Towards Maximizing Nonlinear Delay Sensitive Rewards in Queuing Systems

We consider maximizing the long-term average reward in a single server queue, where the reward obtained for a job is a non-increasing function of its sojourn time. The motivation behind this work comes from multiple applications, including quantum information processing and multimedia streaming. We introduce a new service discipline, shortest predicted sojourn time (SPST), which, in simulations, performs better than well-known disciplines. We also present some limited analytical guarantees for this highly intricate problem.