This paper provides a new methodology to understand and design communication networks and synthesize researchers’ previous understanding of the network protocol stacks into a unifying framework.

Network architecture determines functionality allocation: "who does what" and "how to connect them," rather than just resource allocation. It is often more influential, harder to change, and less understood than any specific resource allocation scheme. Functionality allocations can happen, for example, between the network management system and network elements, between end-users and intermediate routers, and between source control, routing, and physical resource sharing.

The study of network architectures involves the exploration and comparison of alternatives in functionality allocation. This paper advocates a set of conceptual frameworks and mathematical languages for a clear and rigorous foundation of network architectures. The intellectual goal is to provide a mathematical theory of architectures for networking, just like what people have already done in the past for communication theory, control theory, and computation theory.

Layered architectures form one of the most fundamental structures of communication network design. They adopt a modularized and often distributed approach to network coordination. Each module, called a layer, controls a subset of the decision variables, and observes a subset of constant parameters and the variables from other layers. Each layer in the protocol stack hides the complexity of the layer below and provides a service to the layer above.

Intuitively, layered architectures enable a scalable, evolvable, and implementable network design, while introducing limitations to efficiency and fairness and potential risks to manageability of the network. There is clearly more than one way to "divide and conquer" the network design problem. Examining the choices of modularized design of networks, we would like to tackle the question of "how to" and "how not to" layer.

While the general principle of layering is widely recognized as one of the key reasons for the enormous success of data networks like the Internet and wireless cellular networks, there is little quantitative understanding to guide a systematic, rather than an ad hoc, process of designing a layered protocol stack for wired and wireless networks.

One possible perspective to rigorously and holistically understand layering is to integrate the various protocol layers into a single coherent theory, by regarding them as carrying out an asynchronous distributed computation over the network to implicitly solve a global optimization problem. Different layers iterate on different subsets of the decision variables using local information to achieve individual optimality. Taken together, these local algorithms attempt to achieve a global objective.

Such a design process of modularization can be quantitatively understood through the mathematical language of decomposition theory for constrained optimization. This framework of "Layering as Optimization Decomposition" exposes the interconnections between protocol layers as different ways to modularize and distribute a centralized computation. Even though the design of a complex system will always be broken down into simpler modules, this theory will allow us to systematically carry out this layering process and explicitly trade off design objectives.

Given the layers, crossing layers is tempting. As evidenced by the large and ever-growing number of papers on cross-layer design over the last few years, we expect that there will be no shortage of cross-layer ideas based on piecemeal approaches. The growth of the "knowledge tree" on cross-layer design has been exponential. However, any piecemeal design applied jointly over multiple layers does not bring a more structured thinking process than the ad hoc design of just one layer.

What seems to be lacking is a level ground for fair comparison among the variety of cross-layer designs, a unified view on how (and how not to) layer, and fundamental limits on the impacts of layer-crossing on network performance and robustness metrics.

"Layering as Optimization Decomposition" provides a candidate for such a unified framework. It attempts to shrink the "knowledge tree" on cross-layer design rather than growing it, by providing a top-down approach to design-layered protocol stacks from first principles. The resulting conceptual simplicity stands in contrast to the ever-increasing complexity of communication networks.

The applications of "Layering As Optimization Decomposition" is broad, encompassing the Internet, wireless networks, and broadband access networks. Among the many applications to practical networks used by people in their daily lives, I will highlight two multi-institution projects that I am currently involved in. One is an NSF-sponsored project called "FAST Copper", on fiber/DSL broadband access network design. It traverses the boundaries of spectrum management, scheduling, admission control, congestion control, topology design, and both voice and video signal processing, and its architectural design is based on "Layering As Optimization Decomposition."

The second large-scale project is a DARPA-sponsored project on Control-Based Mobile Ad-hoc Networks, which is building prototypes of a future generation wireless ad-hoc network’s protocol stack based on the theory of "Layering As Optimization Decomposition."

Given that this paper presents a new view on the under-explored but important area of the theoretical foundation of network architectures, I think many applications will follow in the future as society’s reliance on networked communications continues to expand.