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A derivation of the ballot theorem from the Spitzer–Pollaczek identity

Published online by Cambridge University Press:  24 October 2008

C. C. Heyde
C. C. Heyde
Affiliation:
University of Manchester
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Extract

Over a period of many years there has developed an extensive literature on ballot problems. These, in effect, constitute a very special class of random walk problems, and their recent continued development has been justified by the apparent difficulty of reducing expressions given by the general theory down to the very simple ones that it is possible to obtain in an elementary fashion. In this short note we show that the obstacle presented by this reduction problem is actually a rather small one. For background to the above comments, together with a fairly comprehensive list of references to the ballot theory and its attendant applications, the reader is referred to Takács(2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 3 , May 1969 , pp. 755 - 757
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Prabhtt, N. U.Queues and inventories (New York: Wiley, 1965).Google Scholar
(2)Takács, L.Applications of ballot theorems in the theory of queues. Proc. Symp. on Congestion Theory. U. North Carolina Press, pp. 337–398 (including discussion) (1965).Google Scholar