Title: Analysis of the Increase and Decrease Algorithms for Congestion Avoidance in Computer Networks
1Analysis of the Increase and Decrease Algorithms
for Congestion Avoidance in Computer Networks
- Dah-Ming Chiu and Raj Jain
- Presented by Yao Zhao
2Motivation (1)
- Internet is heterogeneous
- Different bandwidth of links
- Different load from users
- Congestion control
- Help improve performance after congestion has
occurred - Congestion avoidance
- Keep the network operating off the congestion
3Motivation (2)
- Fig. 1. Network performance as a function of the
load. Broken curves indicate performance with
deterministic service and interarrival times
4Relate Works
- Centralized algorithm
- Information flows to the resource managers and
the decision of how to allocate the resource is
made at the resource Sanders86 - Decentralized algorithms
- Decisions are made by users while the resources
feed information regarding current resource usage
Jaffe81, Gafni82, Mosely84 - Binary feedback signal and linear control
- Synchronized model
- What are all the possible solutions that converge
to efficient and fair states
5Control System
6Linear Control (1)
-
- 4 examples of linear control functions
- Multiplicative Increase/Multiplicative Decrease
- Additive Increase/Additive Decrease
- Additive Increase/Multiplicative Decrease
- Additive Increase/ Additive Decrease
7Linear Control (2)
- Multiplicative Increase/Multiplicative Decrease
- Additive Increase/Additive Decrease
- Additive Increase/Multiplicative Decrease
- Multiplicative Increase/ Additive Decrease
8Criteria for Selecting Controls
- Efficiency
- Closeness of the total load on the resource to
the knee point - Fairness
- Users have the equal share of bandwidth
-
- Distributedness
- Knowledge of the state of the system
- Convergence
- The speed with which the system approaches the
goal state from any starting state
9Responsiveness and Smoothness of Binary Feedback
System
- Equlibrium with oscillates around the optimal
state
10Vector Representation of the Dynamics
11Example of Multiplicative Increase/
Multiplicative Decrease Function
12Example of Additive Increase/ Multiplicative
Decrease Function
13Convergence to Efficiency
14Convergence to Fairness (1)
15Convergence to Fairness (2)
- cgt0 implies
-
- Furthermore, combined with (3) we have
-
16Distributedness
- Having no knowledge other than the feedback y(t)
- Each user tries to satisfy the negative feedback
condition by itself -
- Implies (10) to be
17Truncated Case
18Important Results
- Proposition 1 In order to satisfy the
requirements of distributed convergence to
efficiency and fairness without truncation, the
linear increase policy should always have an
additive component, and optionally it may have a
multiplicative component with the coefficient no
less than one. - Proposition 2 For the linear controls with
truncation, the increase and decrease policies
can each have both additive and multiplicative
components, satisfying the constrains in
Equations (16)
19Vectorial Representation of Feasible conditions
20Optimizing the Control Schemes
- Optimal convergence to Efficiency
- Tradeoff of time to convergent to efficiency te,
with the oscillation size, se. - Optimal convergence to Fairness
21Optimal convergence to Efficiency
-
- Given initial state X(0), the time to reach Xgoal
is
22Optimal convergence to Fairness
- Equation (7) shows faireness function is
monotonically increasing function of ca/b. - So larger values of a and smaller values b give
quicker convergence to fairness. - In strict linear control, aD0 gt fairness
remains the same at every decrease step - For increase, smaller bI results in quicker
convergence to fairness gt bI 1 to get the
quickest convergence to fairness - Proposition 3 For both feasibility and optimal
convergence to fairness, the increase policy
should be additive and the decrease policy should
be multiplicative.
23Practical Considerations
- Non-linear controls
- Delay feedback
- Utility of increased bits of feedback
- Guess the current number of users n
- Impact of asynchronous operation
24Conclusion
- We examined the user increase/decrease policies
under the constrain of binary signal feedback - We formulated a set of conditions that any
increase/decrease policy should satisfy to ensure
convergence to efficiency and fair state in a
distributed manner - We show the decrease must be multiplicative to
ensure that at every step the fairness either
increases or stays the same - We explain the conditions using a vector
representation - We show that additive increase with
multiplicative decrease is the optimal policy for
convergence to fairness