  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 human cognitive state as a lumped parameter that
captures psychological factors such as workload and fatigue. The operator's
service time distribution 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 the operator is penalized at a fixed rate for each task
waiting in the queue. We address the trade-off between high-quality service of
the task and consequent penalty due to a subsequent increase in queue length
using a discrete-time Semi-Markov Decision Process framework. We numerically
determine an optimal policy and the corresponding optimal value function.
Finally, we establish the structural properties of an optimal fidelity policy
and provide conditions under which the optimal policy is a threshold-based
policy.
