Letter to the Editor---Applicability of the Lognormal Distribution to Servicing Times in Congestion Problems

William J. Horvath
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William J. Horvath: Mental Health Research Institute, University of Michigan, Ann Arbor, Michigan

Operations Research, 1959, vol. 7, issue 1, 126-128

Abstract: This note is to call attention to the applicability of the logarithmic normal distribution [1] in queuing problems where the customary negative exponential gives a poor fit to measured servicing times. A recent example from the literature is the study made by Brigham [2] of the congestion at tool cribs in an aircraft factory. Table I shows data taken from Figs 1 and 2 of his paper together with the lognormally and exponentially fitted values. The exponential fits were obtained from Brigham's paper while the lognormal points were determined from the best straight line fitted to the data plotted on logarithmic probability paper. When a good fit is obtained over the entire range, this crude procedure yields better than 1 per cent accuracy. For a more accurate method based on iterative procedures the reader is referred to Aitchison and Brown's book on the subject [3].

Date: 1959
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