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. Scope and purpose We consider a re-entrant shop with multi-class jobs, in which jobs may visit some machines more than once at different stages of processing, as observed in the wafer fabrication process of semiconductor manufacturing. The re-entrant line also consists of both the single-job machine and the batch machine. The former refers to the ordinary machine processing one job at a time, and the latter means the machine processing several jobs together as a batch at a time. In this paper, we propose an approximation method based on the mean value analysis for estimating the mean cycle time of each class of jobs, the mean queue length of each buffer, and the throughput of the system. (C) 2002 Elsevier Science Ltd. All rights reserved.