Is the error of queueing analysis of a robot-printer cell from print-time variability or from the cell's structure?
research/robofab-cell-ctmc
Is the error of queueing analysis of a robot-printer cell from print-time variability or from structure? An exact Markov chain says structure: cv 1 to 0.33 moves throughput by at most 0.71%, while plain MVA overshoots up to 20% beyond the printer count.
What it found
An exact Markov-chain solution of a stylised cell (one arm, 2–6 printers held through load and unload, one inspector; Erlang print time, cv 0.33–1; illustrative times) used as a noise-free reference. It matches a simulation in 10 settings (largest |z| 1.73). Changing the print-time cv from 1 to 0.33 moves the exact throughput by at most 0.71%, so the error of mean value analysis is structural: plain MVA is within 0.6% when work in process equals the printer count but overshoots by up to 20.3% beyond it (mean error 12.8% at twice the printers), and held-demand MVA is 2.8% off at saturation but −5% to −12% off at low load. One job class, exponential load, unload and inspect times. Stylised, simulation-only.
A figure from its own output
Paper, code and results
More in Robot manufacturing loops
- Does holding the printer through load and unload fix queueing analysis of a robot-printer cell?Does adding load and unload time to the printer's demand fix MVA of the robot-printer cell? Mixed: it cuts the error at saturation (2.9% against 8.2%) but raises it elsewhere (7.3% against 3.6%), so overall plain MVA is better (4.7% against 6.2%). Stylised.
- Does an arm-wait-aware printer demand fix queueing analysis of a robot-printer cell?Does adding the arm's queueing delay (a fixed point, no fitted parameter) to the held printer's demand fix MVA of the robot-printer cell? No: it underpredicts in all 32 settings and is worse overall (7.9% mean error against 6.2% for held-demand and 4.7% for plain MVA). Negative result. Stylised.
- Can a blocking-aware correction to queueing analysis predict a robot-printer cell across loads?Can a blocking-aware correction to MVA predict the held-printer robot cell across loads? A fitted stall helps only at saturation (1.4% error) and worsens other loads (8.5%); keeping latency apart from capacity gives 3.6% against plain MVA's 4.7% on the design grid, but only ties plain MVA (3.4% against 3.5%) on a held-out job mix. Stylised.
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- Can a printed gripper assemble its own next generation?Can a printed gripper assemble its own next generation? With fixed-size jaw pads a gripper builds a copy only at scale ≥ pad thickness in mm (4 mm pads: scale 4); a stroke cap of S mm needs 30·pad ≤ S; seeds of 130 and 140 mm sustain a chain, 60 and 100 mm decay. Largely algebraic given an assumed opening; stylised.
- How long an arm does it take to assemble its own toy gripper?How long an arm does it take to assemble its own toy gripper? A planar two-link arm needs 60–140 mm links as the tray moves 40–400 mm away, and a 90° elbow limit more than doubles it (stylised).
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Other research topics
Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1
Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.