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Learning-Assisted Congestion-Aware Route Scheduling for Semiconductor Fab Material Control Systems

Hao Yin, Meiqi Tu, Anbang Liu, Shaochong Lin, Max Z. J. Shen

arXiv:2608.30520v1cs.AImath.OC

TL;DR

Online MCS routing in semiconductor-fab AMHSs must estimate delivery time and congestion risk before execution despite heterogeneous, partially observed relay queues. TN-DCR combines prediction-time-safe network features with separate time and risk predictors, whose outputs drive risk-constrained route scheduling. In closed-loop evaluation, mean total time fell 16.40% and internal waiting fell 22.59%, with nearly unchanged throughput.

  • Problem

    MCS route selection must estimate delivery cost and severe-congestion risk online while relay queues are heterogeneous, partially observed, and time-varying.

    Source: §I · pp. 1–2

  • Method

    TN-DCR combines structural, dynamic, bottleneck, and graph-aware features under a strict pre-prediction information invariant, then feeds separate time models and an ordinal risk classifier for constrained routing.

    Source: §I · p. 2

  • Results

    16.40% lower mean total time and 22.59% lower internal waiting were achieved in controlled closed-loop routing, with nearly unchanged throughput.

    Source: D. Closed-Loop Routing Results · p. 11, §VI · p. 12

  • Takeaways & Limitations

    The framework links command-level congestion prediction with lightweight risk-constrained route scheduling for heterogeneous relay-based AMHS operations.

    Source: §I · p. 2, §VI · pp. 11–12

    Predictors remain observational under incumbent-dispatcher selection bias, and evaluation covers only a limited scale, horizon, and load regime.

    Source: §VI · p. 12

Abstract

from arXiv · show

Automated material handling systems in semiconductor fabs are operated by a material control system (MCS) that must schedule a relay route for every transport command online, before execution. This is a data-driven scheduling problem in which route cost is dominated in the upper tail by queueing at heterogeneous, partially observable relay equipment, so route selection requires estimating both delivery time and congestion risk at the decision moment. This paper proposes a transport-network-aware dynamic congestion representation (TN-DCR). Built on a static directed transport graph induced by historically observed relay segments, TN-DCR combines structural route priors, multi-window network-wide congestion context, route-level bottleneck exposure, and an inductive graph-aware route embedding, all constructed under a prediction-time-safety invariant that admits only information observed strictly before the prediction moment. The representation feeds separate queue- and transfer-time regressors and an ordinal multi-label classifier producing calibrated multi-threshold exceedance scores, with an empirical-Bayes stock-key residual correction reducing systematic queue-time underprediction. The predictions serve as costs in a risk-constrained route-scheduling rule that minimizes predicted delivery time subject to a bound on extreme-congestion probability, embedding the learned predictors within a lightweight operations-research decision model. In a controlled closed-loop evaluation, mean delivery time falls by 16.4\% and internal resource waiting time by 22.6\% while throughput remains essentially unchanged.

I. INTRODUCTION

Fab MCS routing must choose relay paths online under heterogeneous, partially observed congestion, where queueing creates long-tail delivery risk. TN-DCR addresses this with prediction-time-safe network features, learned time and risk estimates, and risk-constrained route selection.

  • AMHS delays increase cycle time, work-in-process, and Q-time risk, while the MCS must schedule each relay route online.Source: §I · pp. 1–2
  • Static shortest-path routing ignores live congestion, although queues at intermediate relay resources can dominate delivery delay.Source: §I · p. 2, Figure 1 · p. 2
  • The framework targets a gap between detailed but slow simulation and lightweight tabular prediction that does not represent congestion propagation through transport topology.Source: §I · p. 2, A. Scheduling and Delivery-Time… · p. 3
  • TN-DCR combines route structure, multi-window congestion context, bottleneck exposure, and graph-aware neighborhood information using only pre-prediction observations.Source: §I · pp. 2–3
  • Separate queue- and transfer-time models plus ordinal tail-risk estimates supply costs and constraints for chance-constrained route scheduling.Source: §I · pp. 2–3

B. Scheduling and Routing of Automated Transport in Manufacturing and Logistics

Prior manufacturing and logistics methods often assume richer observability or focus on vehicle and processing-resource decisions. This paper instead models asynchronous MCS path selection over a heterogeneous directed transport network using prediction-safe learned costs and risk constraints.

Research gap

Proposed direction

Problem formulation

B. Prediction Problem

The prediction problem enforces a command-specific information boundary: features may use only events and completed transport records observed strictly before that command’s prediction moment.

  • The as-of information set contains dynamic events and completed edge-level records with timestamps earlier than the prediction time.Source: B. Prediction Problem · p. 5
  • Reference statistics and model parameters are frozen before evaluation, while every time-varying feature obeys the command-specific cutoff.Source: B. Prediction Problem · p. 5
  • The prediction-time-safety invariant excludes unavailable events and completed-edge outcomes, preventing look-ahead leakage.Source: B. Prediction Problem · p. 5

1) Delivery-Time Targets:

The point-prediction task estimates queueing and transfer time separately at the edge level, then reconstructs path-level delivery time from those outputs. Queue severity is normalized against an edge-specific transfer-time scale.

C. Route Optimization Problem

The route-selection rule evaluates candidate paths using predicted delivery time and bottleneck congestion risk while preserving prediction-time safety. It retains paths whose highest-threshold risk stays within tolerance, then selects using predicted time.

Route evaluation

  • Candidate paths are evaluated edge by edge using the same decision-time information and fixed command attributes.This preserves the prediction-time-safety invariant during path comparison.Source: C. Route Optimization Problem · pp. 5–6

Time objective

Risk aggregation

Risk constraint

IV. METHODOLOGY

The methodology constructs TN-DCR features from structural, dynamic-context, and graph-aware information, then uses them for edge-level predictions and candidate-path selection. The static graph and graph-derived features remain separate from downstream model fitting.

Framework

Static transport graph

Structural priors

Dynamic context

2) Dynamic Congestion Context:

Dynamic congestion context summarizes recent network-wide and candidate-route activity using only observations preceding the safe telemetry cutoff. Graph-aware features add pooled endpoint and neighborhood states with support diagnostics.

Prediction-time safety

Dynamic context

  • Network-wide context uses 15- and 60-minute windows, with preceding equal-length intervals supporting short-term load comparisons.Source: 2) Dynamic Congestion Context · p. 7
  • Path-local context aggregates waiting, movement, and zone activity across sums, means, maxima, active fractions, and concentration among the most active elements.Source: 2) Dynamic Congestion Context · p. 7

Graph-aware representation

4) Prediction Models and Stock-Key Residual Correction:

TN-DCR feeds separate time and risk predictors, while empirical-Bayes stock-key correction adjusts persistent destination-specific queue residuals. Transfer estimates are used directly in the downstream aggregation.

Prediction models

Stock-key correction

C. Route Optimization Algorithm

The algorithm filters and scores admissible candidate paths, aggregates edge-level predictions, and applies a risk-constrained selection rule; unsupported commands return to incumbent routing. Candidate generation and scoring are bounded, but the policy is myopic and compares observationally supported alternatives.

Candidate-path preparation

  • The admissible set may be supplied by the lower-level dispatcher or generated using bounded Kp-shortest-path enumeration with reference-period median edge delivery times as weights.Source: C. Route Optimization Algorithm · p. 8

Candidate scoring

  • For each remaining path, it constructs the TN-DCR representation, evaluates edge-level predictors, aggregates outputs, and applies the threshold-constrained rule with tolerance ε.The procedure evaluates at most Lp edge-level steps per path and uses the route-selection aggregates from (10) and (11).Source: C. Route Optimization Algorithm · pp. 8–9

Scope boundary

  • Predictions for alternative candidates are observational rather than interventional, so support filtering limits extrapolation without eliminating selection bias.The policy compares empirically supported candidates rather than estimating causal outcomes for arbitrary paths.Source: C. Route Optimization Algorithm · p. 8

Candidate-path preparation

  • The algorithm obtains an admissible candidate set, generates at most Kp loopless paths when needed, and removes infeasible or insufficiently supported candidates.If no candidates remain, it returns the incumbent routing fallback.Source: C. Route Optimization Algorithm · pp. 8–9

Scope boundary

  • The policy uses the network state at decision time without anticipating how future command reassignments alter that state.Long-horizon fab-scale validation remains outside the study’s scope.Source: C. Route Optimization Algorithm · p. 9

Computational bounds

  • Candidate scoring is capped by limits on paths, edge-level evaluations, and retained graph neighbors, while history lookup uses binary search.End-to-end serving latency remains an empirical deployment metric.Source: C. Route Optimization Algorithm · p. 9

V. NUMERICAL EXPERIMENTS

The numerical experiments evaluate edge-level regression, ordinal congestion-risk classification, feature and calibration ablations, and candidate-model comparisons using historical transport records. The setup uses a chronological test partition and prediction-time-safe feature construction.

Experimental scope

  • The evaluation covers time regression, ordinal congestion-risk classification, feature and stock-key-correction ablations, and controlled closed-loop path selection.Source: §V · p. 9

Data and protocol

  • The dataset contains 51,700 successful edge-level transport records from a production MCS in a semiconductor display fab.Records are constructed at command-specific prediction moments and follow the information boundary.Source: A. Experimental Setup · p. 9

Regression targets and models

  • Separate LightGBM regressors predict queue and transfer times, with stock-key calibration applied only to queue output before reconstructing total edge-level time.No separate total-time regressor is trained.Source: A. Experimental Setup · p. 9

Congestion-risk labels

  • Ordinal labels use training-period normalized-ratio thresholds pm ∈ {0.85, 0.90, 0.95}, producing P85, P90, and P95 congestion labels.Test prevalences need not equal exactly 15%, 10%, and 5% because thresholds are estimated from the training distribution.Source: A. Experimental Setup · p. 9
  • The ordinal multi-label LightGBM classifier produces calibrated, nonincreasing edge-level probabilities that serve as ranking scores and are aggregated for path selection.Source: A. Experimental Setup · p. 9

Input features

  • All learned models consume shared structural, dynamic-context, and graph-aware feature blocks, with telemetry and completed-edge histories truncated at prediction-time boundaries.Source: A. Experimental Setup · p. 9

Regressor selection

  • The regressor comparison evaluates Random Forest, ExtraTrees, CatBoost, XGBoost, and LightGBM under the same chronological split, representation, calibration, and protocol.This isolates the choice of regressor.Source: A. Experimental Setup · p. 9

Evaluation metrics

  • MAE is reported in seconds, RMSLE measures logarithmic error, and Cov@25 and Cov@50 measure positive-target records within 25% and 50% relative error.Lower MAE and RMSLE and higher coverage indicate better performance.Source: A. Experimental Setup · p. 10

B. Prediction and Classification Results

The evaluation identifies LightGBM as the strongest regressor, demonstrates multi-threshold congestion-risk discrimination, and finds complementary value from graph-aware and dynamic-context features. In closed-loop simulation, TN-DCR routing reduces delivery, queue, transfer, and internal waiting times while throughput remains nearly unchanged.

Regression model selection

  • LightGBM achieves the best transfer and reconstructed-total-time results, with MAEs of 27.4 ± 0.1 s and 64.9 ± 0.2 s.It is selected for both regressors after also achieving the strongest overall queue-time performance.Source: B. Prediction and Classification Results · p. 10

Multi-threshold congestion-risk classification

Graph-aware and dynamic-context features

  • Removing both graph-aware and dynamic-context features increases queue-time MAE from 49.6 ± 0.2 s to 54.4±0.4 s, a 9.7% degradation.The joint removal also raises RMSLE and lowers Cov@50, supporting complementary contributions from both feature blocks.Source: C. Ablation Study · p. 10, Table III · p. 10

Stock-key residual correction

  • Stock-key residual correction reduces Bias magnitude from −17.8 ± 0.6 s to −9.6 ± 0.6 s, a 46.1% reduction.The remaining negative Bias indicates residual underestimation.Source: C. Ablation Study · p. 10

Closed-loop routing results

  • 16.40% lower mean total time and 22.59% lower internal waiting occur with TN-DCR routing than with static shortest-path selection.Mean P95 total time, queue time, and transfer time also decrease by 10.33%, 8.2%, and 18.9%, respectively; throughput remains nearly unchanged at 295.43 versus 295.68 commands per hour.Source: D. Closed-Loop Routing Results · p. 11, Table IV · p. 11

E. Managerial Insights

The framework concentrates severe-congestion cases for selective intervention, improves prediction quality through complementary features and calibration, and reduces closed-loop delivery and waiting times. Its operational conclusions remain bounded by observational training data and limited evaluation scope.

Operational implications

  • 60.2 ± 0.2% of the highest-scored 5% of edge-level test records are positive, versus 5.9% overall prevalence.This more than tenfold enrichment supports selective operator review, path reconsideration, or priority handling.Source: E. Managerial Insights · p. 11
  • Removing graph-aware and dynamic-context features increases queue-time MAE from 49.6 ± 0.2 s to 54.4±0.4 s, a 9.7% degradation.Coverage metrics are not uniformly monotonic across the ablation.Source: E. Managerial Insights · p. 11
  • 46.1%: stock-key calibration reduces Bias magnitude from 17.8±0.6 s to 9.6±0.6 s.The calibration therefore functions primarily as a bias-control mechanism.Source: E. Managerial Insights · p. 11
  • Closed-loop routing reduces mean total time by 16.40%, P95 total time by 10.33%, and internal waiting by 22.59%, with nearly unchanged throughput.The dominant mechanism is avoidance of intermediate resource waiting rather than only pre-dispatch queue reduction.Source: E. Managerial Insights · p. 11

Framework implications

  • TN-DCR aggregates edge-level predictions into path-level time and bottleneck-risk estimates for risk-constrained route selection.Its shared representation combines structural, dynamic, path-local, and graph-aware information, with stock-key calibration mitigating persistent queue bias.Source: §VI · pp. 11–12
  • On 51,700 edge-level records, closed-loop routing reduces mean total time, P95 total time, and internal waiting by 16.40%, 10.33%, and 22.59%, respectively.LightGBM is the most consistent regressor over five seeds, and throughput remains nearly unchanged.Source: §VI · p. 12

Limitations

  • Support filtering limits but does not eliminate selection bias because training records come from paths chosen by the incumbent dispatcher.The closed-loop evaluation also covers only a limited scale, horizon, and load regime.Source: §VI · p. 12

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