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Diffusion approximations for complex repair systems
Author(s) -
Iglehart Donald L.,
Lalchandani Atam P.
Publication year - 1991
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.3800380603
Subject(s) - objectivity (philosophy) , computer science , citation , library science , operations research , mathematics , philosophy , epistemology
: A wide variety of complex repair systems can be modeled as continuous time Markov chains. These systems are closed networks of queues with a total of n jobs circulating in the network. The process of interest is the number of jobs, X sub n (t), at the various repair centers at time t. After appropriate translation and scaling, we show that the processes (X sub n (t) : t or = 0) converge weakly to a limiting multivariate Ornstein-Uhlenbeck process. This limit process is then used to obtain computable approximations for X sub n (t). Numerical results are presented for three specific repairman models and the approximations are compared with exact results obtained through product form formulae. In most cases the approximation is quite accurate.