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Formal methods for task management for human operators are gathering increasing attention to improve efficiency of human-in-the-loop systems. In this paper, we consider a novel dynamical queue approach to intelligent task management for human operators. We consider a model of a dynamical queue, where the service time depends on the server utilization history. The proposed queueing model is motivated by, but not restricted to, widely accepted empirical laws describing human performance as a function of mental arousal. The focus of the paper is to characterize the throughput of the dynamical queue and design corresponding maximally stabilizing task release control policies, assuming deterministic arrivals. We focus extensively on threshold policies that release a task to the server only when the server state is less than a certain threshold. When every task brings in the same deterministic amount of work, we give an exact characterization of the throughput and show that an appropriate threshold policy is maximally stabilizing. The technical approach exploits the optimality of the one-task equilibria class associated with the server dynamics. When the amount of work associated with the tasks is an independent identically distributed (i.i.d.) random variable with finite support, we show that the maximum throughput increases in comparison to the case where the tasks have the same deterministic amount of work. Finally, we provide preliminary empirical evidence in support of the applicability of the proposed approach to systems with human operators.