Learning When to Automate: Queue Control in Human-AI Service Systems

Autonomous customer-service agents are shifting from conversational interfaces toward operational execution roles: they retrieve firm records, apply service policies, and execute backend writes such as refunds, cancellations, exchanges, order modifications, and reservation changes. This shift creates a service-control problem: firms must keep routine service fast and low-friction while preventing operational errors on requests where customer instructions, policy constraints, firm records, and backend writes interact. We propose a difficulty-routed service-control architecture that asks when service agents should reconsider before acting. A lightweight router keeps routine sessions on a low-cost baseline path and routes operationally coupled sessions to an escalated workflow. The escalated path uses conflict-aware communication and write-triggered reconsideration to concentrate deliberation and safeguards before consequential backend writes, rather than applying additional control uniformly across all service sessions. We evaluate the architecture on human-verified retail and airline tasks from $τ^{2}$-bench. In retail, the method improves reliability consistently on service requests with operational conflict. Routing evidence shows that stronger control is directed toward conflicted requests rather than broadly applied to routine ones. Dialogue and tool-use profiles suggest that gains do not come from indiscriminate interaction expansion or broader tool chains; instead, added turns and tool calls support evidence gathering, write separation, and pre-write reconsideration. Case-level evidence shows that the escalated workflow preserves fallback plans, binds retrieved records to the correct action, sequences writes, and decomposes multi-entity requests. Airline results extend the same service-control logic to reservation operations.

This work considers adaptive shared human-robot control for nonlinear control-affine systems, where the assumption of a fully rational human is relaxed and the robot adapts its assistance to observed boundedly rational human behavior. We use a level-k bounded-rationality model of the two-player game to construct a finite bank of candidate human and robot policies through alternating best-response computations, with the associated value functions and policies approximated using adaptive dynamic programming. During the shared-control interaction, state-transition residuals compare the measured system evolution with the trajectories predicted by the candidate human policies. The residuals are accumulated using a forgetting factor and mapped to a probabilistic human-behavior model over the finite candidate bank. Rather than selecting a single candidate or averaging stored robot policies, the robot computes a distribution-aware one-step best response by minimizing an expected cooperative cost over the complete estimated human behavior distribution. For a quadratic terminal-value approximation and Euler state propagation, this response admits a closed-form solution expressed in terms of the expected human input. The proposed methods are evaluated in simulations of a benchmark nonlinear system stabilization task, and of a planar manipulator shared control setup. The reported results show decreasing Kullback-Leibler divergence between the estimated and simulated human behavior distributions, and a lower accumulated running cost for the robot agent over the shared control interaction period, than the maximum-probability and probability-weighted alternative policies baseline.

We propose a per-task leverage ratio for human-agent collaboration: human work displaced by an agent, divided by the human time required to specify the task, resolve mid-run interrupts, and review the result. The denominator decomposes into three channels through which a conserved per-task information requirement must flow, each with its own time-cost scalar. We show that information density itself is directional and bounded by separate ceilings on human-to-agent and agent-to-human flow, and that the asymptotic behavior of leverage decomposes into two scaling axes (capability and memory) with a non-zero floor on the planning term set by irreducible task novelty bounded by human throughput. We extend this per-task analysis to a windowed leverage measure that accommodates recurring tasks, spawned subtasks, and amortized system-design investment. The per-task ceiling does not bind the windowed measure, though both remain bounded: $L_{\text{task}}$ by per-task novelty, $L_{\text{window}}$ by the stock of accumulated planning investment that pays out within the window. The framework operationalizes aspects of earlier qualitative work on supervisory control (Sheridan, 1992), common ground (Clark & Brennan, 1991), and mixed-initiative interaction (Horvitz, 1999) within a single normative ratio, and produces a list of testable empirical questions that we leave as open problems.