### A Combinatorial Problem Related to Interleaved Memory SystemsA Combinatorial Problem Related to Interleaved Memory Systems

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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