In this paper, a theory of lexicographic optimization for convex and compact feasible sets is presented. Existence, globality, unimodality, and uniqueness of the solution to the problem are proved. Also, necessary and sufficient conditions are derived that establish the relationship between the lexicographic problem and the maxmin problem. This framework is shown to be useful in the problem of designing flow control protocols. Towards this objective, a theory of bottleneck ordering is introduced, which unveils the convergence properties of the flow control problem.

The well-known edge server bottleneck is shown in this paper to be the result of a mismatch between the general-purpose architecture and the special-purpose data functions it was not intended to perform exclusively. Six overheads are identified that contribute significantly to the bottleneck. To solve this bottleneck problem, a solution is to apply the principle of separation between control and data functions. While the idea is not new, the application of this principle to the edge server architecture is novel in the convergence of three technologies: network, server, and storage. Notable performance has been obtained with this approach using ASIC implementation for TCP or UDP streaming applications.

This paper presents the first distributed multi-rate maxmin rate allocation protocol for multicast traffic. The protocol supports minimum rate guarantee for each receiver as a QoS parameter. The protocol is practical and it maintains a good performance-scalability trade-off. While the network is required to participate, the complexity added by the protocol is minimal.

The problem of allocating maxmin rates with minimum rate constraints for connection-oriented networks is considered. This paper proves that the convergence of maxmin rate allocation satisfies a partial ordering in the bottleneck links. This partial ordering leads to a tighter lower bound for the convergence time for any maxmin protocol. An optimally fast maxmin rate allocation protocol called the distributed constraint precedence graph (CPG) protocol is designed based on this ordering theory. The new protocol employs bi-directional minimization and does not induce transient oscillations. The distributed CPG protocol is compared against ERICA, showing far superior performance.

This paper introduces a scalable maxmin flow control protocol which guarantees the minimum rate for each connection-oriented flow without requiring per-flow information. The protocol is called MR-ASAP (minimum rate guaranteeing adaptive source-link accounting protocol). MR-ASAP is an extension of ASAP, the first exact maxmin flow control protocol for best-effort connection-oriented traffic in integrated service networks, without requiring per-flow accounting at the intermediate network node. In the classical maxmin computation, only the maximum rate constraints are considered; in this paper the minimum rate requirements are treated similarly as the maximum rate constraints. Existing protocols that achieve exact maxmin optimality with minimum rate guarantee require per-flow information and complex computation such as sorting of the minimum rates at the switch. By generalizing the concept of constraint, the complex sorting and per-flow accounting required in the existing protocols are avoided. Simulation demonstrates fast convergence to optimality.