The Hidden Mechanics of Waiting Lines: Chapman-Kolmogorov Equations in Queuing Theory

Problem: Traditional methods often need help accurately predict state transitions in queuing systems, particularly under conditions of uncertainty and variability.

Abstract

Approach: This essay leverages the Chapman-Kolmogorov equations to model state transitions in a synthetic queuing system. A logistic regression model is employed to predict the probabilities of future states based on historical data. Hyperparameter tuning, cross-validation, and visualization techniques enhance and evaluate the model’s performance.

Results: The logistic regression model achieved an accuracy of 0.57 on the test set, with a mean cross-validation score of 0.555. Despite moderate performance, the model effectively demonstrated the application of the Chapman-Kolmogorov equations in predicting state transitions. Visualizations, including confusion matrices and ROC curves, provided insights into the model’s strengths and weaknesses.

Conclusions: The study highlights the utility of the Chapman-Kolmogorov equations in queuing theory for state transition prediction. While the model shows potential, further improvements are needed to address class imbalance and enhance predictive accuracy. Advanced modeling techniques and refined feature engineering could produce more robust and reliable predictions…