A Rent-Seeking Framework for Multipath TCP

Network utility maximization (NUM) for Multipath TCP (MPTCP) is a challenging task, since there is no well-defined utility function for MPTCP [6]. In this paper, we identify the conditions under which we can use Kelly's NUM mechanism, and explicitly compute the equilibrium. We obtain this equilibrium by using Tullock's rent-seeking framework from game theory to define a utility function for MPTCP. This approach allows us to design MPTCP algorithms with common delay and/or loss constraints at the subflow level. Furthermore, this utility function has diagonal strict concavity, which guarantees a globally unique (normalized) equilibrium.

Numerical Investigation of Scale Effects in Modelling Scour Below Offshore Pipelines Under Steady Currents

Scale effects must be considered when results of small-scale laboratory tests on scour below offshore pipelines are extrapolated to real-life situations. In the present study, a 2D Finite Element Method (FEM) numerical model for scour simulation was employed to evaluate scale effects in modelling scour below a single pipeline subjected to steady currents. In the model, the Reynolds-Averaged Navier-Stokes (RANS) equations with a k-ω turbulence closure are supplemented by a morphological model with both suspended load and bedload sediment transport rates included. Scour simulations were conducted at a number of scales with various Shields parameter values and sediments of two median grain sizes. The numerical results indicate that for the range of parameters investigated in this study, the normalized equilibrium scour depth below the pipe centre decreases in a linear fashion as the pipe diameter increases. Accordingly, an expression delineating scale-effect trends that relate deviations in normalized equilibrium scour depths to those in pipeline diameters is proposed, thereby contributing to an accurate extrapolation of small-scale model test results to prototype scale in modelling scour below pipelines in currents.

FINDING NORMALIZED EQUILIBRIUM IN CONVEX-CONCAVE GAMES

This paper considers a fairly large class of noncooperative games in which strategies are jointly constrained. When what is called the Ky Fan or Nikaidô-Isoda function is convex-concave, selected Nash equilibria correspond to diagonal saddle points of that function. This feature is exploited to design computational algorithms for finding such equilibria. To comply with some freedom of individual choice the algorithms developed here are fairly decentralized. However, since coupling constraints must be enforced, repeated coordination is needed while underway towards equilibrium. Particular instances include zero-sum, two-person games — or minimax problems — that are convex-concave and involve convex coupling constraints.