On the expected length of an orderly path

Martin Wiegand () and Saralees Nadarajah ()
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Martin Wiegand: University College London
Saralees Nadarajah: Howard University

OPSEARCH, 2024, vol. 61, issue 2, No 18, 963-971

Abstract: Abstract Lutz et al. (Ann Oper Res 289:463–472, 2020) derived an integral expression for the expected length of an orderly path. We show here that the integral expression can be reduced to a closed form expression in terms of the Gauss hypergeometric function, a generalised hypergeometric function and the Appell hypergeometric function of the first kind. We check the correctness of the closed form expression numerically as well as provide a Mathematica code. Finally, we show that the closed form expression is more efficient than known integral expressions.

Keywords: Hypergeometric function; Mathematica; Numerical study (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s12597-023-00709-1

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