This paper proposes a new problem called the dynamic Steiner tree problem. Interest in the dynamic Steiner tree problem is motivated by multipoint routing in communication networks, where the set of nodes in the connection changes over time. This problem, which has its basis in the Steiner tree problem on graphs, can be divided into two cases: one in which rearrangement ofexisting routes is not allowed, and a second in which rearrangement is allowed.For the nonrearrangeable version, it is shown that the worst-case performance for any algorithm is at least lg n times the cost of an optimum solution with complete rearrangement. Here n is the maximum number of nodes to be connected. In addition, a simple, polynomial time algorithm is present that has worst-case performance within two times this bound. In the rearrangeable case, a polynomial time algorithm is presented with worst-case performance bounded by a constant times optimum.

In wide-area Grid computing, geographically distributed computational resources are connected for enabling efficient and large-scale scientific/engineering computations. In the wide-area Grid computing, a data transfer protocol called GridFTP has been commonly used for large file transfers. GridFTP has the following features for solving problems of the existing TCP. First, for accelerating the start-up in TCP's slow start phase and achieving high throughput in TCP's congestion avoidance phase, multiple TCP connections can be established in parallel. Second, according to the bandwidth-delay product of a network, the TCP socket buffer size can be negotiated between GridFTP server and client. However, in the literature, sufficient investigation has not been performed either on the optimal number of TCP connections or the optimal TCP socket buffer size. In this paper, we therefore quantitatively investigate the optimal parameter configuration of GridFTP in terms of the number of TCP connections and the TCP socket buffer size. We first derive performance metrics of GridFTP in steady state (i.e., goodput and packet loss probability). We then derive the optimal parameter configuration for GridFTP and quantitatively show performance limitations of GridFTP through several numerical examples. We also demonstrate validity of our approximate analysis by comparing simulation results with analytic ones.

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In this paper, we propose an analytic approach of modeling a closed-loop network with multiple feedback loops using fluid-flow approximation. Specifically, we model building blocks of a network (i.e., the congestion control mechanism of TCP, propagation delay of a transmission link, and the buffer of a router) as independent continuous-time systems. By interconnecting these systems, we obtain the model for a complex closed-loop network. We improve the accuracy of analytic models for TCP congestion control and RED router by extending existing fluid-flow models. First, we obtain a block diagram for each continuous-time system using a standard CAD tool widely used in control engineering. Second, we evaluate the performance of a closed-loop network with multiple feedback loops by connecting these block diagrams. We also validate the effectiveness of our analytic approach by comparing our analytic results with simulation results. Unlike other fluid-based modeling approaches, our analytic approach is scalable and accurate; our analytic approach is scalable in terms of the number of TCP connections and routers since both input/output of all continuous-time systems are uniformly defined as a packet transmission rate. Our analytic approach is accurate since the timeout mechanism of TCP and the packet dropping algorithm of RED router are rigorously modeled in our continuous-time systems.