Congestion Avoidance

Richard T. B. Ma

School of Computing

National University of Singapore

CS 5229: Advanced Compute Networks

References

K. K. Ramakrishnan, Raj Jain, “A Binary Feedback Scheme for Congestion Avoidance in Computer Networks with a Connectionless Network Layer”, ACM Computer Communication Review, Vol. 18, No. 4, August 1988, pp. 303-313.

Congestion Collapse

When: October 1986

Where: Lawrence Berkeley Laboratory (LBL) to UC Berkeley site, 400 yards and 3 hops away

What: Throughput dropped from 32 Kbps to 40bps

Network Congestion

Dest

Source

Source

Router

1.5-Mbps T1 link

Congestion in a packet-switched network

Flow Control VS Congestion Control

End-to-end flow control looks at “selfish” control function Make sure sufficient buffer at destination

𝑅𝑐𝑣𝑊𝑖𝑛𝑑𝑜𝑤 = 𝑅𝑐𝑣𝐵𝑢𝑓𝑓𝑒𝑟 – (𝐿𝑎𝑠𝑡𝐵𝑦𝑡𝑒𝑅𝑐𝑣𝑑 − 𝐿𝑎𝑠𝑡𝐵𝑦𝑡𝑒𝑅𝑒𝑎𝑑)

Congestion control solves a “social” problem Logical links of network cooperate to

avoid/recover from congestion of the intermediate nodes they share

Congestion Avoidance/Control

Congestion control: Detect and reduce load from the “Cliff”

Congestion avoidance: Operate network at the “Knee”

Connectionless Flows

Dest1

Source

Source

Router

Multiple flows passing through a set of routers

Source

Dest2

Router

Router

DECbit Scheme: 1-bit Feedback

Minimum feedback information One congestion avoidance bit

Set by the router if congested

Destination send it back in ACK

When does the router set avoidance bit?

What does an end-host respond?

0 1

1

Congestion Avoidance Bit

Optimization Criteria (Metrics)

Efficiency Maximize “Power”

𝑃𝑜𝑤𝑒𝑟 ≝ 𝑇𝑕𝑟𝑜𝑢𝑔𝑕𝑝𝑢𝑡𝛼

𝑅𝑒𝑠𝑝𝑜𝑛𝑠𝑒 𝑇𝑖𝑚𝑒, 0 < 𝛼 < 1.

Operate at “Knee” when maximizing for 𝛼 = 1

𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 ≝ 𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒 𝑃𝑜𝑤𝑒𝑟

𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒 𝑃𝑜𝑤𝑒𝑟 𝑎𝑡 𝐾𝑛𝑒𝑒

Less than 100% efficiency can happen when • Underutilize capacity (low throughput)

• Overutilize capacity (high response time)

Optimization Criteria (Metrics)

Fairness Maximize Jain‟s index

𝐽 𝑥 = 𝑥𝑖𝑛𝑖=1

2

𝑛 𝑥𝑖2𝑛

𝑖=1

𝑥𝑖 denotes 𝑖„s resource share, absolute or %

𝐽 𝑥 ∈ 0,1

Independent of scale

Continuous

𝐽 𝑥 = 𝑘/𝑛 if only k users are allocated equally

Optimization Criteria (Metrics)

Distributedness Only depends congestion avoidance bit

End-hosts control independently

Convergence Responsiveness

Smoothness

Congestion Detection at Router

Assumption: single server FIFO type

Metrics: 1) utilization 𝜌, 2) # of users 𝐿

Packet size distribution determine service time distribution

When packet size varies a lot, utilization 𝜌 is not a good measure of congestion

𝐿 is used instead to measure congestion

Hysteresis algorithm

Two thresholds 0 < 𝑇1 < 𝑇2 Set congestion signal when 𝐿 > 𝑇2

Unset congestion signal when 𝐿 < 𝑇1

Equivalently, the algorithm maintains a center 𝐶 and width 𝐾 such that 𝑇1 = 𝐶 − 𝐾 and 𝑇2 = 𝐶 + 𝐾

Power is maximized (in experiment) with 𝐶 = 1 and 𝐾 = 0 (or 𝑇1 = 𝑇2 = 1)

Set congestion avoidance bit when 𝐿 ≥ 1

Feedback Filter at Router

Do not use instantaneous value of 𝐿(𝑡)

Average over time interval 𝑇

Using last (busy + idle) cycle time plus the busy period of the current cycle

User Policy: Decision Frequency

Update after each acknowledgement

Update after receiving 𝑊𝑝 +𝑊𝑐 packets 𝑊𝑝 and 𝑊𝑐 are the

previous & current window sizes

User Policy: Signal Filtering

Use of Received Information Only the most recent 𝑊𝑐 packets are examined

Drop old information (𝑊𝑝 packets) after update

Signal Filtering Reduce 𝑊𝑐 if more than 50% of the bits are set

Increase 𝑊𝑐 otherwise

Why do we use 50% as a cutting point?

User Policy: Signal Filtering

For M/M/1, power =Throughput

𝑅𝑇𝑇≈

1/𝜇

E 𝐷=

1−𝜌

𝜌

Max power is attained at 𝜌∗ = 0.5

At the optimum, 𝜋0∗ = 1 − 𝜌∗ = 0.5 and 𝜋𝑖

∗ =𝜋0∗𝜌𝑖 = 0.5𝑖+1

If use a threshold 𝐶 to set congestion bit At the optimum operating point ⇒ P∗ bit set = 1 − 𝜋0

∗ − 𝜋1∗ −⋯− 𝜋𝐶−1

∗

If more than P∗ bit set × 𝑊𝑐 packets are set, system is overutilized; otherwise, it is underutilized.

User Policy: Signal Filtering

Use of Received Information Only the most recent 𝑊𝑐 packets are examined

Drop old information (𝑊𝑝 packets) after update

Signal Filtering Reduce 𝑊𝑐 if more than 50% of the bits are set

Increase 𝑊𝑐 otherwise

Decision Function How much to increase/decrease?

Decision Function Requirements

Achieve efficiency (high resource power)

Achieve fairness (high Jain‟s index)

Minimize oscillations

Minimize convergence time

Decision Function Choices

1. Additive increase additive decrease (AIAD) ↑: 𝑊𝑐

𝑖 = 𝑊𝑝𝑖 + 𝑏; ↓: 𝑊𝑐

𝑖 = 𝑊𝑝𝑖 − 𝑑

2. Additive increase multiplicative decrease (AIMD) ↑: 𝑊𝑐

𝑖 = 𝑊𝑝𝑖 + 𝑏; ↓: 𝑊𝑐

𝑖 = 𝑑𝑊𝑝𝑖

3. Multiplicative increase additive decrease (MIAD) ↑: 𝑊𝑐

𝑖 = 𝑏𝑊𝑝𝑖; ↓: 𝑊𝑐

𝑖 = 𝑊𝑝𝑖 − 𝑑

4. Multiplicative increase and decrease (MIMD) ↑: 𝑊𝑐

𝑖 = 𝑏𝑊𝑝𝑖; ↓: 𝑊𝑐

𝑖 = 𝑑𝑊𝑝𝑖

References

Dah Ming Chiu and Raj Jain, “Analysis of the Increase and Decrease Algorithms for Congestion Avoidance in Computer Networks”, Computer Networks and ISDN Systems, 1989, Vol. 17, pp. 1-14.

Synchronous Feedback Model

Feedback control loop is synchronous

Congestion state is determined by the number of packets in the system

Single bottleneck

Binary feedback

Distributed Linear Control

Each user 𝑖 adjust the window size 𝑥𝑖 as a function of feedback

𝑥𝑖 𝑡 + 1 = 𝑎𝐼 + 𝑏𝐼𝑥𝑖(𝑡) 𝑖𝑓 𝑦 𝑡 = 0

𝑎𝐷 + 𝑏𝐷𝑥𝑖(𝑡) 𝑖𝑓 𝑦 𝑡 = 1

Decision on the values of 𝑎𝐼, 𝑎𝐷, 𝑏𝐼 and 𝑏𝐷. AIAD: 𝑎𝐼 > 0 > 𝑎𝐷; 𝑏𝐼 = 𝑏𝐷 = 1.

AIMD: 𝑎𝐼 > 0; 0 < 𝑏𝐷 < 𝑏𝐼 = 1.

MIAD: 𝑎𝐷 < 0; 𝑏𝐷 = 1 < 𝑏𝐼 .

MIMD: 0 < 𝑏𝐷 < 1 < 𝑏𝐼 .

Pictorial Explanation/Intuition

Additive Movement

Multiplicative Movement

AIMD Works

AIAD Not Fair (so as MIMD)

Efficiency Convergence

Fairness Convergence

Conclusion: Decrease must be multiplicative in order to achieve fairness and efficiency.

Increase Fairness & Efficiency

Conclusion: Optimal increase is additive in order to achieve fairness and efficiency.

Decision Function Choices

1. Additive increase additive decrease (AIAD) ↑: 𝑊𝑐

𝑖 = 𝑊𝑝𝑖 + 𝑏; ↓: 𝑊𝑐

𝑖 = 𝑊𝑝𝑖 − 𝑑

2. Additive increase multiplicative decrease (AIMD) ↑: 𝑊𝑐

𝑖 = 𝑊𝑝𝑖 + 𝑏; ↓: 𝑊𝑐

𝑖 = 𝑑𝑊𝑝𝑖

3. Multiplicative increase additive decrease (MIAD) ↑: 𝑊𝑐

𝑖 = 𝑏𝑊𝑝𝑖; ↓: 𝑊𝑐

𝑖 = 𝑊𝑝𝑖 − 𝑑

4. Multiplicative increase and decrease (MIMD) ↑: 𝑊𝑐

𝑖 = 𝑏𝑊𝑝𝑖; ↓: 𝑊𝑐

𝑖 = 𝑑𝑊𝑝𝑖

Optimal Convergence To

Efficiency 𝑡𝑒 : time to convergence

Responsiveness improved with large increase/decreases parameters

𝑠𝑒 : oscillation size

Smoothness improved with small increase/decreases parameters

Fairness AIMD is the optimal mechanism

that convergences to fairness

Buffer Management

Buffer over-flow under congestion When to drop packets?

Which packets to drop?

Dest

Source

Source

Router

1.5-Mbps T1 link

References

Sally Floyd and Van Jacobson, “Random Early Detection Gateway for Congestion Avoidance”, IEEE/ACM Transactions on Networking, Vol. 1 No. 4, August 1993.

Congestion Avoidance

“Default” mechanism: FIFO, droptail Congestion can be detected after packet drop

Induce long queues and queueing delays

Main Goal and desirable objectives Provide congestion avoidance by controlling the

average queue length

High throughput and low delay

Routers can detect congestion better Distinguish propagation and queueing delay

Random Early Detection (RED)

Does not assume cooperative end hosts, and provide probabilistic fairness to flows

General buffer management scheme that can be used with other congestion control mechanisms, e.g. TCP, scheduling mechanisms, e.g. FIFO, priority queueing.

Does not require all routers in the Internet to implement in order for RED to work (incremental deployment is possible)

Avoid global synchronization

RED VS DECbit

Computing average queue size DECbit: last (busy+idle) cycle + current busy

cycle for averaging queue size

RED: time-based exponential decay

Notifying congestion DECbit: no separation of detection and marking,

biased against bursty traffic

RED: randomized marking, avoid global synchronization

RED Algorithm (high-level)

For each packet arrival

calculate the average queue size 𝑎𝑣𝑔

𝑖𝑓 𝑡𝑚𝑖𝑛≤ 𝑎𝑣𝑔 < 𝑡𝑚𝑎𝑥

calculate probability 𝑝𝑎

mark the arriving packet with probability 𝑝𝑎

𝑒𝑙𝑠𝑒 𝑖𝑓 𝑡𝑚𝑎𝑥 ≤ 𝑎𝑣𝑔

mark the arriving packet

RED Active Queue Management

𝑝 𝑥 =

0, 0 ≤ 𝑥 < 𝑡𝑚𝑖𝑛

𝑥 − 𝑡𝑚𝑖𝑛

𝑡𝑚𝑎𝑥 − 𝑡𝑚𝑖𝑛𝑝𝑚𝑎𝑥 , 𝑡𝑚𝑖𝑛 ≤ 𝑥 ≤ 𝑡𝑚𝑎𝑥

1, 𝑡𝑚𝑎𝑥 < 𝑥

𝒕𝒎𝒊𝒏 𝒕𝒎𝒂𝒙

𝒑𝒎𝒂𝒙

1

0

RED Algorithm (part 1)

Initialization: a𝑣𝑔 = 0; 𝑐𝑜𝑢𝑛𝑡 = −1;

for each packet arrival

calculate the average queue size 𝑎𝑣𝑔:

𝑖𝑓 𝑞𝑢𝑒𝑢𝑒 𝑖𝑠 𝑛𝑜𝑛𝑒𝑚𝑝𝑡𝑦: 𝑎𝑣𝑔 = 1 − 𝑤𝑞 𝑎𝑣𝑔 + 𝑤𝑞𝑞

𝑒𝑙𝑠𝑒: 𝑚 = 𝑓 𝑡𝑖𝑚𝑒 − 𝑞_𝑡𝑖𝑚𝑒 ;

𝑎𝑣𝑔 = 1 − 𝑤𝑞𝑚𝑎𝑣𝑔

RED Algorithm (part2)

𝑖𝑓 𝑡𝑚𝑖𝑛≤ 𝑎𝑣𝑔 < 𝑡𝑚𝑎𝑥

𝑐𝑜𝑢𝑛𝑡 = 𝑐𝑜𝑢𝑛𝑡 + 1;

calculate probability 𝑝𝑎:

𝑝𝑏 = 𝑝𝑚𝑎𝑥(𝑎𝑣𝑔 − 𝑡𝑚𝑖𝑛)/(𝑡𝑚𝑎𝑥 − 𝑡𝑚𝑖𝑛);

𝑝𝑎 = 𝑝𝑏/(1 − 𝑐𝑜𝑢𝑛𝑡 × 𝑝𝑏);

with probability 𝑝𝑎:

mark the arriving packet; 𝑐𝑜𝑢𝑛𝑡 = 0;

𝑒𝑙𝑠𝑒 𝑖𝑓 𝑡𝑚𝑎𝑥 ≤ 𝑎𝑣𝑔

mark the arriving packet; 𝑐𝑜𝑢𝑛𝑡 = 0;

𝑒𝑙𝑠𝑒 𝑐𝑜𝑢𝑛𝑡 = −1;

When queue becomes empty: 𝑞_𝑡𝑖𝑚𝑒 = 𝑡𝑖𝑚𝑒

Relationship between 𝑝𝑎 and 𝑝𝑏

𝑝𝑎 = 𝑝𝑏/(1 − 𝑐𝑜𝑢𝑛𝑡 × 𝑝𝑏)

𝑝𝑎 increases slowly with 𝑐𝑜𝑢𝑛𝑡

Ensure that the router does not wait too long before marking a packet

Make inter-dropping time uniform

Relationship between 𝑝𝑎 and 𝑝𝑏

Use 𝑝𝑏 as the final dropping probability Inter-dropping time 𝑇𝑏 is geometric

Prob 𝑇𝑏 = 𝑛 = 1 − 𝑝𝑏𝑛−1𝑝𝑏; E 𝑇𝑏 = 1/𝑝𝑏

More desirable to have uniform distribution

Use 𝑝𝑎 as the final dropping probability

Prob 𝑇𝑎 = 𝑛

=

𝑝𝑏1 − 𝑛 − 1 𝑝𝑏

1−𝑝𝑏

1 − 𝑖𝑝𝑏

𝑛−2

𝑖=0= 𝑝𝑏 1 ≤ 𝑛 ≤ 1/𝑝𝑏

0 𝑛 > 1/𝑝𝑏

E 𝑇𝑎 =1

2𝑝𝑏+1

2

How About TCP?

How to control congestion window sizes?

How to infer congestion?

Why and how to estimate and smooth RTT?

What is Slow Start? Why do we need it?

Retransmit timer back-off policy

Acknowledgement sending policy

References

Van Jacobson, “Congestion Avoidance and Control”, ACM Computer Communication Review Vol. 18, No. 4, August 1988, pp. 314-329.