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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