IJPAM: Volume 74, No. 2 (2012)


Edmond J. Vanderperre
Department of Decision Sciences
University of South Africa
P.O. Box 392, Pretoria, 0003, SOUTH AFRICA
Correspondence Address: Ruzettelaan 183, Bus 158, B-8370, Blankenberge, BELGIUM

Abstract. We analyse the point availability of a duplex system characterized by warm stand-by and attended by 2 heterogeneous repairmen. In order to describe the random behaviour of the engineering system, we employ a stochastic process endowed with time dependent transition measures satisfying (coupled) partial differential equations. The solution procedure is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. As an application, we consider the particular but important case of Erlang repair.

Received: December 1, 2011

AMS Subject Classification: 60K10, 35M10

Key Words and Phrases: warm standby, dual transform, functional equation, Cauchy principal value, point availability, Erlang repair, inversion theorem

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 74
Issue: 2