Machine Learning and its Application to Queue Theory

ABSTRACT

Finding solutions to queue theory problems using traditional methods has become challenging due to introduction of modern technology in solving queue problems. A good system dynamics that can portray the mathematical complexity becomes important, hence the introduction of Machine Learning techniques to handle these complexities. Due to the fact that the cost of speed and accuracy of predictions is extremely high, there is a need to develop optimization techniques aimed at improving the quality of training for Machine Learning tools. Several optimizers for machine learning have been developed. But in their development, the variability in past objective values has not been captured in the adjustment of the update rule. Hence this study is aimed at improving on this draw back from previous studies. In doing this, a new parameter which adjusts the update rule by capturing the difference between the past objective values is introduced. The convergence property of the algorithm is shown for estimating error bound of optimization methods. The convergence analysis of New optimization method for convex and non convex objective functions is given using the Regret analysis. Theorems that illustrate the properties that guarantee the convergence of New optimizer are stated with proofs. A structure for making predictions for performance measures of a queue system is represented using the Artificial Neural Network and the K-Means Clustering method. Subsequently, an illustration of the impact of the parameters that were introduced into the queue was done. The results obtained from the analysis showed it exhibited the properties of a better model when compared with existing models. The developed optimization method had better accuracy and faster convergence.