Method and system for generating packet delay variation with a uniform distribution
View Patent ↗Embodiments of the present invention provide packet timing recovery stress testing by generating packet delay variation (PDV) with a uniformly distributed probability density function (PDF). A delay-step method determines a delay for each packet in a stream of packets generated at a regular interval. In the delay-step method, delay-steps are determined for each packet based on delay target values. To generate PDV with a uniform PDF, the delay target values are randomly selected based on a pre-biased PDF which is a uniform distribution that is pre-biased by a pre-bias function. The pre-bias function increases the values of small delay target values so that an increased number of delay target values are at the extremes of the uniform distribution, which causes the delay-step method to result in a PDV with a uniform distribution.
1. A method for generating packet delay variation (PDV) with a uniformly distributed probability density function (PDF) for packet timing recovery stress testing of a network, comprising:
receiving, by a PDV generator, a stream of packets, each packet generated at a regular interval by a packet generator;
determining, by the PDV generator, a delay for each packet based on delay target values determined based on a pre-biased PDF comprising a uniform PDF that is pre-biased with a pre-bias transfer function; and
transmitting, by the PDV generator, each packet over the network with the delay determined for that packet,
wherein, for a uniformly distributed random number greater than or equal to zero, the pre-bias transfer function is based on an Nth root of the uniformly distributed random number, and for a uniformly distributed random number less than zero, the pre-bias transfer function is based on a negative of the Nth root of an absolute value of the uniformly distributed random number.
2. The method of claim 1 , wherein the pre-bias transfer function generates delay targets at extremes of the uniform PDF.
3. The method of claim 1 , wherein the pre-bias transfer function is an Nth root square filter.
4. The method of claim 3 , wherein a flatness of the PDV is adjustable based on a value of N.
5. The method of claim 1 , wherein the pre-bias transfer function is given by:
For
U
(
t
)
≥
0
,
B
D
(
t
)
=
U
(
t
)
N
For
U
(
t
)
<
0
,
B
D
(
t
)
=
-
1
×
U
(
t
)
N
,
and the pre-biased PDF is given by:
D total ( t )= D MIN +B D ( t )×( D MAX −D MIN ),
where B D (t) is the pre-bias transfer function, U(t) is a uniformly generated random number between +1 and −1, N is a root power of the pre-bias transfer function, D total (t) is a total delay experienced by a packet, D MAX is a maximum delay, and D MIN is a minimum delay.
6. The method of claim 1 , wherein said step of determining a delay for each packet comprises:
(a) selecting a random delay target value based on said pre-biased PDF;
(b) adjusting the delay of sequential packets in said stream of packets by delay-steps determined based on the random delay target value, until the delay of packet is equal to the random delay target value; and
(c) repeating steps (a) and (b) to determine a delay value for each packet in said stream of packets.
7. The method of claim 6 , wherein step (b) comprises for each of said sequential packets:
determining a difference between a current delay for the packet and the random delay target value;
if the difference between the current delay for the packet and the random delay target value is negative, adjusting the current delay for the packet by a delay-step determined as a uniformly distributed value between 0 and a maximum step size; and
if the difference between the current delay for the packet and the random delay target value is positive, adjusting the current delay for the packet by a delay-step determined as a uniformly distributed value between a minimum step size and 0.
8. The method of claim 6 , wherein step (b) comprises for each of said sequential packets:
determining a difference between a current delay for the packet and the random delay target value;
if the difference between the current delay for the packet and the random delay target value is negative, adjusting the current delay for the packet by a fixed positive delay-step; and
if the difference between the current delay for the packet and the random delay target value is positive, adjusting the current delay for the packet by a fixed negative delay-step.
9. A system for generating packet delay variation (PDV) with a uniformly distributed probability density function (PDF) for packet timing recovery stress testing of a network, comprising:
means for generating a stream of packets, each packet generated at a regular interval;
means for determining a delay for each packet based on delay target values determined based on a pre-biased PDF comprising a uniform PDF that is pre-biased with a pre-bias transfer function; and
means for transmitting each packet on the network with the delay determined for that packet,
wherein, for a uniformly distributed random number greater than or equal to zero, the pre-bias transfer function is based on an Nth root of the uniformly distributed random number, and for a uniformly distributed random number less than zero, the pre-bias transfer function is based on a negative of the Nth root of an absolute value of the uniformly distributed random number.
10. The system of claim 9 , wherein the pre-bias transfer function generates delay target values at extremes of the uniform PDF.
11. The system of claim 9 , wherein the pre-bias transfer function is an Nth root square filter.
12. The system of claim 11 , wherein a flatness of the PDV is adjustable based on a value of N.
13. The system of claim 9 , wherein the pre-bias transfer function is given by:
For
U
(
t
)
≥
0
,
B
D
(
t
)
=
U
(
t
)
N
For
U
(
t
)
<
0
,
B
D
(
t
)
=
-
1
×
U
(
t
)
N
,
and the pre-biased PDF is given by:
D total ( t )= D MIN +B D ×( D MAX −D MIN ),
where B D (t) is the pre-bias transfer function, U(t) is a uniformly generated random number between +1 and −1, N is a root power of the pre-bias transfer function, D total (t) is a total delay experienced by a packet, D MAX is a maximum delay, and D MIN is a minimum delay.
14. The system of claim 10 , wherein said step of determining a delay for each packet comprises:
means for selecting a random delay target value based on said pre-biased PDF; and
means for adjusting the delay of sequential packets in said stream of packets by delay-steps determined based on the random delay target value, until the delay of packet is equal to the random delay target value.
15. The system of claim 14 , wherein said means for adjusting comprises:
means for determining a difference between a current delay for the packet and the random delay target value; and
means for adjusting the current delay for the packet by a delay-step determined as a uniformly distributed value between a minimum step size and a maximum step size based on the difference between the current delay for the packet and the random delay target value.
16. The system of claim 14 , wherein said means for adjusting comprises:
means for determining a difference between a current delay for the packet and the random delay target value; and
means for adjusting the current delay for the packet by one of a fixed positive delay-step and a fixed negative delay-step based on the difference between the current delay for the packet and the random delay target value.
17. A non-transitory computer readable medium storing computer executable instructions for generating packet delay variation (PDV) with a uniformly distributed probability density function (PDF) for packet timing recovery stress testing of a network, said computer executable instructions defining steps comprising:
receiving a stream of packets, each packet generated at a regular interval;
determining a delay for each packet based on delay target values determined based on a pre-biased PDF comprising a uniform PDF that is pre-biased with a pre-bias transfer function; and
transmitting each packet on the network with the delay determined for that packet,
wherein, for a uniformly distributed random number greater than or equal to zero, the pre-bias transfer function is based on an Nth root of the uniformly distributed random number, and for a uniformly distributed random number less than zero, the pre-bias transfer function is based on a negative of the Nth root of an absolute value of the uniformly distributed random number.
18. The non-transitory computer readable medium of claim 17 , wherein the pre-bias transfer function generates delay targets at extremes of the uniform PDF.
19. The non-transitory computer readable medium of claim 17 , wherein the pre-bias transfer function is an Nth root square filter.
20. The non-transitory computer readable medium of claim 19 , wherein a flatness of the PDV is adjustable based on a value of N.
21. The non-transitory computer readable medium of claim 17 , wherein the pre-bias transfer function is given by:
For
U
(
t
)
≥
0
,
B
D
(
t
)
=
U
(
t
)
N
For
U
(
t
)
<
0
,
B
D
(
t
)
=
-
1
×
U
(
t
)
N
,
and the pre-biased PDF is given by:
D total ( t )= D MIN +B D ( t )×( D MAX −D MIN ),
where B D (t) is the pre-bias transfer function, U(t) is a uniformly generated random number between +1 and −1, N is a root power of the pre-bias transfer function, D total (t) is a total delay experienced by a packet, D MAX is a maximum delay, and D MIN is a minimum delay.
22. The non-transitory computer readable medium of claim 17 , wherein said step of determining a delay for each packet comprises:
(a) selecting a random delay target value based on said pre-biased PDF;
(b) adjusting the delay of sequential packets in said stream of packets by delay-steps determined based on the random delay target value, until the delay of packet is equal to the random delay target value; and
(c) repeating steps (a) and (b) to determine a delay value for each packet in said stream of packets.
23. The non-transitory computer readable medium of claim 22 , wherein step (b) comprises for each of said sequential packets:
determining a difference between a current delay for the packet and the random delay target value;
if the difference between the current delay for the packet and the random delay target value is negative, adjusting the current delay for the packet by a delay-step determined as a uniformly distributed value between 0 and a maximum step size; and
if the difference between the current delay for the packet and the random delay target value is positive, adjusting the current delay for the packet by a delay-step determined as a uniformly distributed value between a minimum step size and 0.
24. The non-transitory computer readable medium of claim 22 , wherein step (b) comprises for each of said sequential packets:
determining a difference between a current delay for the packet and the random delay target value;
if the difference between the current delay for the packet and the random delay target value is negative, adjusting the current delay for the packet by a fixed positive delay-step; and
if the difference between the current delay for the packet and the random delay target value is positive, adjusting the current delay for the packet by a fixed negative delay-step.
25. A method for generating packet delay variation (PDV) with a uniformly distributed probability density function (PDF) for packet timing recovery stress testing of a network, comprising:
receiving, by a PDV generator, a stream of packets, each packet generated at a regular interval by a packet generator;
determining, by the PDV generator, a delay for each packet based on delay target values determined based on a pre-biased PDF comprising a uniform PDF that is pre-biased with a pre-bias transfer function; and
transmitting, by the PDV generator, each packet over the network with the delay determined for that packet,
wherein the pre-bias transfer function is given by:
For
U
(
t
)
≥
0
,
B
D
(
t
)
=
U
(
t
)
N
For
U
(
t
)
<
0
,
B
D
(
t
)
=
-
1
×
U
(
t
)
N
,
and the pre-biased PDF is given by:
D total ( t )= D MIN +B D ( t )×( D MAX −D MIN ),
where B D (t) is the pre-bias transfer function, UN is a uniformly generated random number between +1 and −1, N is a root power of the pre-bias transfer function, D total (t) is a total delay experienced by a packet, D MAX is a maximum delay, and D MIN is a minimum delay.
26. A system for generating packet delay variation (PDV) with a uniformly distributed probability density function (PDF) for packet timing recovery stress testing, comprising:
means for generating a stream of packets, each packet generated at a regular interval;
means for determining a delay for each packet based on delay target values determined based on a pre-biased PDF comprising a uniform PDF that is pre-biased with a pre-bias transfer function; and
means for transmitting each packet with the delay determined for that packet,
wherein the pre-bias transfer function is given by:
For
U
(
t
)
≥
0
,
B
D
(
t
)
=
U
(
t
)
N
For
U
(
t
)
<
0
,
B
D
(
t
)
=
-
1
×
U
(
t
)
N
,
and the pre-biased PDF is given by:
D total (t)=D MIN +B D (t)×(D MAX −D MIN ),
where B D (t) is the pre-bias transfer function, U(t) is a uniformly generated random number between +1 and −1, N is a root power of the pre-bias transfer function, D total (t) is a total delay experienced by a packet, D MAX is a maximum delay, and D MIN is a minimum delay.
27. A non-transitory computer readable medium storing computer executable instructions for generating packet delay variation (PDV) with a uniformly distributed probability density function (PDF) for packet timing recover stress testing, said computer executable instructions defining steps comprising:
receiving a stream of packets, each packet generated at a regular interval;
determining a delay for each packet based on delay target values determined based on a pre-biased PDF comprising a uniform PDF that is pre-biased with a pre-bias transfer function; and
transmitting each packet with the delay determined for that packet,
wherein the pre-bias transfer function is given by:
For
U
(
t
)
≥
0
,
B
D
(
t
)
=
U
(
t
)
N
For
U
(
t
)
<
0
,
B
D
(
t
)
=
-
1
×
U
(
t
)
N
,
and the pre-biased PDF is given by:
D total ( t )= D MIN +B D ( t )×( D MAX −D MIN ),
where B D (t) is the pre-bias transfer function, U(t) is a uniformly generated random number between +1 and −1, N is a root power of the pre-bias transfer function, D total (t) is a total delay experienced by a packet, D MAX is a maximum delay, and D MIN is a minimum delay.