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Flow Control KAIST CS644 Advanced Topics in Networking. Jeonghoon Mo <[email protected]> School of Engineering Information and Communications University. Acknowledgements. Part of slides is from tutorial of R. Gibbens and P. Key at SIGCOMM 2000 S. Low’s OFC presentation. Overview. Problem

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flow control kaist cs644 advanced topics in networking

Flow Control KAIST CS644Advanced Topics in Networking

Jeonghoon Mo

<[email protected]>

School of Engineering

Information and Communications University

acknowledgements
Acknowledgements
  • Part of slides is from
    • tutorial of R. Gibbens and P. Key at SIGCOMM 2000
    • S. Low’s OFC presentation
overview
Overview
  • Problem
  • Objectives
  • Kelly’s Framework - Wired Data Networks
  • Extensions
    • Quality of Service
    • Wireless Network
    • High Speed Network: Aggregated Flow Control
problem
Problem

Flows share links:

How to share the links bandwidth?

problem1
Problem
  • How to control the network to share the bandwidth efficiently and fairly?
link model
Link Model
  • Set of resources, J; set of routes, R
  • A route r is a subset r J.
  • Let
  • Capacity of resource j is Cj.

A’x  c

x  0

a few system objectives
A Few System Objectives
  • Max Throughput
  • Max-min Fairness (Most Common)
  • Proportional Fairness (Kelly)
  • -Fairness (Mo, Walrand)
max system throughput
Maximize:

x(1) + x(2) + x(3)

x*= (0,6,6) maximizes the total system throughput.

However, user 1 does not get anything. => unfair

6

6

x1

x3

x2

Max System Throughput
  • Two links with capacity 6
  • Three users: 1,2,3
  • x(i) : bandwidth to user i
  • x(1)+x(2) <= 6
  • x(1)+x(3) <= 6
max min fairness
Most commonly used definition of fairness.

Maximize Minimum of the x(i), recursively.

x*= (3,3,3) is the max-min allocation.

However, user 1 uses more resources.

6

6

x1

x3

x2

Max-Min Fairness
proportional fairness

6

6

x1

x3

x2

Proportional Fairness
  • Proposed by Frank Kelly
  • Social Welfare: Sum of Utilities of Users
  • Maximize the Social Welfare
  • x*= (2,4,4) is the Proportional Fair Allocation.
  • Can be generalized into “Utility Fairness”.
fairness

x(1-)

1-

Max i pi

-Fairness
  • Generalized Fairness Definition
  • System Objective:
  • includes proportional-fair, max-min-fair, max throughput
    •  = 0 : Maximum allocation (p=1)
    •   1 : Proportional fair allocation
    •  = 2 : TCP-fair allocation
    •    : Max-min fair allocation (p=1)
fairness1
-Fairness
  • Trade-off between Fairness and Efficiency
    • Bigger  favors Fairness
    • Smaller  favors Efficiency

(source: Is Fair Allocation Inefficient, INFOCOM 04)

algorithms

Algorithms

How to achieve those system objectives?

players
Players
  • source
    • controls its rate or window based on (implicit or explicit) network feedback
  • router (link)
    • Generate (implicit) feedback or controls packets
source algorithm
Source Algorithm
  • TCP Vegas, RENO, ECN
  • XCP
active queue management aqm
Active Queue Management (AQM)
  • Priority Queue
  • WFQ
  • RED
  • REM
  • XCP Router
user rate and utility
User: rate and utility
  • Each route has a user: if xr is the rate on route r, then the utility to user r is Ur(xr).
  • Ur() --- increasing, strictly concave, continuously differentiable on xr [0 , ) --- elastic traffic
  • Let C=(Cj, j J), x=(xr, r  R) then Ax  C.
system problem
System problem
  • Maximize aggregate utility, subject to capacity constraints
user problem
User problem
  • User r chooses an amount to pay per unit time wr, and receives in return a flow xr = wr/r
network problem
Network problem
  • As if the network maximizes a logarithmic utility function, but with constants (wr, rR) chosen by the users
three optimization problems
Three optimization problems
  • SYSTEM(U,A,C)
  • USERr(Ur;r)
  • NETWORK(A,C;w)
decomposition theorem
Decomposition theorem
  • There exist vectors  , w and x such that
    • wr = rxr for r  R
    • wr solves USERr(Ur; r)
    • x solves NETWORK(A, C; w)

The vector x then also solves SYSTEM(U, A, C).

slide25
Thus the system problem may be solved by solving simultaneously the network and user problems
result
Result
  • A vector x solves NETWORK(A, C; w) if and only if it is proportionally fair per unit charge
solution of network problem
Solution of network problem
  • Strategy: design algorithms to implement proportional fairness
  • Several algorithms possible: try to mimic design choices made in existing standards
interpretation of primal algorithm
Interpretation of primal algorithm
  • Resource j generates feedback signals at rate j(t)
  • signals sent to each user r whose route passes through resource j
  • multiplicative decrease in flow xr at rate proportional to stream of feedback signals received
  • linear increase in flow xr at rate proportional to wr
related work
Related Work
  • Optimization Flow Control (S. Low)
  • Window based Model (Mo, Walrand)
optimization flow control
Optimization Flow Control
  • Distributed algorithm to share network resources
  • Link algorithm: what to feed back
    • RED
  • Source algorithm: how to react
    • TCP Tahoe, TCP Reno, TCP Vegas

Source alg

Link alg

welfare maximization
Welfare maximization

Primal problem:

  • Capacity can be less than real link capacity
  • Primal problem hard to solve & does not adapt
model

x1

c1

c2

x2

x3

Model
  • Network: Links l each of capacity cl
  • Sources s:(L(s), Us(xs), ms, Ms)

L(s) - links used by source s

Us(xs) - utility if source rate = xs

distributed solution
Distributed Solution

Dual problem:

BW price along path of s

  • Given sources can max own benefit individually
  • indeed primal optimal if is dual optimal
  • Solve dual problem!
distributed solution cont
Distributed Solution (cont…)
  • Dual problem:
  • Grad projection alg:
  • Update rule:
  • A distributed computation system to solve the dual problem by gradient projection algorithm
source algorithm1
Source Algorithm

Decentralized: Source s needs only and

router link algorithm
Router (Link) Algorithm
  • Decentralized
  • Rule of supply and demand
  • Any work-conserving service discipline
  • Simple

aggregate

source rate

random exponential marking rem
Random Exponential Marking (REM)
  • Source algorithm
    • Identical but does not communicate source rate
  • Link algorithm
    • At update time t, sets price to a fraction of buffer occupancy:
  • Theorem: Synchronous convergence
  • Under same conditions (with possibly smaller ) :
    • Price update maintains descent direction
    • Gradient estimate converge to true gradient
    • Limit point is primal-dual optimal
slide39
RED
  • Idea: early warning of congestion
  • Algorithm

Link: Source (Reno):

marking

window

1

queue

time

B

slide40

rate

fraction

of marks

1

RED
  • Idea: marks for estimation of shadow price
  • Algorithm

Link Source

Global behavior of network of REM: stochastic gradient algorithm to solve dual problem

marking

1

queue

Q

window based model mo walrand

d1

q11

q21

w1

x1

c2

c1

x3

x2

q23

q12

d2

d3

A’x  c

Q(c - A’x) = 0

w = X(d + qA)

Window-based Model [Mo,Walrand]

Q = diag{qi }; X = diag{xi }.

xi  0, i = 1, 2, 3

qi  0, i = 1, 2,

x1+x2 c1

q1(c1 - x1 - x2) = 0

w1=x1d1 + x1 q1 + x1 q2

window based algorithm
Window-based Algorithm

Theorem:[Mowlr98]

Let

dwi

si := wi - xi di - pi

di si

= - k

ti := end-to-end delay

dt

ti wi

Then x(t) -> unique weighted -fair point x*

Proof:

2

The function

(si /wi )

i

is a Lyapunov function

extensions
Extensions
  • Aggregated Flow Control
  • Quality of Service
  • Wireless Network
  • Maxnet and Sumnet
aggregate flow control
Aggregate Flow Control
  • Motivations:
    • High Capacity of Optical Fiber
  • Idea:
    • player are core routers and access routers.
      • access router: regulates the rate of aggregated flow
      • core router: provide feedbacks to access routers
quality of service
Quality of Service
  • Only bandwidth is modeled.
  • QoS is affected by
    • loss and delay also
  • How to incorporate other parameters?
non convex utility function lee04
Considered sigmoidal utility function

Non-convex optimization problem =>duality gap

Non-Convex Utility Function (Lee04)

(source: J. Lee et. al. Non-convexity Issues, INFOCOM 04)

non convex utility functions
Non-Convex Utility Functions

Dual Algorithm with

Self-Regulating Property

Without Self-Regulation

With Self-Regulation

(source: J. Lee et. al. Non-convexity Issues, INFOCOM 04)

wireless ad hoc network rad04
Wireless Ad-Hoc Network [RAD04]
  • Physical Model:Rate r is an increasing function of SINR.
  • MAC : Each time slot determines power pn,which determines rate xn
  • Routing matrix R and flow to path matrix F are given.
random topology results
Random Topology Results

100m x100m grid

12 random node, with 6 pairs of transmissions

in the wireless ad hoc networks
In the wireless Ad-hoc Networks
  • The max-min fair rate allocation of any network has all rates equal to the worst node.
  • The capacity maximization objective leads to starving users.
  • Proportional Fair Allocation give reasonable trade-off between fairness and efficiency.
    • The worst node does not starve.
maxnet and sumnet
MaxNet and SumNet
  • Source takes max(d1,d2,…, dN) in the maxnet architecture
  • Source takes sum(d1,d2,…,dN) in the sumnet architecture.
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