Mean value analysis of re-entrant line with batch machines and multi-class jobs |
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| Affiliation: | 1. Faculty of Science, Beirut Arab University, P.O. Box 11-5020 Riad El Solh, Beirut 1107 2809, Lebanon;2. Department of Physics, Khalifa University, Abu Dhabi, United Arab Emirates;1. Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA;2. Department of Materials Science and Engineering, Texas A&M University, College Station, TX 77843, USA;3. LEM3, UMR 7239, Arts et Mtiers ParisTech, Metz-Lorraine, 57078 Metz, France;1. Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China;2. Department of Physics, College of Science, Qiqihar University, Qiqihar 161006, China;3. Laboratory of Optical Physics, Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;1. Institute of Low Temperature and Structure Research Polish Academy of Sciences, Department of Spectroscopy of Excited States, ul. Okólna 2, 50-422 Wrocław, Poland;2. University of Wrocław, Faculty of Chemistry, ul. F. Joliot-Curie 14, 50-383 Wrocław, Poland;1. Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain;2. Graduate School of Education, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-5824, Japan |
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| Abstract: | 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 purposeWe 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. |
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