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Analysis of Single Work Stations

  • Tayfur Altiok
Part of the Springer Series in Operations Research book series (ORFE)

Abstract

We start the analysis of manufacturing systems by first explaining the way we perceive them. Then we will focus on some simple cases of work stations with and without failures and demonstrate how these systems can be analyzed. A work station can be thought of as a work place in the shop floor as depicted in Fig3.1, where jobs arrive to be processed or machined. They are kept in the buffer zone (work-in-process (WIP) inventory) until their process begins and are transferred to other areas in the facility after their process is completed. The machines may experience random failures. Our approach in studying work stations in manufacturing environments is to perceive them as queueing systems. The flow of incoming jobs, either one by one or in batches, forms the arrival stream, which can be identified by the statistical characteristics of the time between consecutive arrivals. Service times are usually the processing times of jobs in the work station. Processing times may be augmented by random failures and repairs. Thus, a work station may very well be looked at as a queueing system with single or multiple servers, with finite or infinite waiting room (input buffer), and with a service policy depending on the operating characteristics of the work place. Queueing theory is a fairly well-developed field, and a considerable amount of research is being done on a variety of queueing systems and queueing networks. We demonstrate in this and other chapters that with some level of abstraction, queueing theory and queueing networks can be very useful in the analysis and design of manufacturing systems. In fact, queueing modeling of numerous systems have already been studied and can be found in Gross and Harris ([1974]), Cooper ([1990]), and Kleinrock ([1975]), among various others. Next we give a short introduction on the formulation and the analysis of queueing systems.

Keywords

Processing Time Work Station Busy Period Shop Floor Repair Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Altiok, T., 1989, Queueing Modeling of a Single Processor with Failures. Performance Evaluation, Vol. 9, pp. 93–102.CrossRefGoogle Scholar
  2. Avi-Itzhak, B., and P. Naor, 1963, Some Queueing Problems with the Service Station Subject to Breakdown. Operations Research, Vol. 10, pp. 303–320.CrossRefGoogle Scholar
  3. Bhat, U. N., 1984, Elements of Applied Stochastic Processes. John Wiley, New York.Google Scholar
  4. Buzacott, J. A., and J. G. Shanthikumar, 1993, Stochastic Models of Manufacturing Systems. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
  5. Çinlar, E., 1975, Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, NJ. Cobham, A., 1954, Priority Assignment in Waiting Lines. Operations Research, Vol. 2, pp. 70–76.Google Scholar
  6. Cooper, R. B., 1990, Introduction to Queueing Theory., 2nd ed. North Holland, Amsterdam.Google Scholar
  7. Federgruen, A., and L. Green, 1986, Queueing Systems with Service Interruptions. Operations Research, Vol. 34, pp. 752–768.CrossRefGoogle Scholar
  8. Feller, W., 1968, Introduction to Probability Theory and Its Applications. John Wiley, New York.Google Scholar
  9. Gaver, D. P., 1962, A Waiting Line with Interrupted Service Including Priorities. J. Royal Stat. Soc., B24, pp. 73–90.Google Scholar
  10. Gross, D., and C. M. Harris, 1974, Fundamentals of Queueing Theory. John Wiley, New York.Google Scholar
  11. Heyman, D. R, and M. J. Sobel, 1982, Stochastic Models in Operations Research., Vol. 1. McGraw Hill, New York.Google Scholar
  12. Jaiswal, N. K., 1968, Priority Queues. Academic Press, New York.Google Scholar
  13. Kashyap, B. R. K., and M. L. Chaudhry, 1988, An Introduction to Queueing Theory. A & A Publications, Kingston, Ontario.Google Scholar
  14. Keilsen J., 1962, Queues Subject to Service Interruption. Ann. Math. Stat., Vol. 33, pp. 1314–1322.CrossRefGoogle Scholar
  15. Kelly, F. R, 1979, Reversibility and Stochastic Networks. John Wiley, New York.Google Scholar
  16. Kleinrock, L., 1975, Queueing Systems, Vol. 1: Theory. John Wiley, New York.Google Scholar
  17. Kraemer, W., and M. Langenbach-Belz, 1976, Approximate Formulae for the Delay in the Queueing System G/G/1. Proc. 8th Intl. Teletraffic Congress, Melbourne.Google Scholar
  18. Mikou, N., O. Kacimi, and S. Saadi, 1994, Two Processors Interacting Only During Breakdown: The Case Where the Load Is Not Lost. to appear in Queueing Systems Google Scholar
  19. Mitrani, I. L., and B. Avi-Itzhak, 1968, A Many Server Queue with Service Interruptions. Operations Research, Vol. 16, pp. 628–638.CrossRefGoogle Scholar
  20. Neuts, M. F., 1981, Matrix-Geometric Solutions in Stochastic Models-An Algorithmic Approach. Johns Hopkins University Press, Baltimore, MD.Google Scholar
  21. Nicola, V. F., 1986, A Single Server Queue with Mixed Types of Interruptions. Acta Informatica, Vol. 23, pp. 465–486.CrossRefGoogle Scholar
  22. Palm, C., 1947, The Distribution of Repairmen in Servicing Automatic Machines. Industritidningen Norden, Vol. 75, pp. 75–80,90–94,119–123.Google Scholar
  23. Perros, H. G., 1994, Queueing Networks with Blocking. Oxford University Press, NewGoogle Scholar
  24. York. Ross, S. M., 1980, Introduction to Probability Models. Academic Press, New York.Google Scholar
  25. Shanthikumar, J. G., 1982, On Reducing Time Spent in M/G/1 Systems. European J. Operations Research, Vol. 9, pp. 286–294.CrossRefGoogle Scholar
  26. Shanthikumar, J. G., 1989, Level Crossing Analysis of Priority Queues and a Conservation Identity for Vacation Models. Naval Research Logistics, Vol. 36, pp. 797–806. 112 3. Analysis of Single Work StationsCrossRefGoogle Scholar
  27. Stecke, K. E. and J. E. Aronson, 1985, Review of Operator/Machine Interference Models. Intl. J. Production Research, Vol. 23, pp. 129–151.CrossRefGoogle Scholar
  28. Suri, R., J. L. Sanders, and M. Kamath, 1993, Performance Evaluation of Production Networks. Handbooks in OR and MS (S. Graves, et al., eds.), Elsevier Science Publishers.Google Scholar
  29. Thiruvengadam, K., 1963, Queueing with Breakdowns. Operations Research, Vol. 11, pp. 62–71.CrossRefGoogle Scholar
  30. Tijms, H. C., 1986, Stochastic Modeling and Analysis —A Computational Approach. John Wiley, New York.Google Scholar
  31. White, H.C., and L. S. Christie, 1958, Queueing with Preemptive Priorities or with Breakdown. Operations Research, Vol. 6, pp. 79–95.CrossRefGoogle Scholar
  32. Whitt, W., 1983, The Queueing Network Analyzer. Bell Syst. Technical J. Vol. 62, pp. 2779–2815.Google Scholar
  33. Wolff, R. W., 1989, Stochastic Modeling and the Theory of Queues. Prentice Hall, Englewood Cliffs, NJ.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Tayfur Altiok
    • 1
  1. 1.Department of Industrial EngineeringRutgers UniversityPiscatawayUSA

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