1. Information flows through networks:
Models and algorithms
HDR, Laurent Massoulié
2/24/2019

2. Scales of Internet data transfers
Data packet (1460 B)
Packets per transfer: 103 – 106
Simultaneous transfers: 108
Reachable network locations: 108
Data items available: 109
Per month: order of bytes transferred: exabytes, ie 10^18 bytes
2/24/2019

3. Focus Data flows for File downloads Real-time streaming media
 Accommodate competing requests at massive scale
2/24/2019

4. Philosophy Achieve global efficiency from local controls
Emphasis: simple rules (greedy, lazy, random,...)
Statistical Physics: from “hard core model” of atomic interactions to law of perfect gas
But we can invent the local rules (maybe “hard cubes” better than “hard spheres”)
Microeconomics: “market efficiency” holds as welfare is optimised by free exchanges
2/24/2019

5. Roadmap File download (single or multi- path)
“Mesoscopic” scale [data transfer level]
 Network Utility Maximisation
“Macroscopic” scale [dynamics of collections of transfers]
 Greedy or Fair, Myopic or Aware
Peer-to-Peer Live Streaming
Deprived peer selection
Delay- and rate-optimal epidemics
Perspectives
2/24/2019

6. “Mesoscopic” scale: Data transfer as a fluid
Encode local control mechanisms via suitable equations
e.g. First-In-First-Out Buffer
Microscopic scale:
Discrete event pkt transmissions
Continuous “fluid” rate x(t)
xout, yout
xin, yin
This is precisely how we reason about status of connections; this also simplifies analysis. Eg:
2/24/2019

7. Example
Fixed window control, size wi for connection i, i=1,2,3
type 3: send to link with smallest
backlog (normalised by link capacity)
Fluid model’s fixed points:
rates x1, x2, x3 solutions of
under feasibility constraints x1 ≤ c1, x2 ≤ c2, x1+x2+x3 ≤ c1+c2.
This extends to any network topology
Queues coupled with fixed window control achieve system-wide optimization [LM&Roberts], [Walton] 1 1 1 3 2 2 2 3
Mention “proportional fairness”, Kelly
2/24/2019

8. The Network Utility Maximisation (NUM) paradigm
Allocate flow rates xi to achieve
subject to feasibility of rates xi
[Kelly-Maulloo-Tan]
TCP utility: [Kunnyur-Srikant]
Distributed scheme: each sender adjusts rate in proportion to Marginal Utility minus Marginal Cost (loss-based, delay-based, or other).
A greedy, myopic policy, interpreting user value as Ui(x)-pi x
2/24/2019

9. Roadmap File download (single or multi- path)
“Mesoscopic” scale [data transfer level]
 Network Utility Maximisation
“Macroscopic” scale [dynamics of collections of transfers]
 Greedy or Fair, Myopic or Aware
Peer-to-Peer Live Streaming
Deprived peer selection
Delay- and rate-optimal epidemics
Perspectives
2/24/2019

10. “Macroscopic” scale: dynamic collections of flows
Dynamic model for numbers ni of active type i transfers
type i transfers initiated at rate i
Transfer (random, exponential) volume with mean i
Rate per type i transfer xi(n) from NUM allocation (or other)
Question: does the allocation exploit the network resources optimally?
Result: For NUM with strictly concave utility functions, YES: transfer times bounded (in probability) provided enough network resources for offered load [Bonald&LM]
Key equations:
This is the scale at which one observes completion of transfers, which is essentially what matters to end-users.
2/24/2019

11. Alternatives to NUM?
“Maximum weight” policies [Tassiulas-Ephremides] also maximally stable
NUM: rates xi solutions of
Max Weight: rates xi solutions of
For increasing weight functions fi
Known implementations:
Needs estimation of numbers ni of competing transfers per type
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12. What can fail (single path case)
Too greedy at mesoscopic scale
Linear utility function Ui(x)=x
NUM achieves bounded delays only for
Strict reduction compared to
Class 1
Class 2
Class 3
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13. What can fail with multipath [Key-LM-Towsley]
Too myopic
No synchronisation between paths
 For equal loads  per class, TCP utility,
stability iff  < 1/2 instead of  < 1
Greedy with distorted signals
Strategy: Switch to fastest TCP path
 Short thin paths preferred to
Long fat paths when
Then stable iff <1/2 instead of  <1
2/24/2019

14. Underlying mathematics
Dynamical systems – understanding convergence to suitable equilibria
Key technique: Lyapunov function identification
e.g., for utility functions Ui(x) = x1-a/(1-a),
Maximal stability region: a “first order” result
Refinements: heavy traffic / large deviations
For a=1 (proportional fairness) ,
function L = rate function of large deviations principle
2/24/2019

15. Roadmap File download (single or multi- path)
“Mesoscopic” scale [data transfer level]
 Network Utility Maximisation
“Macroscopic” scale [dynamics of collections of transfers]
 Greedy or Fair, Myopic or Aware
Peer-to-Peer Live Streaming
Deprived peer selection
Delay- and rate-optimal epidemics
Perspectives
2/24/2019

16. Back to Microscopic - Mesoscopic Scales: P2P Live Streaming
Aim: timely delivery of data stream to all receivers
Peer-to-Peer: systematic sharing of end-user resources (storage, bandwidth)
For each peer, which packet to send to whom?
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17. NUM-inspired objectives
Setup: V receivers, data source s injecting content at rate 
Determine data rates cij between users i,j ensuring content access to receivers, at minimum network cost
Feasibility: cut constraints
A convex program (for convex network costs)
 “Primal-Dual” algorithms exist 
Basic implementation requires maintenance of (|V|) variables per receiver 
Look for simpler alternatives, analysed in isolation
2/24/2019

18. Roadmap File download (single or multi- path)
“Mesoscopic” scale [data transfer level]
 Network Utility Maximisation
“Macroscopic” scale [dynamics of collections of transfers]
 Greedy or Fair, Myopic or Aware
Peer-to-Peer Live Streaming
Deprived peer selection
Delay- and rate-optimal epidemics
Perspectives
2/24/2019

19. Network with access (node) constraints
Scarce resource = access capacity
Complete communication graph: everyone can send to anyone
Maximal streaming rate …

20. Deprived Peer / Random Useful Chunk
Sender’s packets 1 2 4 5 7 8 5 1 5 7 8 1 4
Potential receiver 1
Potential receiver 2
Result: When λ < λ* all nodes receive all packets with delay bounded in probability
[LM, A. Twigg, C. Gkantsidis & P. Rodriguez]

21. Deprivation versus backpressure
Single-receiver flows: “backpressure” = adequate measure for scheduling decision [Tassiulas-Ephremides]
In broadcast scenario (all nodes receivers):
deprivation adequate measure instead 1 2 4 5 i
=3
=1 3 6 7 8 j k
2/24/2019

22. Multiple commodities … Several sources s, Dedicated receiver sets V(s)
Can overlap
Sources are not receivers
Nodes cannot relay commodities they don’t consume …

23. Multiple commodities Result: System maximally stable [LM & A. Twigg]
Bundled most deprived / random useful: do not distinguish between commodities when
measuring deprivation
Choosing random useful packet
 Deprivation: an adequate signal for neighbour selection
Result: System maximally stable [LM & A. Twigg]
Hence deprivation appears to be a good “signal” for neighbour selection.

24. Roadmap File download (single or multi- path)
“Mesoscopic” scale [data transfer level]
 Network Utility Maximisation
“Macroscopic” scale [dynamics of collections of transfers]
 Greedy or Fair, Myopic or Aware
Peer-to-Peer Live Streaming
Deprived peer selection
Delay- and rate-optimal epidemics
Perspectives
2/24/2019

25. A naive scheme: random peer / earliest useful pkt
Fraction of nodes reached
Sender’s packets
0.01
0.02 40 20 1 1 2 4 5 7 8 2
1st useful packet 3 1 2 3 4
Receiver’s packets
Privileges direct benefit to receiver
Expliquer que delai optimal = log_2(N)…
Time

26. A better scheme: random target / latest useful pkt
Sender’s packets 1 2 4 5 7 8
Latest useful pkt ? 1 ? 2 ? 3 ? 8
Receiver’s packets
Privileges global system efficiency
[compare to BitTorrent’s “rarest first” prioritisation]

27. A better scheme: random target / latest useful pkt
Result: For injection rate λ<1 and constant x>0,
Each peer receives fraction 1- 1/x of packets in time log2(N)+O(x)
I.e: Diffusion at rates arbitrarily close to optimal feasible under optimal delay ( plus constant)
Prioritisation of “latest gossip” a good strategy for content selection
[T. Bonald, LM, F. Mathieu, D. Perino & A. Twigg]

28. Summary NUM at mesoscopic scale  Efficiency at macroscopic scale
For Multipath transfers
 synchronisation necessary
 greedy path selection underperforms with RTT bias
User deprivation: adequate measure for target selection
Prioritisation of latest data optimises delays
2/24/2019

29. Perspectives
Networking becomes content-centric as opposed to location-centric
Van Jacobson’ CCN proposal
P2P file download and VoD
Expectations:
leverage any free computing resources
wherever located
The Internet Computer era: “Cloud and Crowd”
Need novel schemes for managing Internet resources
VoD, Backup [bandwidth & memory]
Distributed computing [CPU & GPU]
2/24/2019

30. Perspectives Lazy content replication / cache management
 promising in homogeneous scenarios, with bandwidth bottleneck at access
Extensions to heterogeneous scenarios, multiple bottlenecks
Light-weight schemes for “NUM”-compliant P2P live streaming
finer performance control (beyond “first order”) for both live streaming and VoD
2/24/2019

31. Question time!
2/24/2019