Performance evaluation of re-entrant lines with multi-class jobs and multi-server workstations

Abstract

An approximation method is proposed for estimating the performance measures of re-entrant lines with multi-server workstations based on the Mean Value Analysis (MVA) technique. The system of interest can be found in the semiconductor wafer fabrication line in which several circuit types are manufactured through re-entrant processes at both the single-job and the batch workstations. Each workstation may have several identical machines. Multi-class jobs are assumed to be processed in a predetermined routing, in which some processes may utilize the same workstation several times in the re-entrant fashion. The performance measures of interest are the steady-state average 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 modelled by a product form queueing network due to the inclusion of batch machines, multi-class jobs with different processing times, and multi-server workstations. Thus, a methodology is proposed for analysing such a reentrant line approximately using the iterative procedures based upon the MVA and some heuristic adjustments. Results of numerical tests are provided to show the performance of the proposed approach against the simulation results.