Directed network-based connectivity probability evaluation for urban bridges

Compared with an undirected network, a directed network can describe urban traffic flow and traffic infrastructure, such as ubiquitous one/two-way streets and single/double-deck bridges, more accurately. As the most important network performance indicator, the connectivity probability for a directed network is difficult to calculate owing to the NP-hard problem. This study examined the modelling and connectivity probability analyses of directed networks for urban bridges. To establish a directed bridge network, a directed topological graph was constructed based on actual crossroads and the direction of bridges and streets. Then, the failure probability, which is determined from single/double-deck bridge inspection results, was assigned to the directed edges to form an extended directed bridge network. For connectivity probability analysis, Monte Carlo simulations and an improved Dijkstra algorithm were employed for state combination enumeration and connectivity judgement of the directed bridge network. The all-terminal connectivity probability was approximately evaluated by summing the probability of the state combinations leading to the connected bridge network. The relative importance of directed edges was determined by combining the failure probability of the edge and the impact of its failure on network connectivity. By applying it to an urban city with 299 bridges, the effectiveness and accuracy of the proposed method was demonstrated, thereby providing scientific support for the evaluation, maintenance, and evolution of the urban bridge network.