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Approximations for Product Departures from a Single-Server Station with Batch Processing in Multi-Product Queues

Author

Listed:
  • Gabriel R. Bitran

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • D. Tirupati

    (College of Business Administration, University of Texas, Austin, Texas 78712)

Abstract

In this paper we consider a single-server station processing jobs belonging to multiple product classes. The processing at the station is in batches of fixed size, r. Job arrivals in different product classes are independent of the arrivals in other classes. The arrivals within each product class and the service times are assumed to have general, independent and identical distributions. Based on approximate analyses, we present an estimate for the mean number of jobs and provide two complementary characterizations of the product departure streams. We present methods to compute the squared coefficient of variation of the departure intervals and the probability distribution of the lot sizes of product departures. The computational results reported in this paper demonstrate that the accuracy of the approximations is acceptable in most applications. Based on these results, we identify conditions under which the estimates can be expected to perform well. The methods developed in this paper complement the decomposition approach for open queueing networks proposed by Shanthikumar and Buzacott (Shanthikumar, J. G., J. A. Buzacott. 1981. Open queueing network models of job shops. Internat. J. Production Res. 19(3) 255--266.) and Whitt (Whitt, W. 1983. The queueing network analyzer. Bell System Tech. J. 62(9) 2779--2815.) and permit analysis of networks with some types of batch processing.

Suggested Citation

  • Gabriel R. Bitran & D. Tirupati, 1989. "Approximations for Product Departures from a Single-Server Station with Batch Processing in Multi-Product Queues," Management Science, INFORMS, vol. 35(7), pages 851-878, July.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:7:p:851-878
    DOI: 10.1287/mnsc.35.7.851
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    Cited by:

    1. Jens Baetens & Bart Steyaert & Dieter Claeys & Herwig Bruneel, 2018. "Delay analysis of a two-class batch-service queue with class-dependent variable server capacity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(1), pages 37-57, August.
    2. Ruth Sagron & Uri Yechiali, 2024. "Inter-Departure Time Correlations in PH / G /1 Queues," Mathematics, MDPI, vol. 12(9), pages 1-23, April.
    3. Justus Schwarz & Judith Stoll née Matzka & Eda Özden, 2015. "A general model for batch building processes under the timeout and capacity rules," Annals of Operations Research, Springer, vol. 231(1), pages 5-31, August.
    4. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    5. Wu, Kan, 2014. "Taxonomy of batch queueing models in manufacturing systems," European Journal of Operational Research, Elsevier, vol. 237(1), pages 129-135.
    6. Subba Rao, S. & Gunasekaran, A. & Goyal, S. K. & Martikainen, T., 1998. "Waiting line model applications in manufacturing," International Journal of Production Economics, Elsevier, vol. 54(1), pages 1-28, January.
    7. Sarang Deo & Milind Sohoni, 2015. "Optimal Decentralization of Early Infant Diagnosis of HIV in Resource-Limited Settings," Manufacturing & Service Operations Management, INFORMS, vol. 17(2), pages 191-207, May.
    8. Marc R. Lambrecht & Philip L. Ivens & Nico J. Vandaele, 1998. "ACLIPS: A Capacity and Lead Time Integrated Procedure for Scheduling," Management Science, INFORMS, vol. 44(11-Part-1), pages 1548-1561, November.
    9. Bitran, Gabriel R. & Morabito, Reinaldo., 1994. "Open queueing networks : optimization and performance evaluation models for discrete manufacturing systems," Working papers 3743-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.

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