- By
**flann** - Follow User

- 121 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about 'Charge-Sensitive TCP and Rate Control' - flann

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

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

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

- Network with a set J of links and a set I of users

Model (Kelly)

- system is not likely to know
- impractical for a centralized system to compute and allocate the user rates

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

- 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 & 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

- 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

- 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 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

- At time t, each user i updates its price according to

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

- 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

- 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 .

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).

Download Presentation

Connecting to Server..