Reliability evaluation of a multicast over coded packet networks

Network coding is a generalization of conventional routing methods that allows a network node to code information flows before forwarding them. While it has been theoretically proved that network coding can achieve maximum network throughput, theoretical results usually do not consider the stochastic nature in information processing and transmission, especially when the capacity of each arc becomes stochastic due to failure, attacks, or maintenance. Hence, the reliability measurement of network coding becomes an important issue to evaluate the performance of the network under various system settings. In this paper, we present analytical expressions to measure the reliability of multicast communications in coded networks, where network coding is most promising. We define the probability that a multicast rate can be transmitted through a coded packet network under a total transmission cost constraint as the reliability metric. To do this, we first introduce an exact mathematical formulation to construct multicast connections over coded packet networks under a limited transmission cost. We then propose an algorithm based on minimal paths to calculate the reliability measurement of multicast connections and analyze the complexity of the algorithm. Our results show that the reliability of multicast routing with network coding improved significantly compared to the case of multicast routing without network coding.     

A novel approach to subgraph selection with multiple weights on arcs

In this paper, an extension of the minimum cost flow problem is considered in which multiple incommensurate weights are associated with each arc. In the minimum cost flow problem, flow is sent over the arcs of a graph from source nodes to sink nodes. The goal is to select a subgraph with minimum associated costs for routing the flow. The problem is tractable when a single weight is given on each arc. However, in many real-world applications, several weights are needed to describe the features of arcs, including transit cost, arrival time, delay, profit, security, reliability, deterioration, and safety. In this case, finding an optimal solution becomes difficult. We propose a heuristic algorithm for this purpose. First, we compute the relative efficiency of the arcs by using data envelopment analysis techniques. We then determine a subgraph with efficient arcs using a linear programming model, where the objective function is based on the relative efficiency of the arcs. The flow obtained satisfies the arc capacity constraints and the integrality property. Our proposed algorithm has polynomial runtime and is evaluated in rigorous experiments.