Systems and methods of network analysis and characterization

1. A network analyzer configured to characterize a communication network, comprising:

a processor configured to:

obtain an initial model of the communication network in which the capacities of individual network components are known, where the initial model comprises:

a definition of individual transmitters and receivers within the communication network;

a definition of a structure of the communication network; and

a definition of connections within the communication network;

determine that a specific network performance characteristic of the initial model cannot be directly characterized despite knowing the capacities of individual network components and the structure of the communication network by identifying a component of the initial model in a library of component substitutions;

when the specific network performance characteristic of the initial model cannot be directly characterized, automatically perform at least one substitution that replaces the identified component of the initial network model with at least one model selected from the group consisting of an equivalent model and a bounding model to produce a simplified network model that is capable of being characterized by the network analyzer, where the at least one model used to perform the at least one substitution is associated with the identified component in the library of component substitutions; and

characterize the specific network performance characteristic of the initial model by characterizing the simplified network model.

2. The network analyzer of claim 1 , wherein the specific network performance characteristic of the initial model that cannot be directly characterized is a performance characteristic selected from the group consisting of:

maximal data rate;

minimal distortion with which data can be delivered;

latency; and

robustness to component failures.

3. The network analyzer of claim 1 , wherein the definition of the structure of the communication network includes the definition of at least one of:

a capacitated bit pipe; and

a stochastic channel.

4. The network analyzer of claim 1 , wherein the at least one substitution includes substituting an equivalent or bounding network model for at least one stochastic component of the initial model.

5. The network analyzer of claim 4 , wherein the at least one stochastic component is replaced with an equivalent or bounding bit-pipe model.

6. The network analyzer of claim 1 , wherein the at least one substitution includes substituting an equivalent or bounding network model for at least one deterministic component of the initial model.

7. The network analyzer of claim 1 , wherein the at least one substitution includes modifying at least one bit-pipe component of the initial model.

8. The network analyzer of claim 1 , wherein the processor is configured to bound the accuracy of at least one of the models substituted for a component of the initial model to evaluate the impact of the substitution on the accuracy with which the network analyzer can characterize the initial model.

9. The network analyzer of claim 1 , wherein the processor is configured to characterize the simplified network model by outputting the simplified network model.

10. The network analyzer of claim 1 , wherein the processor is configured to characterize the simplified network model by bounding the specific network performance characteristic of the simplified network model.

11. The network analyzer of claim 10 , wherein the bound on the specific network performance characteristic of the simplified network model is selected from the group consisting of:

a bound with respect to the capacity region of the simplified network model;

a bounding network on the capacity region of the simplified network model;

a bound on the joint source-channel coding region of the simplified network model; and

a bounding network on the joint source-channel coding region of the simplified network model.

12. The network analyzer of claim 10 , wherein the processor is further configured to assess the bounding accuracy of the bound on the specific network performance characteristic of the simplified network model.

13. The network analyzer of claim 12 , wherein the processor is configured to repeat the at least one substitution using at least one alternative substitution in the event that the bounding accuracy of the characterization of the simplified network model is not sufficiently accurate.

14. The network analyzer of claim 1 , wherein the processor is further configured to factor the initial network model by partitioning the network into a series of independent network components.

15. The network analyzer of claim 1 , wherein the processor is further configured to perform the at least one substitution as part of a recursive substitution process in which components of the initial network model are replaced with equivalent or bounding models to produce a simplified network that is capable of being characterized by the network analyzer.

16. The network analyzer of claim 15 , wherein the recursive substitution process is a hierarchical substitution process.

17. A network analyzer configured to characterize a communication network, comprising:

a processor configured to:

obtain an initial model of the communication network in which the capacities of individual network components are known, where the initial model comprises:

a definition of individual transmitters and receivers within the communication network;

a definition of a structure of the communication network; and

a definition of connections within the communication network;

determine that a specific network performance characteristic of the initial model cannot be directly characterized despite knowing the capacities of individual network components and the structure of the communication network by identifying a component of the initial model in a library of component substitutions;

when the specific network performance characteristic of the initial model cannot be directly characterized, automatically factor the identified component of the initial model by partitioning the network model into a series of independent network components that form a simplified network model that is capable of being characterized by the network analyzer; and

characterize the specific network performance characteristic of the initial model by characterizing the simplified network model.

18. The network analyzer of claim 17 , wherein the specific network performance characteristic of the initial model that cannot be directly characterized is a performance characteristic selected from the group consisting of:

maximal data rate;

minimal distortion with which data can be delivered;

latency; and

robustness to component failures.

19. A method of characterizing a communication network, comprising:

obtaining an initial model of the communication network in which the capacities of individual network components are known, where the initial model comprises:

a definition of individual transmitters and receivers within the communication network;

a definition of a structure of the communication network; and

a definition of connections within the communication network;

determining that a specific network performance characteristic of the initial model cannot be directly characterized despite knowing the capacities of individual network components and the structure of the communication network by identifying a component of the initial model in a library of component substitutions;

when the specific network performance characteristic of the initial model cannot be directly characterized, automatically performing at least one substitution that replaces the identified component of the initial network model with at least one model selected from the group consisting of an equivalent model and a bounding model to produce a simplified network model that is capable of being characterized by the network analyzer, where the at least one model used to perform the at least one substitution is associated with the identified component in the library of component substitutions; and

characterizing the specific network performance characteristic of the initial model by characterizing the simplified network model.

20. The method of claim 19 , wherein the specific network performance characteristic of the initial model that cannot be directly characterized is a performance characteristic selected from the group consisting of:

maximal data rate;

minimal distortion with which data can be delivered;

latency; and

robustness to component failures.