Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks

The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a cone-based distributed topology control algorithm. This algorithm, introduced in [16], does not assume that nodes have GPS information available; rather it depends only on directional information. Roughly speaking, the basic idea of the algorithm is that a node $u$ transmits with the minimum power $p_{u,\alpha}$ required to ensure that in every cone of degree $\alpha$ around $u$, there is some node that $u$ can reach with power $p_{u,\alpha}$. We show that taking $\alpha = 5\pi/6$ is a necessary and sufficient condition to guarantee that network connectivity is preserved. More precisely, if there is a path from $s$ to $t$ when every node communicates at maximum power, then, if $\alpha <= 5\pi/6$, there is still a path in the smallest symmetric graph $G_\alpha$ containing all edges $(u,v)$ such that $u$ can communicate with $v$ using power $p_{u,\alpha}$. On the other hand, if $\alpha > 5\pi/6$, connectivity is not necessarily preserved. We also propose a set of optimizations that further reduce power consumption and prove that they retain network connectivity. Dynamic reconfiguration in the presence of failures and mobility is also discussed. Simulation results are presented to demonstrate the effectiveness of the algorithm and the optimizations.Comment: 10 page

Specifying and Placing Chains of Virtual Network Functions

Network appliances perform different functions on network flows and constitute an important part of an operator's network. Normally, a set of chained network functions process network flows. Following the trend of virtualization of networks, virtualization of the network functions has also become a topic of interest. We define a model for formalizing the chaining of network functions using a context-free language. We process deployment requests and construct virtual network function graphs that can be mapped to the network. We describe the mapping as a Mixed Integer Quadratically Constrained Program (MIQCP) for finding the placement of the network functions and chaining them together considering the limited network resources and requirements of the functions. We have performed a Pareto set analysis to investigate the possible trade-offs between different optimization objectives