Michaelis–Menten-Based Supervised Learning for Nonlinear Performance Modelling in Bulk-Service Queueing System

Bulk service queueing systems such as M/Mb/1/N and M/Mb/c/N, which are characterised by multiple servers c, fixed batch-size service b, and finite capacity N, indicate the performance measures that are numerically derivable but mathematically complex to evaluate across various parameter ranges. This study addresses that challenge by applying the Michaelis–Menten (M-M) regression model, originally formulated for enzyme kinetics, as an empirical substitute for these measures. The steady-state probabilities are obtained by forming the generator matrix Q, which is solved via LU decomposition process. This yields the exact expressions for average queue length Lq, average system length L, average waiting time Wq, effective arrival rate λeff, blocking probability pblock, and server utilisation. Identifying the inherently saturating, nonlinear relationship between these performance measures and the traffic intensity ρ, the M-M kinetics regression model, originally evolved for enzyme reaction rates, is utilised as an empirical substitute for capturing saturating behaviour. Levenberg–Marquardt, a non-linear least-squares regression algorithm, is used for estimating model parameters Vmax and Kmax. The fitted M-M model signifies excellent agreement with the exact solutions solved by using LU decomposition across a wide range of system configurations, with the coefficient of determination R2 reaching as high as 99.5%. Beyond accuracy, the regression-based approach offers substantial computational efficiency over complex numerical evaluation, making it attractive for rapid system design and optimisation. Results establish Michaelis–Menten regression as a feasible non-linear regression approach for bulk queueing analysis, spanning classical queueing theory and modelling approaches. It offers practical applications for improving decision-making in the analysis of congestion, capacity optimisation, and dynamic resource allocation, which arise frequently in transportation networks, cloud computing job schedulers, and manufacturing assembly lines.