SP17302 SERVS - Servers

Suppose we want to replicate a file over a collection of n servers, labeled _S_ $ _{1} $ , _S_ $ _{2} $ , ..., _S_ $ _{n} $ . To place a copy of the file at server _S_ $ _{i} $ results in a placement cost of _c_ $ _{i} $ , for an integer _c_ $ _{i} $ > 0. Now, if a user requests the file from server _S_ $ _{i} $ , and no copy of the file is present at _S_ $ _{i} $ , then the servers _S_ $ _{i + 1} $ , _S_ $ _{i + 2} $ , _S_ $ _{i + 3} $ ... are searched in order until a copy of the file is finally found, say at server _S_ $ _{j} $ , where _j_ > _i_. This results in an access cost of _j_−_i_. (Note that the lower-indexed servers _S_ $ _{i−1} $ , _S_ $ _{i−2} $ , ... are not consulted in this search.) The access cost is 0 if _S_ $ _{i} $ holds a copy of the file. We will require that a copy of the file be placed at server _S_ $ _{n} $ , so that all such searches will terminate, at the latest, at _S_ $ _{n} $ .

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