Reverse Engineering TCP/IP-like Networks using Delay-Sensitive Utility Functions

TCP/IP can be interpreted as a distributed primal-dual algorithm to maximize aggregate utility over source rates. It has recently been shown that an equilibrium of TCP/IP, if it exists, maximizes the same delay-insensitive utility over both source rates and routes, provided pure congestion prices are used as link costs in the shortest-path calculation of IP. In practice, however, pure dynamic routing is never used and link costs are weighted sums of both static as well as dynamic components. In this paper, we introduce delay-sensitive utility functions and identify a class of utility functions that such a TCP/IP equilibrium optimizes. We exhibit some counter-intuitive properties that any class of delay-sensitive utility functions optimized by TCP/IP necessarily possess. We prove a sufficient condition for global stability of routing updates for general networks. We construct example networks that defy conventional wisdom on the effect of link cost parameters on network stability and utility

Asynchronous Distributed Averaging on Communication Networks

Distributed algorithms for averaging have attracted interest in the control and sensing literature. However, previous works have not addressed some practical concerns that will arise in actual implementations on packet-switched communication networks such as the Internet. In this paper, we present several implementable algorithms that are robust to asynchronism and dynamic topology changes. The algorithms are completely distributed and do not require any global coordination. In addition, they can be proven to converge under very general asynchronous timing assumptions. Our results are verified by both simulation and experiments on Planetlab, a real-world TCP/IP network. We also present some extensions that are likely to be useful in applications

Optimization and Stability of TCP/IP with Delay-Sensitive Utility Functions

TCP/IP can be interpreted as a distributed primal-dual algorithm to maximize aggregate utility over source rates. It has recently been shown that an equilibrium of TCP/IP, if exists, maximize the same aggregate utility function over both source rates and routes, provided pure congestion prices are used as link costs in the shortest-path calculation of IP. Moreover, the utility functions are delay-insensitive, i.e., they are functions of rates only. We extend this result in several ways. First, we show that if utility functions are delay-insensitive, then there are networks for which TCP/IP optimizes aggregate utility only if routing is based on pure congestion prices. Routing based on the weighted sum of congestion prices and propagation delays optimizes aggregate utility for general networks only if the utility functions are delay-sensitive. Moreover, we identify such a class of delay-sensitive utility functions that is implicitly optimized by TCP/IP. As for the delay-insensitive case, we show for this class of utility functions, equilibrium of TCP/IP exists if and only if the optimization problem has zero duality gap. In that case, there is no penalty for not splitting the traffic. We exhibit some counter-intuitive properties of this class of utility functions. We also prove that any class of delay-sensitive utility functions that are optimized by TCP/IP necessarily possess some strange properties. We prove that, for general networks, if the weight on congestion prices is small enough, only minimum-propagation-delay paths are selected. Hence if all source-destination pairs have unique minimum-propagation-delay paths, then equilibrium of TCP/IP exists and is asymptotically stable. For general networks, their equilibrium properties are the same as a modified network where paths with non-minimum propagation delays are deleted and routing is based on pure congestion prices. It is commonly believed that there is generally an inevitable tradeoff between utility maximization and stability in TCP/IP networks. In particular, as the weight on congestion prices increases, the routing will change from stable to unstable. We exhibit a counterexample where routing changes from stable to unstable and then to stable again, as the weight on congestion prices increases. Moreover, one can construct a network with any given utility profile as a function of the weight on congestion prices.</p

Distributed averaging on asynchronous communication networks

Abstract — Distributed algorithms for averaging have attracted interest in the control and sensing literature. However, previous works have not addressed some practical concerns that will arise in actual implementations on packet-switched communication networks such as the Internet. In this paper, we present several implementable algorithms that are robust to asynchronism and dynamic topology changes. The algorithms do not require global coordination and can be proven to converge under very general asynchronous timing assumptions. Our results are verified by both simulation and experiments on a real-world TCP/IP network. I