Network virtualization helps overcome shortcomings of the current Internet architecture. The virtualized network architecture enables coexistence of multiple virtual networks (VNs) on an existing physical infrastructure. VN embedding (VNE) problem, which deals with the embedding of VN components onto a physical network, is known to be -hard. In this paper, we propose two VNE algorithms: MaVEn-M and MaVEn-S. MaVEn-M employs the multicommodity flow algorithm for virtual link mapping while MaVEn-S uses the shortest-path algorithm. They formalize the virtual node mapping problem by using the Markov decision process (MDP) framework and devise action policies (node mappings) for the proposed MDP using the Monte Carlo tree search algorithm. Service providers may adjust the execution time of the MaVEn algorithms based on the traffic load of VN requests. The objective of the algorithms is to maximize the profit of infrastructure providers. We develop a discrete event VNE simulator to implement and evaluate performance of MaVEn-M, MaVEn-S, and several recently proposed VNE algorithms. We introduce profitability as a new performance metric that captures both acceptance and revenue to cost ratios. Simulation results show that the proposed algorithms find more profitable solutions than the existing algorithms. Given additional computation time, they further improve embedding solutions.

We discuss distributed denial of service attacks in the Internet. We were motivated by the widely known February 2000 distributed attacks on Yahoo!, Amazon.com, CNN.com, and other major Web sites. A denial of service is characterized by an explicit attempt by an attacker to prevent legitimate users from using resources. An attacker may attempt to: "flood" a network and thus reduce a legitimate user's bandwidth, prevent access to a service, or disrupt service to a specific system or a user. We describe methods and techniques used in denial of service attacks, and we list possible defenses. In our study, we simulate a distributed denial of service attack using ns-2 network simulator. We examine how various queuing algorithms implemented in a network router perform during an attack, and whether legitimate users can obtain desired bandwidth. We find that under persistent denial of service attacks, class based queuing algorithms can guarantee bandwidth for certain classes of input flows.

Abstract-Efficient and robust computation of one or more of the operating points of a nonlinear circuit is a necessary first step in a circuit simulator. This paper discusses the application of so-called globally convergent probability-one homotopy methods to various systems of nonlinear equations that arise in circuit simulation. The so-called "coercivity conditions" required for such methods are established using concepts from circuit theory. The theoretical claims of global convergence for such methods are substantiated by experiments with a collection of examples that have proved difficult for commercial simulation packages that do not use homotopy methods. Moreover, by careful design of the homotopy equations, the performance of the homotopy methods can be made quite reasonable. An extension to the steady-state problem in the time domain is also discussed.

In this paper we give algorithms for constructing the Brayton-Moser's mixed potential function for a class of nonlinear reciprocal RLC networks, and we state necessary conditions for their existence. We have attempted to find the largest possible class of networks for which such a scalar function of state variables consisting of capacitor voltages and inductor currents can be constructed explicitly. Our results are applicable to a certain subclass of complete networks. From a mathematical point of view, we show that the corresponding network equations belong to the class of index 1 systems.