teleo-codex/domains/internet-finance/optimal-queue-policies-have-threshold-structure-making-simple-rules-near-optimal.md

type	domain	description	confidence	source	created
claim	internet-finance	MDP research shows threshold policies are provably optimal for most queueing systems	proven	Li et al., 'An Overview for Markov Decision Processes in Queues and Networks' (2019)	2026-03-11

Optimal queue policies have threshold structure making simple rules near-optimal

Six decades of operations research on Markov Decision Processes applied to queueing systems consistently shows that optimal policies have threshold structure: "serve if queue > K, idle if queue < K" or "spawn worker if queue > X and workers < Y." This means even without solving the full MDP, well-tuned threshold policies achieve near-optimal performance.

For multi-server systems, optimal admission and routing policies follow similar patterns: join-shortest-queue, threshold-based admission control. The structural simplicity emerges from the mathematical properties of the value function in continuous-time MDPs where decisions happen at state transitions (arrivals, departures).

This has direct implications for pipeline architecture: systems with manageable state spaces (queue depths across stages, worker counts, time-of-day) can use exact MDP solution via value iteration, but even approximate threshold policies will perform near-optimally due to the underlying structure.

Evidence

Li et al. survey 60+ years of MDP research in queueing theory (1960s to 2019), covering:

• Continuous-time MDPs for queue management with decisions at state transitions
• Classic results showing threshold structure in optimal policies
• Multi-server systems where optimal policies are simple (join-shortest-queue, threshold-based)
• Dynamic programming and stochastic optimization methods for deriving optimal policies

The key challenge identified is curse of dimensionality: state space explodes with multiple queues/stages. Practical approaches include approximate dynamic programming and reinforcement learning for large state spaces.

Emerging direction: deep RL for queue management in networks and cloud computing.

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