Mean value analysis of re-entrant line with batch machines and multi-class jobs

We propose an approximate approach for estimating the performance measures of the re-entrant line with single-job machines and batch machines based on the mean value analysis (MVA) technique. Multi-class jobs are assumed to be processed in predetermined routings, in which some processes may utilize the same machines in the re-entrant fashion. The performance measures of interest are the steady-state averages of the cycle time of each job class, the queue length of each buffer, and the throughput of the system. The system may not be modeled by a product form queueing network due to the inclusion of the batch machines and the multi-class jobs with different processing times. Thus, we present a methodology for approximately analyzing such a re-entrant line using the iterative procedures based upon the MVA and some heuristic adjustments. Numerical experiments show that the relative errors of the proposed method are within 5% as compared against the simulation results.