Optimal Fidelity Selection for Human-in-the-loop Queues using Semi-Markov Decision Processes

We study optimal fidelity selection for a human operator servicing a queue of homogeneous tasks. The service time distribution of the human operator depends on her cognitive dynamics and the level of fidelity selected for servicing the task. Cognitive dynamics of the operator evolve as a Markov chain in which the cognitive state increases (decreases) with high probability whenever she is busy (resting). The tasks arrive according to a Poisson process and each task waiting in the queue loses its value at a fixed rate. We address the trade-off between high quality service of a task and consequent loss in value of future tasks using a Semi-Markov Decision Process (SMDP) framework. We numerically determine an optimal policy and establish its structural properties.