Foundations of Dispatchability for Simple Temporal Networks with Uncertainty

Simple Temporal Networks (STNs) are a widely used formalism for representing and reasoning about temporal constraints on activities. The dispatchability of an STN was originally defined as a guarantee that a specific real-time execution algorithm would necessarily satisfy all of the STN’s constraints while preserving maximum flexibility but requiring minimal computation. A Simple Temporal Network with Uncertainty (STNU) augments an STN to accommodate actions with uncertain durations. However, the dispatchability of an STNU was defined differently: in terms of the dispatchability of its so-called STN projections. It was then argued informally that this definition provided a similar real-time execution guarantee, but without specifying the execution algorithm. This paper formally defines a real-time execution algorithm for STNUs that similarly preserves maximum flexibility while requiring minimal computation. It then proves that an STNU is dispatchable if and only if every run of that real-time execution algorithm necessarily satisfies the STNU's constraints no matter how the uncertain durations play out. By formally connecting STNU dispatchability to an explicit real-time execution algorithm, the paper fills in important elements of the foundations of the dispatchability of STNUs.