This work addresses the problem of optimal traffic engineering in a connectionless autonomous system. Based on nonlinear control theory, the approach taken in This work provides a family of optimal adaptation laws. These laws enable each node in the network to independently distribute traffic among any given set of next hops in an optimal way, as measured by a given global utility function of a general form. This optimal traffic distribution is achieved with minimum information exchange between neighboring nodes. Furthermore, this approach not only allows for optimal multiple forwarding paths but also enables multiple classes of service, e.g., classes of service defined in the differentiated services architecture. Moreover, the proposed decentralized control scheme enables optimal traffic redistribution in the case of link failures. Suboptimal control laws are also presented in an effort to reduce the computational burden imposed on the nodes of the network. Finally, an implementation of these laws with currently available technology is discussed.

In this paper, we address the problem of optimal decentralized traffic engineering when multiple paths are available for each call. More precisely, given a set of possible paths for each call, we aim at distributing the traffic among the available paths in order to maximize a given utility function. To solve this problem, we propose a large family of decentralized sending rate control laws having the property that each of the members of this family "steers" the traffic allocation to an optimal operation point. The approach taken relies on the control theory concept of Sliding Modes. These control laws allow each ingress node to independently adjust its traffic sending rates and/or redistribute its sending rates among multiple paths. The only nonlocal information needed is binary feedback from each congested node in the path. The control laws presented are applicable to a large class of utility functions, namely, utility functions that can be expressed as the sum of concave functions of the sending rates. We show that the technique can be applied not only to usual rate adaptive traffic with multiple paths, but also to rate adaptive traffic with minimum service requirements and/or maximum allowed sending rate and to assured service with targeted rate guarantee, all allowing for multiple paths. It is also shown that these control laws are robust with respect to failures; i.e., they automatically reroute traffic if a link failure occurs. Finally, we provide some insight on how to choose the "right" control law. In particular, we provide a way of choosing a member of the family of control laws that reduces the sending rate oscillation caused by implementation constraints like delays and quantization. An example of application of the approach delineated in this paper is also presented. This example provides some insights on the implementation aspects and illustrates the robustness of the control laws developed in this paper.