Performability evaluation of water distribution systems during maintenance procedures

A Water Distribution System (WDS) is a critical infrastructure for society and economy, subject to frequent maintenance either for contingencies or planned operations. Maintenance procedures affect the hybrid dynamics of a WDS at stochastic time points, representing the completion of repair activities that change the WDS topology and operation mode. Hence, the problem of performability evaluation of the WDS behavior during a maintenance intervention falls in the class of Stochastic Hybrid Systems (SHSs), for which existing numerical or simulative approaches cannot afford the complexity of realistic WDSs. We propose a viable approach that computes the expected demand not served during a maintenance procedure by integrating fluid-dynamic analysis of the WDS with quantitative evaluation of the procedure timing, notably assuming non-Markovian repair times over a bounded support. Different solution techniques are presented to evaluate the joint distribution of the times when the WDS is affected by the procedure, performing either simulation of the procedure model or state-space analysis based on an extension of the method of stochastic state classes. Feasibility and effectiveness of the proposed methods are assessed on a real WDS in terms of results accuracy and computational complexity, showing that the overall approach could be efficiently applied in higher level tasks including activity scheduling, resource planning, and budget allocation.