Method and apparatus for simulating packet delay variation of a multi-switch network

1. A packet delay variation simulation system comprising:

a packet generator configured to generate a plurality of signals indicative of packets;

a packet delay variation generator configured to receive the signals from the packet generator and delay the signals;

a packet delay analyzer configured to receive the delayed signals from the packet delay variation generator and signals from the packet generator and generate a profile of the delayed signals, thereby constructing a total delay model for a multi-switch network,

wherein the packet delay variation generator comprises one or more packet delay distribution modules each comprising:

a deterministic delay process packet delay input; and

a statistical delay process packet delay input;

wherein the one or more packet delay variation generators are configured to determine a packet delay distribution for the signals;

a packet delay distribution compiler configured to determine a total packet delay variation based on the packet delay distributions determined at the one or more packet delay distribution modules; and

a packet delay scheduler configured to receive the total packet delay variation from the packet delay distribution compiler and signals from the packet generator and determine a probability density function profile of the signals.

2. The system of claim 1 wherein the packet delay analyzer is configured to generate a histogram of the delayed signals.

3. A method of modeling, by a simulation system, packet delay variation of packets to construct a total delay model for a multi-switch network comprising:

determining a delay offset of a first packet;

determining, by at least one packet delay distribution module, a delay distribution of the first packet;

calculating, by a packet delay distribution compiler, a total delay of the first packet based at least in part on the delay offset and a delay based on the distribution of the first packet;

determining, by the at least one packet delay distribution module, a delay distribution of a second packet, the delay distribution of the second packet different from the delay distribution of the first packet;

calculating, by the packet delay distribution compiler, the total delay of the second packet based at least in part on the delay offset and a delay based on the distribution of the second packet; and

determining, by a packet delay scheduler, a complex packet delay variation profile by:

determining a total delay of a first plurality of packets based at least in part on the delay offset and the delay based on the distribution of the first packet; and

determining a total delay of a second plurality of packets based at least in part on the delay offset and the delays based on the distribution of the second packet, thereby constructing the total delay model for the multi-switch network.

4. The method of claim 3 wherein determining a complex packet delay variation profile further comprises:

determining a ratio of the first plurality of packets to the second plurality of packets; and

determining a statistical delay based on the ratio of the first plurality of packets to the second plurality of packets and the distributions of the first and second pluralities of packets.

5. The method of claim 4 wherein:

the distribution of the first plurality of packets is a Gamma distribution;

the distribution of the second plurality of packets is a uniform distribution;

determining the ratio of the first plurality of packets to the second plurality of packets comprises determining the equation 100%=ΣR G (t)+ΣR U (t) wherein R G (t) is the ratio of Gamma distributed packets and R U (t) is the ratio of uniformed distributed packets; and

the total delay is calculated as

D total ( t )= D Off +R G ( t )[ D G ( U ( t ),α,β)]+ R U ( t )[ D min +( D Max −D Min ) U ( t )]

wherein:

D G (U i (t),α,β) is the Gamma distribution of the first plurality of packets;

α is the shape parameter and β is the scale parameter of the Gamma distribution;

U(t) is a random number generator between 0 and 1 at time (t);

[D min +(D Max −D Min )U(t)] is the uniform distribution of the second plurality of packets;

D min is the sum of a no traffic delay and two standard deviations of the distribution of the second plurality of packets; and

D max is the maximum delay in the second plurality of packets.

6. The method of claim 3 further comprising:

applying a delay value to the first packet based on the calculated total delay of the first packet; and

applying a delay value to the second packet based on the calculated total delay of the second packet.

7. The method of claim 6 wherein applying the delay values based on the calculated total delays comprises:

delaying the first and second packets using a fixed delay step.

8. The method of claim 6 wherein applying the delay values based on the calculated total delays comprises:

delaying the first and second packets using a variable delay step.

9. The method of claim 3 wherein:

calculating the total delay of the first packet comprises:

determining D total1 (t)=D Off +D p1 (t) wherein D p1 (t) is the packet delay due to the distribution of the first packet, D Off is the delay offset, and D total1 (t) is the total delay experienced by the first packet; and

calculating the total delay of the second packet comprises:

determining D total2 (t)=D Off +D p2 (t) wherein D p2 (t) is the packet delay due to the distribution of the second packet, D Off is the delay offset, and D total2 (t) is the total delay experienced by the second packet.

10. The method of claim 9 wherein:

the distribution of the first packet is a Gamma distribution;

D p (t)=D Gamma (U(t),α,β) wherein:

α is the shape parameter and β is the scale parameter of a Gamma distribution;

U(t) is a random number generator between 0 and 1 at time (t); and

calculating a total delay of the first packet based at least in part on the delay based on the distribution of the first packet further comprises:

determining the α shape and β scale parameters; and

calculating a delay D p (t) of the first packet based on the Gamma distribution delay.

11. The method of claim 9 wherein the distribution of the second packet is a user-defined distribution.

12. A non-transitory machine readable medium having program instructions stored thereon, wherein, when the instructions are executed by a processor, the processor implements a method of modeling packet delay variation of packets to construct a total delay model for a multi-switch network, the method comprising:

determining a delay offset of a first packet;

determining a delay distribution of the first packet;

calculating a total delay of the first packet based at least in part on the delay offset and a delay based on the distribution of the first packet;

determining a delay distribution of a second packet, the delay distribution of the second packet different from the delay distribution of the first packet;

calculating the total delay of the second packet based at least in part on the delay offset and a delay based on the distribution of the second packet; and

determining a complex packet delay variation profile by:

determining a total delay of a first plurality of packets based at least in part on the delay offset and the delay based on the distribution of the first packet; and

determining a total delay of a second plurality of packets based at least in part on the delay offset and the delays based on the distribution of the second packet, thereby constructing the total delay model for the multi-switch network.

13. The non-transitory machine readable medium of claim 12 wherein determining a complex packet delay variation profile further comprises:

determining a ratio of the first plurality of packets to the second plurality of packets; and

determining a statistical delay based on the ratio of the first plurality of packets to the second plurality of packets and the distributions of the first and second pluralities of packets.

14. The non-transitory machine readable medium of claim 12 further comprising:

applying a delay value to the first packet based on the calculated total delay of the first packet; and

applying a delay value to the second packet based on the calculated total delay of the second packet.

15. The non-transitory machine readable medium of claim 14 wherein applying the delay values based on the calculated total delays further comprises:

delaying the first and second packets using a fixed delay step.

16. The non-transitory machine readable medium of claim 14 wherein applying the delay values based on the calculated total delays further comprises:

delaying the first and second packets using a variable delay step.

17. The non-transitory machine readable medium of claim 12 wherein:

calculating the total delay of the first packet further comprises:

determining D total1 (t)=D Off +D p1 (t) wherein D p1 (t) is the packet delay due to the distribution of the first packet, D Off is the delay offset, and D total1 (t) is the total delay experienced by the first packet; and

calculating the total delay of the second packet further comprises:

determining D total1 (t)=D Off +D p1 (t) wherein D p1 (t) is the packet delay due to the distribution of the second packet, D Off is the delay offset, and D total1 (t) is the total delay experienced by the second packet.

18. The non-transitory machine readable medium of claim 17 further comprising using a user-defined distribution as the distribution of the first packet and the second packet.