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 continuous-parameter 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