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