Scheduling "Last Minute" Updates for Timely Decision-Making

We consider a setting where requests for updates regarding time-varying processes are required prior to making a sequence of decisions. Each request has a finite length time window during which the update should be received. The end of the window reflects the time at which a decision is to be made, while the start of the window models the earliest possible time at which a useful update could be sent. An update scheduled as near to the end of the window as possible is deemed the best, i.e., reflects the most timely information about the process' state. This is modelled by a reward depending on the time difference between the decision point and the last scheduled update. Requests arrive arbitrarily and share a limited communication resource, e.g., a single request can be scheduled per time slot, hence not all decisions can be based on the latest possible update. We consider update scheduling policies which maximize the overall reward rate. In particular we consider an adversarial request model and evaluate proposed algorithms via their Competitive Ratio (CR). Specifically, we first derive a lower bound on the CR of any causal policy. We then propose two scheduling policies, denoted adversarial and greedy, and provide further analysis and insights on regimes where one might be superior to the other. We validate these observations via simulation for a setting with stochastic arrivals.