Priority assignment of repair services for spatially distributed infrastructure

Critical infrastructure, such as telecom base stations, comprises spatially distributed facilities that alternate between operational and down states. When the facilities are down, service engineers need to travel to the site to repair and restore them to operation. In the event of a disruption, multiple facilities might be down. However, repair priorities are often assigned on an ad hoc basis, leading to suboptimal decisions. This paper studies the optimal repair priority policy for a service engineer managing facilities within their service region. We formulate a continuous-time Markov decision process for optimal decision-making. We show that the famous cμ-rule in the job scheduling literature is not optimal for assigning repair priorities in our setting. For the general case, we identify certain facilities that should always be prioritized over others when they are down and determine the optimal repair priority at some system states. Nevertheless, a full characterization of the optimal policy structure of the general case is intractable due to its complexity. We identify three special cases where the optimal policy structure exhibits an index structure, referred to as the cμ/λ-rule. By combining these structural properties with the famous cμ-rule, we develop an index-based heuristic. Numerical experiments, based on a telecom base station failure dataset from Qiqihar, China, demonstrate the effectiveness of the heuristic in a variety of settings, including non-Markovian system dynamics.