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Author Burnett, G. J. ♦ Coffman, E. G.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1973
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract A combinatorial problem arising from the analysis of a model of interleaved memory systems is studied. The performance measure whose calculation defines this problem is based on the distribution of the number of modules in operation during a memory cycle, assuming saturated demand and an arbitrary but fixed number of modules.In general terms the problem is as follows. Suppose we have a Markov chain of $\textit{n}$ states numbered 0, 1, ···, $\textit{n}$ - 1. For each $\textit{i}$ assume that the one-step transition probability from state $\textit{i}$ to state $(\textit{i}$ + 1) mod $\textit{n}$ is given by the parameter $\textit{α}$ and from state $\textit{i}$ to any other state is $\textit{β}$ = (1 - $\textit{α})/(\textit{n}$ - 1). Given an initial state, the problem is to find the expected number of states through which the system passes before returning to a state previously entered. The principal result of the paper is a recursive procedure for computing this expected number of states. The complexity of the procedure is seen to be small enough to enable practical numerical studies of interleaved memory systems.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1973-01-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 20
Issue Number 1
Page Count 7
Starting Page 39
Ending Page 45


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Source: ACM Digital Library