Foundations of Dispatchability for Simple Temporal Networks with Uncertainty

Simple Temporal Networks (STNs) are a widely used formalism for representing and reasoning about tem- poral 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 preserv- ing 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 dispatch- able 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.