---
type: source
title: "An Overview for Markov Decision Processes in Queues and Networks"
author: "Quan-Lin Li, Jing-Yu Ma, Rui-Na Fan, Li Xia"
url: https://arxiv.org/abs/1907.10243
date: 2019-07-24
domain: internet-finance
format: paper
status: processed
tags: [pipeline-architecture, operations-research, markov-decision-process, queueing-theory, dynamic-programming]
processed_by: rio
processed_date: 2026-03-11
claims_extracted: ["optimal-queue-control-policies-have-threshold-structure-for-single-server-systems.md", "curse-of-dimensionality-makes-exact-mdp-solutions-intractable-for-multi-queue-networks.md", "deep-rl-for-queue-management-is-emerging-direction-for-cloud-and-network-systems.md"]
extraction_model: "anthropic/claude-sonnet-4.5"
extraction_notes: "Academic survey paper establishing theoretical foundations for queue control via MDPs. Three claims extracted covering: (1) threshold structure of optimal policies for tractable systems, (2) curse of dimensionality as the barrier to scaling, (3) deep RL as emerging solution for large-scale systems. No entity data or enrichments—purely theoretical/methodological content. Relevance to Teleo: confirms that pipeline's state space (~10^3-10^4 states) is in the tractable regime for exact MDP solution, and that threshold policies are theoretically grounded for this scale."
---

# An Overview for Markov Decision Processes in Queues and Networks

Comprehensive 42-page survey of MDP applications in queueing systems, covering 60+ years of research from the 1960s to present.

## Key Content

- Continuous-time MDPs for queue management: decisions happen at state transitions (arrivals, departures)
- Classic results: optimal policies often have threshold structure — "serve if queue > K, idle if queue < K"
- For multi-server systems: optimal admission and routing policies are often simple (join-shortest-queue, threshold-based)
- Dynamic programming and stochastic optimization provide tools for deriving optimal policies
- Key challenge: curse of dimensionality — state space explodes with multiple queues/stages
- Practical approaches: approximate dynamic programming, reinforcement learning for large state spaces
- Emerging direction: deep RL for queue management in networks and cloud computing

## Relevance to Teleo Pipeline

Our pipeline has a manageable state space (queue depths across 3 stages, worker counts, time-of-day) — small enough for exact MDP solution via value iteration. The survey confirms that optimal policies for our type of system typically have threshold structure: "if queue > X and workers < Y, spawn a worker." This means even without solving the full MDP, a well-tuned threshold policy will be near-optimal.


## Key Facts
- Survey covers 60+ years of MDP research in queueing theory (1960s-2019)
- Continuous-time MDPs for queues: decisions at state transitions (arrivals, departures)
- Dynamic programming and stochastic optimization are core solution methods
- Approximate dynamic programming and RL are practical approaches for large state spaces