Reliability and quality of service in weighted probabilistic networks using Algebraic Decision Diagrams

In network reliability studies, nodes and links are usually represented as binary entities (either up or down). In many cases the analysis of the performance of the system requires a richer representation by associating to each arc a weight representing a specific attribute of the arc (e.g. capacity, resistance, cost, length). For example, the amount of traffic characterizing the connections in communication or transport systems or the distance between nodes in a highway network are fundamental for a full description of these networks. The paper explores the problem of the quantitative evaluation of reward functions in stochastic weighted networks, where the weights assigned to the arcs my have different physical interpretations. We discuss two types of interpretation of weights: weights as distances and weights as capacities. Correspondingly, two different algorithms based on a data structure called algebraic decision diagram (ADD), are discussed and presented. The first evaluates the probability that the terminal node can be reached from the source within a determinate distance or cost. The second computes the probability that a flow greater than a threshold can be transmitted between the source and the sink. The algorithms have been tested with several examples and with some benchmark network taken from the literature.