
Accession Number : AD0748006
Title : Approximations for the Repairman Problem with Two Repair Facilities. I. No Spares.
Descriptive Note : Technical rept.,
Corporate Author : CONTROL ANALYSIS CORP PALO ALTO CALIF
Personal Author(s) : Iglehart,Donald L. ; Lemoine,Austin J.
Report Date : AUG 1972
Pagination or Media Count : 30
Abstract : The model considered here consists of n operating units which are subject to stochastic failure according to an exponential failure time distribution. Failures can be of two types. With probability p(q) a failure is of type 1(2) and is sent to repair facility 1(2) for repair. Repair facility 1(2) operates as a S(Sup 1) (Sub n) (S(Sup 2)(Sub n))server queue with exponential repair times having parameter (Mu sub 1) (Mu sub 2). The number of units waiting for or undergoing repair each of the two facilities is a continuousparameter Markov chain with finite state space. The paper derives limit theorems for the stationary distribution of this Markov chain as n becomes large under the assumption that both S (Sup 1) (Sub n) and S(Sup 2) (Sub n) grow linearly with n. These limit theorems give very useful approximations, in terms of the six parameters characterizing the model, to a distribution that would be impossible to use in practice. (Author)
Descriptors : (*STOCHASTIC PROCESSES, MAINTENANCE), (*QUEUEING THEORY, MAINTENANCE), LOGISTICS, MATHEMATICAL MODELS, STATISTICAL DISTRIBUTIONS, THEOREMS
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE