A technique efficiently selects a path computation element (PCE) to compute a path between nodes of a computer network. The PCE selection technique is illustratively based on dynamic advertisements of the PCE's available path computation resources, namely a predictive response time (PRT). To that end, the novel technique enables one or more PCEs to dynamically send (advertise) their available path computation resources to one or more path computation clients (PCCs). In addition, the technique enables the PCC to efficiently select a PCE (or set of PCEs) to service a path computation request based upon those available resources.