The generalized Banach match-box problem: Application in disc storage management
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A computer system manages disc storage of finite capacity c blocks. This storage must be divided among N files in such a way that the expected number of disc accesses accomplished until the necessary reorganization is maximized. Each access to the disc appends a record of a fixed length to the ith file with probability pi (i=1,h., N). The reorganization is needed when the chosen file has run out of space. It is shown that the above problem is a generalization of Banach's match-box problem known from the probability theory. A detailed separate analysis for the N=2 case and for the multivariate case is performed and some approximate results for large c are given.
AMS (MOS) subject classifications (1980)60C05 68B15
Key wordsSerial file system De Moivre-Laplace theorem probabilistic criterion optimal allocation
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