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Charge-Sensitive TCP and Rate Control . Richard J. La Department of EECS UC Berkeley November 22, 1999. Motivation. Network users have a great deal of freedom as to how they can share the available bandwidth in the network

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charge sensitive tcp and rate control

Charge-Sensitive TCP and Rate Control

Richard J. La

Department of EECS

UC Berkeley

November 22, 1999

motivation
Motivation
  • Network users have a great deal of freedom as to how they can share the available bandwidth in the network
  • The increasing complexity and size of the Internet renders centralized rate allocation impractical
    • distributed algorithm is desired
  • Two classes of flow/congestion control mechanisms
    • rate-based : directly controls the transmission rate based on feedback
    • window-based : controls the congestion window size to adjust the transmission rate and backlog
motivation3
Motivation
  • Transmission Control Protocol (TCP) does not necessarily results in a fair or efficient allocation of the available bandwidth
  • Many algorithms have been proposed to achieve fairness among the connections
  • Fairness alone may not be a suitable objective
    • most algorithms do not reflect the user utilities or preferences
    • good rate allocation should not only be fair, but should also maximize the overall utility of the users
model
Model
  • Network with a set J of links and a set I of users
model kelly
Model (Kelly)
  • system is not likely to know
  • impractical for a centralized system to compute and allocate the user rates
background kelly s work
Background (Kelly’s work)
  • One can always find vectors and such that

1) solves for all

2) solves

3)

4) is the unique solution to

fairness
Fairness
  • Max-min fairness :
    • a user’s rate cannot be increased without decreasing the rate of another user who is already receiving a smaller rate
    • gives an absolute priority to the users with smaller rates
  • (weighted) proportional fairness :
    • is weighted proportionally fair with weight vector if is feasible and for any other feasible vector
fluid model mo walrand10
Fluid Model (Mo & Walrand)
  • Theorem 1 (Mo & Walrand) : For all w there exists a uniquex that satisfies the constraints (1)-(4)
    • this theorem tells us that the rate vector is a well defined function of the window sizes w.
    • denote the function by x(w)
    • x(w) is continuous and differentiable at an interior point
    • q(w) may not be unique, but the sum of the queuing delay along any route is well defined
mo walrand s algorithm
Mo & Walrand’s Algorithm
  • (p, 1)-proportionally fair algorithm :

where

mo walrand s algorithm12
Mo & Walrand’s Algorithm
  • Theorem 2 (Mo & Walrand) :The window sizes converge to a unique point w*such that for all

Further, the resulting rate at the unique stable point w*is weighted proportionally fair that solves NETWOKR(A, C ; p).

pricing scheme
Pricing Scheme
  • Price per unit flow at a switch is the queuing delay at the switch, i.e.,
    • the total price per unit flow of user i is given by

where is connection i’s queue size at resource j

user optimization assumption
User Optimization & Assumption
  • User optimization problem :

where is the price per unit flow, which is the queuing delay

  • Assumption 1 : The optimal price

is a decreasing function of .

price updating rule
Price Updating Rule
  • At time t, each user i updates its price according to
price updating rule17
Price Updating Rule
  • Define a mapping to be
  • Fixed point of the mapping T is a vector p such that T(p) = p.
  • Theorem : There exists a unique fixed point p* of the mapping T, and the resulting rate allocation from p* is the optimal rate allocation x* that solves SYSTEM(U,A,C).
algorithm i
Algorithm I
  • Suppose that users update their prices according to
  • Assumption 2 : There exists M > 0 such that

(a) for all p such that

(b) for allpsuch that

convergence in single bottleneck case
Convergence in Single Bottleneck Case
  • Theorem : Under the assumptions 1 and 2, the user prices p(n) converges to the unique fixed point of the mapping T under both Jacobi and the totally asynchronous update schemes as .
algorithm ii
Algorithm II
  • Suppose that users update their window sizes according to

where

assumption convergence
Assumption & Convergence
  • Assumption 3: The utility functions satisfy

where

  • Theorem : Under assumption 3, the window sizes converge to a unique stable point of the algorithm II, where the resulting rates solve SYSTEM(U,A,C).
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