Structural Properties of Optimal Fidelity Selection Policies for Human-in-the-loop Queues

We study optimal fidelity selection for a human operator servicing a queue of homogeneous tasks. The agent can service a task with a normal or high fidelity level, where fidelity refers to the degree of exactness and precision while servicing the task. Therefore, high fidelity servicing results in higher-quality service but leads to larger service times and increased operator tiredness. We treat the cognitive state of the human operator as a lumped parameter that captures psychological factors such as workload and fatigue. The service time distribution of the human operator depends on her cognitive dynamics and the fidelity level selected for servicing the task. Her cognitive dynamics evolve as a Markov chain in which the cognitive state increases with high probability whenever she is busy and decreases while 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 the task and consequent loss in value of subsequent tasks using a Semi-Markov Decision Process (SMDP) framework. We numerically determine an optimal policy and the corresponding optimal value function. Finally, we establish structural properties of an optimal fidelity policy and provide conditions under which the optimal policy is a threshold-based policy.