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Analysis of Page Replacement Policies in the Fluid Limit

Analysis of Page Replacement Policies in the Fluid Limit,10.1287/opre.1090.0761,Operations Research,Ryo Hirade,Takayuki Osogami

Analysis of Page Replacement Policies in the Fluid Limit   (Citations: 2)
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Journal: Operations Research , vol. 58, no. 4-Part-1, pp. 971-984, 2010
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    • ...Hirade and Osogami [7] show that the miss probabilities for LRU and the 2Q cache algorithm [12], respectively, can be closely approximated with those analyzed in a fluid limit...
    • ...Our fluid limit is a non-trivial extension of the fluid limits for the independent reference model in [8], [7]...
    • ...Such scaled systems are also considered in [7], [8]...
    • ...For example, the m-th scaled system, S (m) , of [7] can be seen...
    • ...Also, in contrast to [7], [8], we will define a sequence of scaled systems for each ei, so that the scaled systems for different items have different dependencies in Φk .L etT (m) i be the m-th scaled system for ei. For each ei, we will study the miss probability for the ei in T (∞) i .I nT...
    • ...The following corollary can be compared against the stationary miss probabilities in the fluid limits obtained in [8], [7]...
    • ...Since our fluid limit differs from the fluid limits defined in [8], [7], our ¯ (∞) i differs from those derived in [8], [7]...
    • ...Since our fluid limit differs from the fluid limits defined in [8], [7], our ¯ (∞) i differs from those derived in [8], [7]...
    • ...i and that in [7] is that, in [7], τi(K) is replaced with τ (K )= C −1 (K), where C −1 (·) is the inverse function of C(t )=...
    • ...i and that in [7] is that, in [7], τi(K) is replaced with τ (K )= C −1 (K), where C −1 (·) is the inverse function of C(t )=...
    • ...The differences between the fluid limits in [8] and [7] are discussed in [7]...
    • ...The differences between the fluid limits in [8] and [7] are discussed in [7]...
    • ...To this end, Hirade and Osogami [7] show that, in a fluid limit, the 2Q cache algorithm [12] can be made to have a lower miss probability than LRU by choosing the right value of the parameter of 2Q, assuming that the requests follow independent Poisson processes...

    Takayuki Osogami. A Fluid Limit for Cache Algorithms with General Request Processes

    • ...Hirade and Osogami [7] show that the miss probabilities for LRU and the 2Q cache algorithm [12], respectively, can be closely approximated with those analyzed in a fluid limit...
    • ...Our fluid limit is a non-trivial extension of the fluid limits for the independent reference model in [8], [7]...
    • ...Such scaled systems are also considered in [7], [8]...
    • ...For example, the -th scaled system, , of [7] can be seen as a superposition of independent replications of the origi nal system...
    • ...Also, in contrast to [7], [8], we will define a sequence of scaled systems for each , so that the scaled systems for different items have different dependencies in . Let be the -th scaled system for . For each , we will study the miss probability for the in . In , we assume that is stochastically identical to (i.e., for , it holds that for any measurable set, ). However, we assume that for depend on each other...
    • ...The following corollary can be compared against the stationary miss probabilities in the fl uid limits obtained in [8], [7]...
    • ...Since our fluid limit differs from the fluid limits defined in [8], [7], our differs from those derived in [8], [7]...
    • ...Since our fluid limit differs from the fluid limits defined in [8], [7], our differs from those derived in [8], [7]...
    • ...However, the only difference between our and that in [7] is that, in [7], is replaced with , where is the inverse function of . The differences between the fluid limits in [8] and [7] are discussed in [7]...
    • ...However, the only difference between our and that in [7] is that, in [7], is replaced with , where is the inverse function of . The differences between the fluid limits in [8] and [7] are discussed in [7]...
    • ...However, the only difference between our and that in [7] is that, in [7], is replaced with , where is the inverse function of . The differences between the fluid limits in [8] and [7] are discussed in [7]...
    • ...However, the only difference between our and that in [7] is that, in [7], is replaced with , where is the inverse function of . The differences between the fluid limits in [8] and [7] are discussed in [7]...
    • ...To this end, Hirade and Osogami [7] show that, in a fluid limit, the 2Q cache algorithm [12] can be made to have a lower miss probability than LRU by choosing the right value of the parameter of 2Q, assuming that the requests follow independent Poisson processes...

    Takayuki Osogami. A fluid limit for cache algorithms with general request processes (ext...

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