Abstract
Human-agent hybrid teams are the operational unit of modern AI governance, yet their design treats human supervisors as infinitely available oversight resources. This assumption is empirically false. Cognitive psychology establishes that human attention is a finite, depletable resource subject to fatigue decay, context-switching penalties, and diminishing returns under sustained load. When governance systems ignore these constraints, the result is predictable: supervisors miss critical escalations, approve decisions without genuine review, and develop alert fatigue that undermines the entire oversight architecture. This paper formalizes the cognitive load balancing problem for hybrid teams. We model human cognitive capacity as a bounded resource C(t) that depletes under load and recovers during rest, with a non-linear fatigue function that captures diminishing marginal capacity. The attention allocation problem is formulated as a constrained optimization: maximize the weighted coverage of decisions requiring human review, subject to the constraint that no supervisor's instantaneous load exceeds the safe operating threshold L_max. We derive closed-form solutions for optimal alert scheduling under M/G/1 queueing assumptions and extend to priority-class models with preemptive escalation. Experimental validation on a 12-supervisor, 84-agent MARIA OS deployment demonstrates 97.3% oversight coverage (vs 78.1% under naive round-robin), fatigue threshold violations below 2.1%, and median alert response latency of 4.2 seconds for priority-1 escalations.
1. Introduction
The promise of human-in-the-loop AI governance rests on a simple premise: humans review the decisions that matter. The failure of this premise in practice is not a technology problem but a workload design problem. A single human supervisor monitoring 15 autonomous agents generates approximately 40-120 oversight events per hour, depending on agent autonomy level and domain volatility. Under naive scheduling, these events arrive as a Poisson process with no regard for the supervisor's current cognitive state, competing task demands, or accumulated fatigue.
The consequences are well-documented in adjacent fields. Air traffic control research shows that controller error rates increase by 340% when sustained task density exceeds 80% of capacity for more than 45 minutes. Nuclear plant operators exhibit a characteristic 'vigilance decrement' where detection probability drops from 0.95 to below 0.60 after four hours of continuous monitoring. Yet AI governance systems routinely assign human supervisors to eight-hour monitoring shifts with no formal workload modeling.
This paper addresses the cognitive load balancing problem directly. We do not propose reducing human oversight — the responsibility architecture of MARIA OS requires human judgment at designated gate points. Instead, we propose scheduling human oversight intelligently so that human attention is allocated where it produces the highest governance value, and withheld where the cognitive cost exceeds the governance benefit.
The core insight is that oversight quality is not binary. A supervisor reviewing their 5th escalation in 10 minutes does not provide the same quality of judgment as a supervisor reviewing their 1st escalation after a 20-minute rest period. Modeling this quality gradient — and optimizing scheduling against it — is the contribution of this paper.
2. The Cognitive Capacity Model
Let C(t) denote the available cognitive capacity of a human supervisor at time t, normalized to [0, 1] where C = 1 represents full capacity and C = 0 represents complete depletion. We model cognitive dynamics using a differential equation that captures both depletion under load and recovery during rest:
where L(t) in [0, 1] is the instantaneous workload at time t, alpha > 0 is the depletion rate (how quickly cognitive capacity drains under load), and beta > 0 is the recovery rate (how quickly capacity replenishes during rest). The multiplicative C(t) term in depletion captures the empirical observation that cognitive fatigue accelerates as capacity decreases — a fatigued person drains faster under the same load. The (1 - C(t)) term in recovery captures the diminishing returns of rest — recovery is fastest when capacity is low and slows as full capacity is approached.
2.1 Fatigue Decay Function
Under constant workload L, the steady-state capacity is obtained by setting dC/dt = 0:
This yields several important properties. When L = 0 (no load), C* = 1 — full recovery. When L = 1 (maximum load), C* = 0 — complete depletion. The relationship between steady-state capacity and load is non-linear and concave, meaning that the marginal capacity cost of additional load increases as load increases. Going from 50% to 60% load costs more capacity than going from 20% to 30%.
For realistic parameter values calibrated against vigilance decrement studies (alpha = 0.035 min^-1, beta = 0.020 min^-1), a supervisor under 70% sustained load reaches steady-state capacity of C* = 0.22 — well below the safe operating threshold. Under 50% sustained load, C* = 0.36, which is marginal. Only below 40% sustained load does the supervisor maintain C* > 0.46, consistent with acceptable oversight quality.
2.2 Context-Switching Penalty
Each time a supervisor switches between tasks (e.g., from reviewing an agent escalation to responding to a parallel query), a fixed cognitive penalty delta_s is incurred. We model this as an instantaneous capacity reduction:
Empirically, delta_s increases with the dissimilarity between the source and target tasks. Switching between two escalations from the same agent class incurs delta_s approx 0.03, while switching from a risk assessment review to an evidence verification task incurs delta_s approx 0.07. Over a shift with 200 context switches, the cumulative penalty is substantial: 200 * 0.05 = 10.0 capacity-units drained solely from switching.
3. The Attention Allocation Problem
Given a set of n supervisors S = {s_1, ..., s_n} and a stream of oversight events E = {e_1, e_2, ...} arriving over time, the attention allocation problem is to assign each event e_j to a supervisor s_i (or defer it) such that total governance value is maximized subject to cognitive constraints.
3.1 Formal Optimization
Define the governance value of supervisor s_i reviewing event e_j as V(i, j) = w_j * Q(C_i(t_j)), where w_j is the importance weight of event e_j (derived from the decision's Responsibility Demand score) and Q(C) is the oversight quality function — the probability that the supervisor makes the correct approve/reject decision given current capacity C. We model Q(C) as a sigmoid:
where C_50 is the capacity at which oversight quality is 50% (calibrated to C_50 = 0.30) and k controls the steepness of the quality transition (calibrated to k = 12). The optimization problem is then:
subject to: (1) each event is assigned to at most one supervisor: sum_i x_ij <= 1 for all j; (2) no supervisor exceeds the load threshold: L_i(t) <= L_max for all i, t; (3) cognitive capacity remains above minimum: C_i(t) >= C_min for all i, t; and (4) assignment is binary: x_ij in {0, 1}.
3.2 Priority Classes
Events are partitioned into priority classes P_1 (critical, must be reviewed), P_2 (important, should be reviewed), and P_3 (routine, may be deferred or auto-approved). Priority-1 events receive preemptive scheduling — they interrupt lower-priority reviews and are assigned to the supervisor with the highest current capacity. Priority-2 events are scheduled using the optimization above. Priority-3 events are only assigned when supervisor capacity exceeds C_idle = 0.60, ensuring they never compete with higher-priority oversight.
4. Queueing-Theoretic Analysis
We model the oversight system as a multi-server queue with cognitive-state-dependent service rates. Each supervisor is a server whose service rate mu_i(t) depends on cognitive capacity:
where mu_0 is the baseline review rate at full capacity and gamma in (0, 1) captures the sub-linear relationship between capacity and speed (a fatigued supervisor slows down, but not proportionally to capacity loss). Events arrive according to a Poisson process with rate lambda. The system is an M/G/n queue where the G distribution arises from the capacity-dependent service times.
4.1 Stability Condition
The queue is stable (waiting times remain bounded) if and only if the effective arrival rate is below the aggregate service capacity:
Under the cognitive dynamics model with sustained load L, the expected capacity is E[C_i^gamma] approx (C_i*)^gamma, yielding the practical stability condition. For n = 12 supervisors, mu_0 = 8 reviews/hour, gamma = 0.7, and mean load L = 0.5, the system handles up to lambda = 12 * 8 * 0.36^0.7 = 42.7 events/hour while maintaining cognitive safety. This is 44% less than the naive capacity estimate of 12 * 8 = 96 events/hour that ignores cognitive depletion.
4.2 Optimal Rest Scheduling
We derive the optimal rest interval T_rest that maximizes long-run throughput. A supervisor works for duration T_work and rests for T_rest, with capacity following the dynamics in Section 2. The long-run average capacity is:
Numerical optimization over the calibrated parameters yields T_work = 52 min, T_rest = 13 min as the throughput-maximizing schedule — remarkably close to the empirically validated Pomodoro technique ratio of 50:10. The key insight is that shorter, more frequent breaks outperform longer, less frequent breaks: a schedule of 52/13 minutes yields 23% higher average capacity than a schedule of 120/30 minutes with the same total rest fraction.
5. Alert Scheduling Algorithms
We present three scheduling algorithms of increasing sophistication, each building on the previous one.
5.1 Capacity-Weighted Round-Robin (CWRR)
The simplest cognitive-aware algorithm replaces uniform round-robin with capacity-weighted selection. When event e_j arrives, select supervisor s_i* = argmax_i C_i(t). This requires O(n) computation per assignment and produces a 12-18% improvement over naive round-robin in simulations. However, CWRR is greedy and does not account for future arrivals or the depletion trajectory of selected supervisors.
5.2 Predictive Load Balancing (PLB)
PLB extends CWRR by projecting each supervisor's capacity trajectory forward by a horizon H (typically 15-30 minutes) using the differential equation model. Assignment decisions consider not only current capacity but predicted capacity at the time the review will be completed. The assignment rule becomes s_i* = argmax_i C_i(t + tau_review) * Q(C_i(t)), balancing current oversight quality against future capacity preservation. PLB requires O(n * H / dt) computation per assignment but produces 28-35% improvement over naive round-robin.
5.3 Batch Optimization with Deferred Assignment (BODA)
BODA collects incoming events into micro-batches of duration Delta (typically 30-60 seconds) and solves the full optimization problem from Section 3.1 over each batch. Events that cannot be assigned without violating cognitive constraints are deferred to the next batch or escalated to a backup supervisor pool. BODA produces the highest coverage (97.3% in experiments) but requires solving an integer program per batch. For typical batch sizes (5-15 events, 12 supervisors), the solver completes in under 50ms.
| Algorithm | Coverage | Fatigue Violations | Median Latency | Computation |
| --- | --- | --- | --- | --- |
| Naive Round-Robin | 78.1% | 14.7% | 8.9s | O(1) |
| CWRR | 87.4% | 8.3% | 6.1s | O(n) |
| PLB | 93.8% | 4.6% | 5.0s | O(n * H) |
| BODA | 97.3% | 2.1% | 4.2s | O(IP solve) |
6. Experimental Validation
We validated the cognitive load balancing framework on a MARIA OS deployment with 12 human supervisors overseeing 84 agents across 3 universes (Sales, Audit, FAQ). The experiment ran for 14 consecutive business days, with supervisors randomly assigned to one of four scheduling conditions (naive round-robin, CWRR, PLB, BODA) on alternating days, controlling for individual differences through within-subjects design.
6.1 Cognitive Capacity Estimation
Real-time cognitive capacity was estimated using a composite proxy: (a) response latency to standardized probe tasks inserted every 10 minutes, (b) decision accuracy on known-answer escalations injected as calibration events, and (c) self-reported fatigue on a 1-5 scale collected every 30 minutes. The composite proxy was validated against the Karolinska Sleepiness Scale and NASA-TLX with correlations of r = 0.81 and r = 0.77 respectively.
6.2 Results
The BODA algorithm achieved 97.3% coverage of priority-1 and priority-2 events, compared to 78.1% under naive round-robin. Fatigue threshold violations (episodes where estimated C(t) < C_min = 0.20) occurred in 2.1% of supervisor-hours under BODA versus 14.7% under round-robin. Median response latency for priority-1 alerts was 4.2 seconds under BODA versus 8.9 seconds under round-robin. Decision accuracy on calibration events was 94.1% under BODA versus 82.3% under round-robin, confirming that cognitive-aware scheduling improves not just speed but judgment quality.
6.3 Fatigue Recovery Validation
We measured capacity recovery trajectories during scheduled breaks and found close agreement with the model predictions. After 52 minutes of active oversight at 55% mean load, supervisors had a mean estimated capacity of C = 0.31. After a 13-minute rest, capacity recovered to C = 0.72, consistent with the model prediction of C = 0.69 (error: 4.3%). The recovery rate parameter beta showed individual variation (range: 0.015 to 0.028), suggesting that personalized parameter calibration would further improve scheduling performance.
7. Conclusion
Human oversight in AI governance is only as good as the cognitive state of the human providing it. This paper demonstrates that treating cognitive capacity as a formal constraint — rather than assuming infinite human availability — produces measurable improvements in oversight quality, coverage, and supervisor well-being. The cognitive load balancing framework integrates naturally with MARIA OS's responsibility gate architecture: gates that require human review route escalations through the cognitive-aware scheduler, ensuring that the human judgment at each gate is genuine rather than perfunctory. The key takeaway for system designers is that adding more human oversight without workload modeling can paradoxically reduce oversight quality by pushing supervisors past their cognitive capacity limits. Fewer, better-scheduled reviews outperform more, poorly-scheduled ones.