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The Two-Machine Job-Shop with Exponential Processing Times

  • Hamilton Emmons
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 86)

Abstract

Using a generalized random walk model, we analyze the problem of processing a fixed number of jobs on each of two machines. The order of processing is unconstrained, and the processing times are exponential random variables. Rather simple formulas are obtained for the machine idle time distribution and the mean makespan.

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References

  1. 1.
    Feller, W. (1957), An Introduction to Probability Theory and its Applications, Vol. 1, John Wiley, N. Y., Chapter III.Google Scholar
  2. 2.
    Milch, P. R. and M. H. Waggoner (1970), “A Random Walk Approach to a Shutdown Queueing System,” SIAM J. Appl. Math., 19, 103–115.CrossRefGoogle Scholar
  3. 3.
    Pearson, K. (1956) ed., Tables of the Incomplete Beta-Function, Cambridge.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1973

Authors and Affiliations

  • Hamilton Emmons
    • 1
  1. 1.Case Western Reserve UniversityClevelandUSA

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