Constant gain controller for active queue management
View Patent ↗Various techniques for queue management based on random early detection (RED) are disclosed herein. In particular, a method for generating a drop probability for an incoming packet in a device having a queue to buffer packets between segments of a network is provided. The method comprises determining, upon receipt of an incoming packet, a size of the queue and determining an error based at least in part on a difference between the queue size and a threshold. The method further comprises determining a drop probability for the incoming packet based at least in part on the error and a constant gain factor. The constant gain factor may be based at least in part on a linearized second order dynamic model of the network.
1. In a device having a queue to buffer packets between segments of a network, a method for generating a drop probability for an incoming packet comprising:
receiving an incoming packet;
determining, upon receipt of the incoming packet, a size of the queue;
determining an error based at least in part on a difference between the queue size and a threshold; and
generating a drop probability for the incoming packet based at least in part on the error and a constant gain factor.
2. The method as in claim 1 , further comprising filtering the queue size using an exponentially weighted moving average (EWMA) filter to generate a filtered queue size and wherein the error is determined based on a difference between the filtered queue size and the threshold.
3. The method as in claim 2 , wherein the queue size is filtered based on the equation:
{circumflex over (q)} ( n )=(1−β) {circumflex over (q)} ( n− 1)+β q ( n )
where q(n) represents the queue size, {circumflex over (q)}(n) represents the filtered queue size at a current time instant, {circumflex over (q)}(n−1) represents a filtered queue size of a previous time instant and β represents a filter gain value between 0 and 1.
4. The method as in claim 1 , wherein the drop probability is determined based on an equation:
P d ( n )=min[max(− k c e ( n ),0),θ]
where P d (n) represents the drop probability for the incoming packet, e(n) represents the error, k c represents the constant gain factor and θ represents a value between 0 and 1.
5. The method as in claim 1 , wherein the constant gain factor is selected from a range of values:
-
2
N
(
R
0
C
+
2
N
)
z
1
(
R
0
C
)
3
sin
(
z
1
)
<
k
c
<
4
N
2
(
R
0
C
)
3
where N represents a number of connections to the network device, C represents a link capacity of the network, R 0 represents a round trip time of a packet in the network, and z 1 represents a solution to
cot
(
z
1
)
=
z
1
2
-
2
N
/
R
0
C
z
1
(
R
0
C
+
2
N
)
/
R
0
C
such that z 1 ε(0,π).
6. The method as in claim 1 , wherein the constant gain factor is selected from a range of values:
max
j
=
od
,
od
+
2
{
-
2
N
(
R
0
C
+
2
N
)
z
j
(
R
0
C
)
3
sin
(
z
j
)
}
<
k
c
<
min
j
=
ev
,
ev
+
2
{
-
2
N
(
R
0
C
+
2
N
)
z
j
(
R
0
C
)
3
sin
(
z
j
)
}
where N represents a number of connections to the network device, C represents a link capacity of the network, R 0 represents a round trip time of a packet in the network, z j is a solution of the equation
cot
(
z
)
=
z
2
-
2
N
/
R
0
C
z
(
R
0
C
+
2
N
)
/
R
0
C
in the interval ((j−1)π,jπ); od is an odd natural number defined as
od
=
arg
min
j
odd
{
z
min
-
z
j
}
subject to z min −z j ≧0, and ev is an even natural number or zero defined as
ev
=
arg
min
j
even
{
z
min
-
z
j
}
subject to z min −z j ≧0 and
z
min
=
R
0
2
N
R
0
3
C
-
(
R0C
+
2
N
R
0
2
C
)
2
2
.
7. The method as in claim 1 , wherein the drop probability is implemented in an active queue management (AQM) mechanism to manage the queue.
8. The method as in claim 1 , wherein the network includes a Transport Control protocol (TCP)-based network.
9. The method as in claim 1 , wherein the constant gain factor is based at least in part on a linearized second order dynamic model of the network.
10. At least one processor readable medium for storing a computer program of instructions configured to be readable by at least one processor for instructing the at least one processor to execute a computer process for performing the method as in claim 1 .
11. In a device having a queue to buffer packets between segments of a network, a method for managing the queue comprising:
generating, for an incoming packet, a drop probability based at least in part on a linearized second order dynamic model of the network;
comparing the drop probability with a random probability; and
dropping the incoming packet when the drop probability is less than or equal to the random probability.
12. The method as in claim 11 , wherein the drop probability is determined based on an equation:
P d ( n )=min[max(− k c e ( n ),0),θ]
where P d (n) represents the drop probability for the incoming packet, e(n) represents an error between a size of the queue and a threshold, θ represents a value between 0 and 1, and k c represents a constant gain factor based at least in part on the linearized second order dynamic model.
13. The method as in claim 12 , wherein the constant gain factor is selected from a range of values:
-
2
N
(
R
0
C
+
2
N
)
z
1
(
R
0
C
)
3
sin
(
z
1
)
<
k
c
<
4
N
2
(
R
0
C
)
3
where N represents a number of connections to the network device, C represents a link capacity of the network, R 0 represents a round trip time of a packet in the network, and z 1 represents a solution to
cot
(
z
1
)
=
z
1
2
-
2
N
/
R
0
C
z
1
(
R
0
C
+
2
N
)
/
R
0
C
such that z 1 ε(0,π).
14. The method as in claim 12 , wherein the constant gain factor is selected from a range of values:
max
j
=
od
,
od
+
2
{
-
2
N
(
R
0
C
+
2
N
)
z
j
(
R
0
C
)
3
sin
(
z
j
)
}
<
k
c
<
min
j
=
ev
,
ev
+
2
{
-
2
N
(
R
0
C
+
2
N
)
z
j
(
R
0
C
)
3
sin
(
z
j
)
}
where N represents a number of connections to the network device, C represents a link capacity of the network, R 0 represents a round trip time of a packet in the network, z j is a solution of the equation
cot
(
z
)
=
z
2
-
2
N
/
R
0
C
z
(
R
0
C
+
2
N
)
/
R
0
C
in the interval ((j−1)π,jπ); od is an odd natural number defined as
od
=
arg
min
j
odd
{
z
min
-
z
j
}
subject to z min −z j ≧0, and ev is an even natural number or zero defined as
ev
=
arg
min
j
even
{
z
min
-
z
j
}
subject to z min −z j ≧0 and
z
min
=
R
0
2
N
R
0
3
C
-
(
R0C
+
2
N
R
0
2
C
)
2
2
.
15. The method as in claim 11 , wherein the network includes a Transport Control Protocol (TCP)-based network.
16. At least one processor readable medium for storing a computer program of instructions configured to be readable by at least one processor for instructing the at least one processor to execute a computer process for performing the method as in claim 11 .
17. In a device having a queue to buffer packets between segments of a network, a queue management apparatus comprising:
a packet drop controller configured to determine a drop probability for an incoming packet based at least in part on an error between a size of the queue and a threshold and a constant gain factor; and
an add/drop module operably connected to the queue controller and is configured to drop the incoming packet when the drop probability is less than or equal to a random probability.
18. The queue management apparatus as in claim 17 , wherein the drop probability is determined based on an equation:
P d ( n )=min[max(− k c e ( n ),0),θ]
where P d (n) represents the drop probability for the incoming packet, e(n) represents the error between a size of the queue and a threshold, θ represents a value between 0 and 1, and k c represents the constant gain factor.
19. The queue management apparatus as in claim 17 , wherein the constant gain factor is selected from a range of values:
-
2
N
(
R
0
C
+
2
N
)
z
1
(
R
0
C
)
3
sin
(
z
1
)
<
k
c
<
4
N
2
(
R
0
C
)
3
where N represents a number of connections to the network device, C represents a link capacity of the network, R 0 represents a round trip time of a packet in the network, and z 1 represents a solution to
cot
(
z
1
)
=
z
1
2
-
2
N
/
R
0
C
z
1
(
R
0
C
+
2
N
)
/
R
0
C
such that z 1 ε(0,π).
20. The queue management apparatus as in claim 17 , wherein the constant gain factor is selected from a range of values:
max
j
=
od
,
od
+
2
{
-
2
N
(
R
0
C
+
2
N
)
z
j
(
R
0
C
)
3
sin
(
z
j
)
}
<
k
c
<
min
j
=
ev
,
ev
+
2
{
-
2
N
(
R
0
C
+
2
N
)
z
j
(
R
0
C
)
3
sin
(
z
j
)
}
where N represents a number of connections to the network device, C represents a link capacity of the network, R 0 represents a round trip time of a packet in the network, z j is a solution of the equation
cot
(
z
)
=
z
2
-
2
N
/
R
0
C
z
(
R
0
C
+
2
N
)
/
R
0
C
in the interval ((j−1)π,jπ); od is an odd natural number defined as
od
=
arg
min
j
odd
{
z
min
-
z
j
}
subject to z min −z j ≧0, and ev is an even natural number or zero defined as
ev
=
arg
min
j
even
{
z
min
-
z
j
}
subject to z min −z j ≧0 and
z
min
=
R
0
2
N
R
0
3
C
-
(
R0C
+
2
N
R
0
2
C
)
2
2
.
21. The queue management apparatus as in claim 17 , wherein the network includes a Transport Control protocol (TCP)-based network.
22. The queue management apparatus as in claim 17 , wherein the constant gain factor is based at least in part on a linearized second order dynamic model of the network.