# Delay Bounded Multi-Source Multicast in Software-Defined Networking
## 1 Introduction
Given a network topology, a set of potential source nodes, a set of destination nodes and a delay bound, the DBMS scheme build _minimum delay cost trees_ with a delay constraint from each potential source node to each destination node, which eventually forms a DBMS-Forest. _Minimum delay cost tree_ in this paper refers to a tree that consists of minimum delay cost links from the source node to its multicast nodes. Combining the processes of tree building with a delay bound constraint and potential source node selection is novel and difficult to solve as these processes are closely related and impact each other. We prove that DBMS problem is NP-Hard. A simple approach would be to divide DBMS as a set of single-source multicasts, each with a different source node. The SMT with the least delay cost among such multicasts just acts as the DBMS of the multi-source multicast. This way, however, suffers from the complexity of solving a set of NP-hard SMT problems. Moreover, the DBMS under non-single sources may may have a total cost less than the picked best SMT with a single source. Thus, prior approaches, relying on traditional multicast, remain inapplicable to the DBMS proposed in this paper. To solve the DBMS problem efficiently, we propose a DBMS algorithm which consists of two sub algorithms. The algorithm selects one of the sources to establish routing paths towards its destination nodes. DBMS algorithm seeks shared nodes among such paths to enhance the possibility of aggregating more links. Thus, it can reduce the number of employed links while ensuring that the delivered content reaches each destination within an acceptable delay. Having multiple potential source nodes ensures that the congestion at the sources will be greatly reduced, on the other hand, the delay bound constraint is an important factor that ensures the quality of service. Our contribution in this work can be summarized as follows:  
* The DBMS problem is formulated as a mixed integer linear programming (MILP) problem, and the problem is found to be an NP-hard problem. * To solve the problem, we propose a DBMS algorithm to ensure that a destination node connect to the potential source node through a minimum delay cost path. Out of the source nodes set, the DBMS algorithm selects a particular potential source based on the total delay cost from the destination node. It ensures that a destination node connects to only one source. By selecting the source with less delay cost, our algorithm ensures that the overall delay cost of the DBMS-Forest is minimized. Based on the formulated MILP, our algorithm bound the end-to-end delay cost path from each source to its multicast nodes. * We conducted extensive simulations to evaluate the proposed technique feasibility and usefulness and also compared the performance of our technique with the previous work in literature. The simulation results demonstrate the effectiveness of our solution. The rest of this paper is organized as follows; In Section 2 the related work is reviewed and discussed. Section 3 presents the system architecture; other corresponding aspects, including Traffic Delay Cost Measurement, Topology Discovery and Multicast Routing Model, are also described. We present the problem description in Section 4. The DBMS algorithm is designed in Section 5. We present the performance evaluation and results of our experiments in Section 6, and finally concluding remarks are given in Section 7.