stochastic optimal multirate multicast in socially selfish wireless

Stochastic Optimal Multirate Multicast in Socially Selfish Wireless Networks

Stochastic Optimal Multirate Multicast inSocially Selfish Wireless Networks

Hongxing Li1, Chuan Wu1, Zongpeng Li2, Wei Huang1, andFrancis C.M. Lau1

1The University of Hong Kong, Hong Kong

2University of Calgary, Canada

Mar. 27, 2012


Introduction

Multirate Multicast

Multirate multicast: non-uniform receivingrates.

Example: media streaming,

High-bandwidth receiver → high quality streaming;

Low-bandwidth receiver → low but acceptablequality streaming.

100 M bps

10 M bps

100 M bps

500 K 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 byeach 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.


Introduction

Multirate Multicast

Multirate multicast: non-uniform receivingrates.Example: media streaming,



100 M bps

10 M bps

100 M bps

500 K bps






Introduction

Multirate Multicast




100 M bps

10 M bps

100 M bps

500 K bps

Layer 1Layer 2

Layer 1Layer 2

Layer 1

Layer 1






Introduction

Multirate Multicast




100 M bps

10 M bps

100 M bps

500 K bps

Layer 1Layer 2

Layer 1Layer 2

Layer 1

Layer 1


Divide the data flow into layers;Base layer: most important and basic information; received byeach destination;Enhancement layers: incremental details for better quality;optionally obtained;Useful only if all lower layers correctly received!



Introduction

Stochastic Wireless Networks

Stochastic wireless network: user mobility and channel fading.

Figure: User mobility → dynamictopology → dynamic routing.

Figure: Channel fading → dynamic linkcapacity → dynamic capacityallocation.

Dynamic throughput → dynamic rate control (number of layersand data rate on each layer).


Introduction

Stochastic Wireless Networks

Stochastic wireless network: user mobility and channel fading.

3 5

4 2 1 7

S

R1 R2

D1 D2 D3

S

R1

R2

D1

D2

S R1

R2

D1

D2

Figure: User mobility → dynamictopology → dynamic routing.

Figure: Channel fading → dynamic linkcapacity → dynamic capacityallocation.

Dynamic throughput → dynamic rate control (number of layersand data rate on each layer).


Introduction

Social Selfishness

Network users in the real world:

Social relationships: social tie between relay node i anddestination d, ρid ∈ [0, 1],

ρid = 1 → strongest tie;ρid = 0 → no tie;

Socially selfish:A user prefers helping others (in data relay) with strongersocial ties;Unit cost for relaying one packet towards d: ξ(ρid),

Non-increasing cost function on ρid;

New challenge to protocol design:

Figure: Routing without socialselfishness: S to R1 to D.

Figure: Routing with social selfishness:S to R2 to D.


Introduction

Social Selfishness

Network users in the real world:Social relationships: social tie between relay node i anddestination d, ρid ∈ [0, 1],








Introduction

Social Selfishness

Network users in the real world:Social relationships: social tie between relay node i anddestination d, ρid ∈ [0, 1],





5 5

2 2

S

R1

R2

D 5 X

2 2

S

R1

R2

D


5 5

2 2

S

R1

R2

D 5 X

2 2

S

R1

R2

D



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.


Introduction


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.


Introduction


Essential questions:

At source: calibrate the number of layers and the data rateon each layer towards each receiver;

At each relay: make packet forwarding decisions;

in each time slot, such that the overall net utility oftime-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.


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 networkstatus.

This work: decide rate control, routing and capacity allocation ineach time slot based on

Network topology;

Channel capacity;

Lengthes of packet queues and virtual queues.


Techniques

Random linear network coding

How?

Divide long flow on each layer into consecutive generations;

Encode packets in the same generation.

Why?

Increase diversity of packets → each packet equivalently useful;

Reduce coding complexity.

)(tQ 3dks

)(tQ 2dks

)(tQ 1dks

)(tr 3dk

)(tr 2dk

)(tr 1dk

Figure: The progress of sending the layer flow at source: an example.

Rate control rdkl(t): data admission of generation k on layer ltowards destination d.


Techniques

Wireless transmission: broadcast

1J

Figure: Example: hyperarc.

Capacity allocation αiJ(t):

αiJ(t) =

{1 hiJ is scheduled

0 Otherwise

12Jdkl

13Jdkl

14Jdkl

Figure: Example: virtual flows.

Routing µdklijJ(t):

packets of generation k on layer l tonode j over hyperarc hiJ towardsdestination d.


Algorithm design

Queues

Packet queue at each node

Qdkli (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 rdkl(t) and packets routed fromother nodes, e.g., µdkl

uiJ (t);

ijJdkldkl uiJ

dklijJdkl

If i not source: packets routed from other nodes, e.g., µdkluiJ (t);

ijJdkluiJ

dklijJdkl

Outgoing rate at slot t: packets routed to other nodes, e.g.,µdklijJ(t).


Algorithm design

Queues

Virtual queues at source

Ydkl(t): if the utility functions Ul(·), ∀l ∈ [1, L], are non-linear,

Incoming rate in slot t: γdkl(t) ∈ [0, R];

Outgoing rate in slot t: rdkl(t);

dkldkl dkl

Remark: Ydkl(t) is stable → γ̄dkl ≤ r̄dkl → Ul(γ̄dkl) ≤ Ul(r̄dkl)


Algorithm design

Queues

Virtual queues at source (Cont.)

Gdkl(t):

Incoming rate in slot t: rdkl+(t) with l+ = l + 1;


dkldkl+ dkl

Remark: Gdkl(t) is stable → r̄dkl+ ≤ r̄dkl → average end-to-endrate of layer l no less than that of layer l + 1

MRC constraint!


Algorithm design

Queues

Virtual queues at source (Cont.)

Gdkl(t):

Incoming rate in slot t: rdkl+(t) with l+ = l + 1;


dkldkl+ dkl

Remark: Gdkl(t) is stable → r̄dkl+ ≤ r̄dkl → average end-to-endrate of layer l no less than that of layer l + 1 MRC constraint!


Algorithm design

Dynamic Algorithm

With Lyapunov optimization framework, we get three optimizationproblems:

Optimization only with auxiliary variable;

Optimization only with rate control variable;

Optimization only with routing and capacity allocationvariables.


Algorithm design

Dynamic Algorithm

Rate control: auxiliary variable

γdkl(t) = max{min{U ′−1l (

Ydkl(t)

V), R}, 0},

Remarks:

Ydkl(t): the amount of packets ready for admission;

Large Ydkl(t) → too many non-admitted packets → smallγdkl(t);


Algorithm design

Dynamic Algorithm

Rate control: data rate variable

rdkl(t) =

min{Pdkl(t), R} if Ydkl(t) + 1{l<L} ·Gdkl(t)

> Qdkls (t) + 1{l>1} ·Gdkl−(t)

0 otherwise

,

Remarks:

Ydkl(t): the amount of packet ready for admission;

Gdkl(t): extra packets received on layer l than layer l + 1;

Qdkls (t): packets for delivery to the network;

Enough packet for admission and satisfaction of MRCconstraint while low congestion → data admission atmaximum rate;


Algorithm design

Dynamic Algorithm

Joint routing and capacity allocationCapacity allocation:

max∑

hiJ∈H(t)

αiJ(t) ·WiJ(t), s.t. Interference Constraints.

Weight WiJ(t): multiplication ofHyperarc capacity;Maximum differential packet queue length minus social cost,over all combinations of

Generation k; Layer l; Destination set DiJ .

Routing:

µdklijJ(t) =

{αiJ(t) · ciJ(t) if (d, k, l, j) = argmax{WiJ(t)}0 otherwise.

.

Remarks: preference toHyperarc with larger capacity;Flow with larger differential packet queue length.Destination with smaller social cost or larger social tie.


Algorithm design

Dynamic Algorithm

Joint routing and capacity allocationCapacity allocation:

max∑

hiJ∈H(t)

αiJ(t) ·WiJ(t), s.t. Interference Constraints.

Weight WiJ(t): multiplication ofHyperarc capacity;Maximum differential packet queue length minus social cost,over all combinations of

Generation k; Layer l; Destination set DiJ .Routing:

µdklijJ(t) =

{αiJ(t) · ciJ(t) if (d, k, l, j) = argmax{WiJ(t)}0 otherwise.

.

Remarks: preference toHyperarc with larger capacity;Flow with larger differential packet queue length.Destination with smaller social cost or larger social tie.


Algorithm design

Dynamic Algorithm

Distributed implementation for capacity allocation

Greedily schedule the hyperarc hiJ with,

Largest weight WiJ(t) among all its interfering hyperarcs;

Largest weight WiJ(t) among all its local hyperarcs, e.g.,hiZ(t) with Z %= J .


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.



Empirical results

Three types of social tie distributions

1) Uniform Distribution of Social Ties (UST): uniformlyrandomly assigned between (0, 1].2) Clustered Distribution of Social Ties 1 (CST1): normalizeddistribution of contact frequencies between two nodes from atrace.

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.



Empirical results

20 30 40 50 60 70 800

0.5

1

1.5

2

2.5

3

3.5

Max link capacity between two nodes (cmax)

Tota

l Net

Utili

ty

Centralized USTCentralized CST1Centralized CST2Distributed USTDistributed CST1Distributed CST2

(a) a 50-node network

20 30 40 50 60 70 800

2

4

6

8

Max link capacity between two nodes (cmax)

Tota

l Net

Utili

ty

Centralized USTCentralized CST1Centralized CST2Distributed USTDistributed CST1Distributed CST2

(b) a 100-node network

Figure: Centralized vs. distributed algorithm on total net utility.



Empirical results

0−0.2 0.2−0.4 0.4−0.6 0.6−0.8 0.8−1.00

0.05

0.1

0.15

0.2

0.25

0.3

Average social tie strengthAver

age

utilit

y pe

r des

tinat

ion

USTCST1CST2

(a) a 50-node network

0−0.2 0.2−0.4 0.4−0.6 0.6−0.8 0.8−1.00

0.05

0.1

0.15

0.2

0.25

0.3

Average social tie strengthAver

age

utilit

y pe

r des

tinat

ion

USTCST1CST2

(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.


Conclusion

Contribution:

First effort on optimal multirate multicast in stochasticwireless networks with user mobility and channel fading;

Investigation on the impact of social selfishness on multicast;

Cross-layer design achieving overall utility arbitrarily close tothe offline optimum.

Future work:

Multirate multicast with delay guarantees;

Reduce the number of queues on each node.


Conclusion

Thank You!

Q&A

stochastic optimal multirate multicast in socially selfish wireless

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