As cloud-based services become more numerous and dynamic, resource provisioning becomes more and more challenging. A QoS constrained resource allocation problem is considered in this paper, in which service demanders intend to solve sophisticated parallel computing problem by requesting the usage of resources across a cloud-based network, and a cost of each computational service depends on the amount of computation. Game theory is used to solve the problem of resource allocation. A practical approximated solution with the following two steps is proposed. First, each participant solves its optimal problem independently, without consideration of the multiplexing of resource assignments. A Binary Integer Programming method is proposed to solve the independent optimization. Second, an evolutionary mechanism is designed, which changes multiplexed strategies of the initial optimal solutions of different participants with minimizing their efficiency losses. The algorithms in the evolutionary mechanism take both optimization and fairness into account. It is demonstrated that Nash equilibrium always exists if the resource allocation game has feasible solutions.A game-theoretic method of fair resource allocation for cloud 253
We study the instability mechanisms leading to slug flow formation in an inclined pipe subject to gravity forces. We use a phase-field approach, where the Cahn–Hillard model is used to model the interface. At the inlet, a stratified flow is imposed with a specified velocity profile. We validate our numerical results by comparing against previous theoretical models and by predicting the various flow regimes for horizontal and inclined pipes, including stratified flow, slug flow, dispersed bubble flow and annular flow. Subsequently, we focus on slug formation in an inclined pipe and connect its appearance with specific vortical dynamics. A two-dimensional channel geometry is first considered. When the heavy fluid is injected as the top layer, inverted vortex shedding emerges, which periodically impacts on the bottom wall, as it develops further downstream. The accumulation of heavy fluid in the bottom wall causes a back flow that induces rolling waves and interacts with the upstream jet. When the heavy fluid is placed as the bottom layer, the heavy fluid accumulates and initially forms a massive slug at the bottom region, close to the inlet. Subsequently, the heavy fluid slug starts to break into smaller pieces, some of which translate along the pipe. During the accumulation phase, a back flow forms also generating rolling waves. Occasionally, a rolling wave can reach the top of the pipe and form a new slug. To describe the generation of vorticity from the two-phase interface and pipe walls in the slug formation, we study the circulation dynamics and connect it with the resulting two-phase flow patterns. Finally, we conduct three-dimensional (3-D) simulations in a circular pipe and compare the differences between the 3-D flow patterns and its circulation dynamics against the 2-D simulation results.
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