Analysis of shortest-path routing algorithms in a dynamic network environment
ACM SIGCOMM Computer Communication Review
Fair end-to-end window-based congestion control
IEEE/ACM Transactions on Networking (TON)
Optimal flow control and routing in multi-path networks
Performance Evaluation - Special issue: Internet performance and control of network systems
ACM SIGCOMM Computer Communication Review
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
The Mathematics of Internet Congestion Control (Systems and Control: Foundations and Applications)
Methodological frameworks for large-scale network analysis and design
ACM SIGCOMM Computer Communication Review
A global stability result for primal-dual congestion control algorithms with routing
ACM SIGCOMM Computer Communication Review
Congestion control for high performance, stability, and fairness in general networks
IEEE/ACM Transactions on Networking (TON)
Stability of end-to-end algorithms for joint routing and rate control
ACM SIGCOMM Computer Communication Review
Part II: control theory for buffer sizing
ACM SIGCOMM Computer Communication Review
Cross-layer optimization in TCP/IP networks
IEEE/ACM Transactions on Networking (TON)
Optimal rate allocation for energy-efficient multipath routing in wireless ad hoc networks
IEEE Transactions on Wireless Communications
Mean FDE models for Internet congestion control under a many-flows regime
IEEE Transactions on Information Theory
Stability of multi-path dual congestion control algorithms
IEEE/ACM Transactions on Networking (TON)
Model Checking Optimisation Based Congestion Control Algorithms
Fundamenta Informaticae - Concurrency Specification and Programming (CS&P)
Flow-level models for multipath routing
Performance Evaluation
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This paper investigates fair, scalable, stable congestion controls which achieve high bandwidth utilisation over networks of operating multi-path routing. The aim is to take advantage of path diversity to achieve efficient bandwidth allocation without causing instability. Two multi-path extensions to the class of dual algorithms are considered. The first is a natural extension previously proposed in the literature, which we show to be similar to a continuous time sub-gradient method for solving a network-wide optimisation problem. We establish that the continuous time fluid model possesses a weak stability property. This analysis assumes the absence of propagation delays. We then show that when propagation delays are present, even the weak stability property disappearsWe develop an alternative multi-path extension of the dual algorithm, which considers path diversity when evaluating fairness. This algorithm is shown to be globally stable in the absence of propagation delays and a sufficient condition for local stability, when heterogeneous propagation delays are present, is found. The sufficient condition we present is decentralised in the following sense: the gain parameter for each dynamic variable is restricted by the average round-trip time of packets passing through the link or source it represents, but not by the round-trip times of any other packets. The delay stability analysis is an extension of results for single-path congestion control. It is obtained by treating possible routes that belong to a given origin-destination pair as behaving as separate sources which pass through a virtual link located at the origin.The models considered apply to networks consisting of arbitrary interconnections of sources and links, with arbitrary, heterogeneous propagation delays.