- Recall that we must find answer to two questions
to develop a congestion control method:
- How to detect
congestion
- How fast do you change transmission rate when you detect congestion/no congestion
- How to detect
congestion
- When have looked at the first question
- The second question has been studied extensively by Raj Jain and this web page is based on his paper: click here
- Assume you have a way to obtain a binary
congestion indication signal from the network:
- congestion indication = 0 means
no congestion
- congestion indication = 1 means congestion
- congestion indication = 0 means
no congestion
- The next important question in the design of the congestion avoidance
method is:
- How fast
do you decrease the transmission rate
if there is congestion
- How fast do you increase the transmission rate if there is no congestion
- How fast
do you decrease the transmission rate
if there is congestion
-
Important considerations
in the design
of the congestion control method:
- The congestion control method
must be fair:
- Ideally, each sender should obtain the same amount of bandwidth (transmission rate) for its use
- The congestion control method
must be stable:
- The method should
converge to a stable state
(An unstable system wil fluctuate erratically (swings wildly)
- The method should
converge to a stable state
- Other design criteria could include "efficiency" and "distributed" (no central node that makes the allocation decisions)
- The congestion control method
must be fair:
- The following material is taken from:
- Raj Jain paper: "Analysis of the Increase and Decrease Algorithms for Congestion Avoidance in Computer Networks" - click here
- Linear function: is a line
y = a x + b
- Definitions:
-
x(t)
be the current transmission data rate
- x(t+1) be the transmission data rate after the rate adjustment (made according to the congestion indication)
-
x(t)
be the current transmission data rate
- Jain has studied the use of
linear increases/decreases
in congestion control
I.e., the change in transmission rate is a linear function
Linear increase/decrease congestion control:
- If
congestion indication = 0 (no congestion), then:
x(t+1) = Aincrease + Bincrease * x(t)
where Aincrease and Bincrease are constant (that will make x(t+1) less than x(t)).
- If
congestion indication = 1 (congestion),
then:
x(t+1) = Adecrease + Bdecrease * x(t)
where Adecrease and Bdecrease are constant (that will make x(t+1) greater than x(t)).
- If
congestion indication = 0 (no congestion), then:
- Additive increase/decrease and
multiplicative increase/decrease
are special cases
of
linear increase/decrease function
- Additive increase/decrease:
x(t+1) = x(t) + Aincrease (Aincrease > 0) x(t+1) = x(t) + Adecrease (Adecrease < 0)
- Multiplicative increase/decrease:
x(t+1) = Bincrease * x(t) (Bincrease > 1) x(t+1) = Bdecrease * x(t) (Bdecrease < 1)
- Jain has mainly focused on these two congestion control technqiues in his paper
- The behavior
of the congestion control mechanism is
understood clearly
by studying the
behavior of only two connections
that share a bottle neck router:
- Assumptions:
- The capacity of the
bottleneck router
is B (bps)
- User 1
transmits with a data rate
U1 (bps)
- User 2
transmits with a data rate
U2 (bps)
- User 1's and user 2's
share a common buffer
in the bottleneck router
- The bottleneck router
will report the same feedback
to both users
I.e.:
- If the bottleneck router is congested (and drops packets), then packets from both streams are dropped
- The capacity of the
bottleneck router
is B (bps)
- Representation of the network state:
Notes on the above figure:
- X-axis represents
User 1's transmission data rate
U1
- Y-axis represents
User 2's transmission data rate
U2
- A point in the grid
represents a certain
transmission state
of the two users.
Example:
- The point A in the figure represents the event that user 1 is transmitting at a data rate U1 = x and user 2 is transmitting at a data rate U2 = y
- The red line in the
figure represent
all operational points
where user 1 and 2 collectively
are transmitted at network capacity
B
- The magenta line represent
all operational points
where
user 1 and 2 transmits with the
same data rate
(i.e., fair !)
- X-axis represents
User 1's transmission data rate
U1
- The 4 operational quadrants:
Quandrants A, B, C and D:
- Points in the
A quadrant are such that:
- Total transmission data rate
is less than the
capacity of network
(i.e., not congested)
- Data rate of user 2 is larger than data rate of user 1
- Total transmission data rate
is less than the
capacity of network
(i.e., not congested)
- Points in the
B quadrant are such that:
- Total transmission data rate
is less than the
capacity of network
(i.e., not congested)
- Data rate of user 1 is larger than data rate of user 2
- Total transmission data rate
is less than the
capacity of network
(i.e., not congested)
- Points in the
C quadrant are such that:
- Total transmission data rate
is greater than the
capacity of network
(i.e., congestion !!!)
- Data rate of user 2 is larger than data rate of user 1
- Total transmission data rate
is greater than the
capacity of network
(i.e., congestion !!!)
- Points in the
D quadrant are such that:
- Total transmission data rate
is greater than the
capacity of network
(i.e., congestion !!!)
- Data rate of user 1 is larger than data rate of user 2
- Total transmission data rate
is greater than the
capacity of network
(i.e., congestion !!!)
- Points in the
A quadrant are such that:
- Quandrants A and B:
- The the system is operating in the
quadrants A
or
quandrant B,
users 1 and 2 will
receive
the congestion = 0
(not congested)
signal
- Correspondingly, both users will increase their data rate.
- The the system is operating in the
quadrants A
or
quandrant B,
users 1 and 2 will
receive
the congestion = 0
(not congested)
signal
- Quandrants C and D:
- The the system is operating in the
quadrants A
or
quandrant B,
users 1 and 2 will
receive
the congestion = 1
(congested)
signal
- Correspondingly, both users will decrease their data rate.
- The the system is operating in the
quadrants A
or
quandrant B,
users 1 and 2 will
receive
the congestion = 1
(congested)
signal
- Suppose before the rate adjustment,
user 1's data rate
is x and
user 2's data rate
is y
- Because both users
will receive the
same congestion indication
- Data rates
after a
rate increase:
- User 1: x + a
- User 2: y + a
- Data rates
after a
rate decrease:
- User 1: x − a
- User 2: y − a
- The following figure show the
effect of
the additive
increase/decrease method
to adjust the transmission data rates:
- Data rates
after a
rate increase:
- User 1: b × x
- User 2: b × y
- Data rates
after a
rate decrease:
- User 1: x / b
- User 2: y / b
- The following figure show the effect
when
the congestion control uses an
multiplicative invrease/decrease
method
to adjust the transmission data rate:
-
The following figure shows the behavior of the ideal
congestion control method:
Notes:
- Starting from any operatinal point, the system moves
towards the ideally fair and maximum throughput point.
- The amplitude of the "swings" decreases monotonically
(this signals stability - if the swings becomes
larger, convergence is not guarantee !)
- The amplitude of the swings should decrease rapidly
- Starting from any operatinal point, the system moves
towards the ideally fair and maximum throughput point.
-
The following figure shows the effect of the
"additive increase and
additive decrease" method:
Conclusion:
- Method does not converge !!!
-
The following figure shows the effect of the
"multiplicative increase
and multiplicative decrease" method:
Conclusion:
- Method does not converge !!!
-
The following figure shows the effect of the
"multiplicative increase
and additive decrease" method:
Conclusion:
- Method diverges away from the ideal point !!!
-
The following figure shows the effect of the
"additive increase and
multiplicative decrease" method:
Conlusion:
- Bingo !!!
Method moves towards the ideal point !!!
- Bingo !!!
- The additive increase and multiplicative decrease scheme will move the system towards a stable and fair equilibrium.
- Raj Jain's theory has held up for over 20 years.
- In Raj's days, network speed wehere around 100Kbps, at most 1Mbps
- Things has changed quite a bit, we have networks with speeds
above 1Tbps (1,000,000,000,000 bps).
- In high speed networks,
additive increase is
TOO SLOW
to allow the sender to fully utilize all the network capacity.
- Recent network research is proposing to use
multiplicative increase
and
multiplicative decrease
to control congestion.
The factor used in multiplicative decrease is different (it is larger) than the one used in the multiplicative increase