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Utility Optimization for Dynamic Peer-to-Peer Networks with Tit-for-Tat Constraints. Network Cloud. 1. 2. 3. 5. 4. Michael J. Neely, Leana Golubchik University of Southern California Proc. IEEE INFOCOM, Shanghai, China, April 2011 PDF of paper at: http://www- bcf.usc.edu /~ mjneely /.

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slide1

Utility Optimization for Dynamic Peer-to-Peer Networks with Tit-for-Tat Constraints

Network Cloud

1

2

3

5

4

Michael J. Neely, LeanaGolubchik

University of Southern California

Proc. IEEE INFOCOM, Shanghai, China, April 2011

PDF of paper at: http://www-bcf.usc.edu/~mjneely/

Sponsored in part by the NSF Career CCF-0747525, ARL Network Science Collaborative Tech. Alliance

slide2

Network Cloud

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  • N nodes.
  • Each node n has download social group Gn.
  • Gn is a subset of {1, …, N}.
  • Each file f is in some subset of nodes Nf.
  • Each node n can request download of a file f from any node in GnNf
slide3

“One-Hop” Network Transmission Model

µ12(t)

µ34(t)

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2

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  • Slotted time t in {0, 1, 2, …}.
  • S(t) = “topology state” on slot t.
  • µab(t) = transmission rate from a to b on slot t.
  • GS(t) = set of matrices (µab(t)) allowed under S(t).
  • Transmissions are supported by the network cloud.
  • Transmission Decision:
  • Every slot t, observe S(t). Then choose (µab(t)) inGS(t).
slide4

“Internet Cloud” Example 1:

Uplink capacity C1uplink

Network Cloud

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  • S(t) = Constant (no variation).
  • ∑bµnb(t) ≤ Cnuplinkfor all nodes n.
  • This example assumes uplink capacity is the bottleneck.
slide5

“Internet Cloud” Example 2:

Network Cloud

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  • S(t) specifies a single supportable (µab(t)).
  • No “transmission rate decisions.” The allowable rates (µab(t)) are given to the peer-to-peer system from some underlying transport and routing protocol.
slide6

“Wireless Basestation” Example 3:

= base station

= wireless device

  • Wireless device-to-device transmission
  • increases capacity.
  • (µab(t)) chosen in GS(t).
  • Transmissions coordinated by base station.
slide7

Network File Request Model

n

Get help from

nodes in:

(An(t), Nn(t))

  • Each node desires at most 1 new file per slot.
  • Assume GnNn(t) is non-empty.
  • Assume 0 ≤ An(t) ≤ Amax.
  • Files larger than Amax packets can be treated as separate files that come in successive slots.

GnNn(t)

An(t) = size of desired file on slot t.

Nn(t) = subset of other nodes that have it.

slide8

“Commodities” for Request Allocation

  • Each file corresponds to a subset of nodes.
  • Queueing files according to subsets would
  • result in O(2N) queues.
  • (complexity explosion!).
  • Instead of that, without loss of optimality, we use the following alternative commodity structure…
slide9

“Commodities” for Request Allocation

n

j

k

m

(An(t), Nn(t))

GnNn(t)

  • Use subset info to determine the decision set.
slide10

“Commodities” for Request Allocation

n

j

k

m

(An(t), Nn(t))

GnNn(t)

  • Use subset info to determine the decision set.
  • Choose which node will help download.
slide11

“Commodities” for Request Allocation

n

j

k

m

(An(t), Nn(t))

Qmn(t)

  • Use subset info to determine the decision set.
  • Choose which node will help download.
  • That node queues the request:
  • Qmn(t+1)= max[Qmn(t) + Rmn(t) - µmn(t), 0]
  • Subset info can now be thrown away.
slide12

Stochastic Network Optimization Problem:

Maximize:

∑ngn(∑a ran)

Subject to:

Qmn < infinity

(Queue Stability Constraint)

α ∑a ran ≤ β + ∑brnb for all n

(Tit-for-Tat Constraint)

slide13

Stochastic Network Optimization Problem:

Maximize:

∑ngn(∑a ran)

Subject to:

Qmn < infinity

(Queue Stability Constraint)

α ∑a ran ≤ β + ∑brnb for all n

(Tit-for-Tat Constraint)

concave utility function

slide14

Stochastic Network Optimization Problem:

Maximize:

∑ngn(∑a ran)

Subject to:

Qmn < infinity

(Queue Stability Constraint)

α ∑a ran ≤ β + ∑brnb for all n

(Tit-for-Tat Constraint)

concave utility function

time average request rate

slide15

Stochastic Network Optimization Problem:

Maximize:

∑ngn(∑a ran)

Subject to:

Qmn < infinity

(Queue Stability Constraint)

α ∑a ran ≤ β + ∑brnb for all n

(Tit-for-Tat Constraint)

concave utility function

time average request rate

α x Download rate

slide16

Stochastic Network Optimization Problem:

Maximize:

∑ngn(∑a ran)

Subject to:

Qmn < infinity

(Queue Stability Constraint)

α ∑a ran ≤ β + ∑brnb for all n

(Tit-for-Tat Constraint)

concave utility function

time average request rate

β + Upload rate

α x Download rate

slide17

Solution Technique

  • Use “Drift-Plus-Penalty” Framework for Stochastic Network Optimization
  • [Georgiadis, Neely, Tassiulas, F&T 2006]
  • [Neely, Morgan & Claypool 2010]
  • No Statistical Assumptions on [S(t); (An(t), Nn(t))]
  • Quick Advertisement: New Book:
  • M. J. Neely, Stochastic Network Optimization with Application to Communication and Queueing Systems. Morgan & Claypool, 2010.
  • http://www.morganclaypool.com/doi/abs/10.2200/S00271ED1V01Y201006CNT007
  • PDF also available from “Synthesis Lecture Series” (on digital library)
  • Lyapunov Optimization theory (including universal scheduling, renewals)
  • Detailed Examples and Problem Set Questions.
slide18

Use “Drift-Plus-Penalty” Framework:

  • Virtual queue for each TFT constraint:
  • α ∑a ran ≤ β + ∑brnb
  • Virtual queue Hn(t) for each concave utility function.
  • L(t) = ∑ Qmn(t)2 + ∑Fn(t)2 + ∑Hn(t)2.
  • Δ(t) = L(t+1) – L(t).
  • Drift-Plus-Penalty Algorithm:
  • Every slot t, choose action to greedily minimize:

Fn(t)

α ∑aRan(t)

β+ ∑bRnb(t)

Δ(t) – V x Utility(t)

slide19

Resulting Algorithm:

  • (Auxiliary Variables) For each n, choose an aux. variable γn(t) in interval [0, Amax] to maximize:
  • Vgn(γn(t)) – Hn(t)gn(t)
  • (Request Allocation) For each n, observe the following value for all m in {GnNn(t)}:
  • -Qmn(t) + Hn(t) + (Fm(t) – αFn(t))
  • Give An(t) to queue m with largest non-neg value,
  • Drop An(t) if all above values are negative.
  • (Scheduling) Choose (µab(t)) in GS(t) to maximize:
  • ∑nbµnb(t)Qnb(t)
slide20

How the Incentives Work for node n:

Node n can only request downloads from others if

it finds a node m with a non-negative value of:

-Qmn(t) + Hn(t) + (Fm(t) – αFn(t))

Fn(t) = “Node n Reputation”

(Good reputation = Low value)

Fn(t)

α x Receive Help(t)

β+ Help Others(t)

slide21

How the Incentives Work for node n:

Node n can only request downloads from others if

it finds a node m with a non-negative value of:

-Qmn(t) + Hn(t) + (Fm(t) – αFn(t))

Bounded

Compare Reputations!

Fn(t) = “Node n Reputation”

(Good reputation = Low value)

Fn(t)

α x Receive Help(t)

β+ Help Others(t)

slide22

How the Incentives Work for node n:

Node n can only request downloads from others if

it finds a node m with a non-negative value of:

-Qmn(t) + Hn(t) + (Fm(t) – αFn(t))

Bounded

Compare Reputations!

Fn(t) = “Node n Reputation”

(Good reputation = Low value)

Fn(t)

α x Receive Help(t)

β+ Help Others(t)

slide23

Concluding Theorem:

For any arbitrary [S(t); (An(t), Nn(t))] sample path,

we guarantee:

Qmn(t) ≤ Qmax = O(V) for all t, all (m,n).

All Tit-for-Tat constraints are satisfied.

For any T>0:

liminfKinf[AchievedUtility(KT)] ≥

liminfKinf (1/K)∑i=1[“T-Slot-Lookahead-Utility[i]”]- BT/V

K

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0

T

2T

3T