall utility arbitrarily close to the offline optimum. Future work: Multirate multicast with delay guarantees; Reduce the number of queues on each node.

42 Conclusion Thank You! Q&A