Supervised learning-based approximation method for single-server open queueing networks with correlated interarrival and service times

Efficient performance evaluation methods are needed to design and control production systems. We propose a method to analyse single-server open queueing network models of manufacturing systems composed of delay, batching, merge and split blocks with correlated interarrival and service times. Our method (SLQNA) is based on using a supervised learning approach to determine the mean, the coefficient of variation, and the first-lag autocorrelation of the inter-departure time process as functions of the mean, coefficient of variation and first-lag autocorrelations of the interarrival and service times for each block, and then using the predicted inter-departure time process as the input to the next block in the network. The training data for the supervised learning algorithm is obtained by simulating the systems for a wide range of parameters. Gaussian Process Regression is used as a supervised learning algorithm. The algorithm is trained once for each block. SLQNA does not require generating additional training data for each unique network. The results are compared with simulation and also with the approximations that are based on Markov Arrival Process modelling, robust queueing, and G/G/1 approximations. Our results show that SLQNA is flexible, computationally efficient, and significantly more accurate and faster compared to the other methods.