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March, 1959 Note on a Moving Single Server Problem
S. Karlin, R. G. Miller Jr., N. U. Prabhu
Ann. Math. Statist. 30(1): 243-246 (March, 1959). DOI: 10.1214/aoms/1177706381


B. McMillan and J. Riordan in [1] derived the generating function for the probability distribution of the number of items completed before absorption in a moving single server problem in two special cases. Through an analogy to the work of L. Takacs [2] on busy period problems for a simple queue, McMillan and Riordan postulated a nonlinear integral equation relation for the generating function. In this note the validity of this relation is proved in general by exploiting the analogy more fully, and the generating function in the two special cases is obtained directly from the integral equation. A similar functional relation is established for the Laplace-Stieltjes transform of the distribution of time until absorption, and the transform is obtained for the two special cases.


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S. Karlin. R. G. Miller Jr.. N. U. Prabhu. "Note on a Moving Single Server Problem." Ann. Math. Statist. 30 (1) 243 - 246, March, 1959.


Published: March, 1959
First available in Project Euclid: 27 April 2007

zbMATH: 0089.13604
MathSciNet: MR101567
Digital Object Identifier: 10.1214/aoms/1177706381

Rights: Copyright © 1959 Institute of Mathematical Statistics

Vol.30 • No. 1 • March, 1959
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