Mean value analysis of re-entrant lines with batch machines processing multiclass jobs

We are concerned with estimating the average performance of a re-entrant line with single-job machines and batch machines. The system has multiclass jobs, which will be processed in predetermined routes. An analytical approach may be intractable since the system would not be modeled by product form queueing networks due to the inclusion of batch machines and the consideration of multiclass jobs which have different processing times. We propose an approximation method based on the Mean Value Analysis (MVA). Our method obtains the mean waiting time in each buffer of a workstation and the mean cycle time using the MVA and heuristics. Numerical experiments show that the errors of our method are within 5% compared with simulation.