# Scheduling a Human Channel

## TL;DR

This paper models a human operator as a use-dependent channel, optimizing task scheduling under utilization constraints to maximize utility, revealing strategies that involve pushing utilization to the maximum and alternating work-rest periods.

## Contribution

It introduces a novel framework modeling human task processing as a use-dependent channel and derives optimal scheduling policies considering psychological utilization effects.

## Key findings

- Optimal policy involves maximizing utilization until the limit
- Tasks are processed with equal time within the same strategy
- Strategies include continuous work up to max utilization and alternating work-rest periods

## Abstract

We consider a system where a human operator processes a sequence of tasks that are similar in nature under a total time constraint. In these systems, the performance of the operator depends on its past utilization. This is akin to $\textit{state-dependent}$ channels where the past actions of the transmitter affects the future quality of the channel (also known as $\textit{action-dependent}$ or $\textit{use-dependent}$ channels). For $\textit{human channels}$, a well-known psychological phenomena, known as $\textit{Yerkes-Dodson law}$, states that a human operator performs worse when he/she is over-utilized or under-utilized. Over such a $\textit{use-dependent}$ human channel, we consider the problem of maximizing a utility function, which is monotonically increasing and concave in the time allocated for each task, under explicit minimum and maximum $\textit{utilization}$ constraints. We show that the optimal solution is to keep the utilization ratio of the operator as high as possible, and to process all the tasks. We prove that the optimal policy consists of two major strategies: utilize the operator without resting until reaching the maximum allowable utilization ratio, and then alternate between working and resting the operator each time reaching the maximum allowable utilization at the end of work-period. We show that even though the tasks are similar in difficulty, the time allocated for the tasks can be different depending on the strategy in which a task is processed; however, the tasks processed in the same strategy are processed equally.