Self-organizing files with dependent accesses

Lam, K. C.; Leung, Ming-Ying; Siu, Man‐Keung

doi:10.2307/3213645

Cited by 35 publications

(23 citation statements)

References 18 publications

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“…Similarly, Q k e is a column vector with elements p 1k ; : : : ;p Nk , so for each r = k, we have C r (I −Q rk ) −1 Q k e as the probability of starting in state r and reaching state k before again visiting state r in the Markov chainP. Then, by Lemmas 3:1:1 and 3:1:2 of [10], it follows that C r (I −Q rk ) −1 Q k e = 1=(m rk + m kr ), which when substituted into Theorem 1 gives (11). To compute the second moment of C t , we square (1) and obtain…”

Section: Mean and Variance Of The Search Costmentioning

confidence: 99%

“…If requests are generated by an aperiodic, irreducible, ÿnite-state Markov chain, R, then the stationary expected search cost is given by [10] …”

Section: Mean and Variance Of The Search Costmentioning

confidence: 99%

“…Our MTF model lies within the broader framework of Markovian request sequences. The MTF scheme with time-dependent Markovian requests was investigated in [10], where a formula for the expected search cost was derived. Special cases of the Markov model that are analytically more tractable were investigated by Rodrigues [13], who also examined convergence to stationarity [12].…”

Section: Introductionmentioning

confidence: 99%

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Performance of the move-to-front algorithm with Markov-modulated request sequences

Coffman¹,

Jelenković

1999

Operations Research Letters

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We study the classical move-to-front (MTF) algorithm for self-organizing lists within the Markov-modulated request (MMR) model. Such models are useful when list accesses are generated within a relatively small set of modes, with the request sequences in each mode being i.i.d. These modes are often called localities of reference and are known to exist in such applications as tra c streams of Ethernet or ATM networks and the locus of control or data accesses of executing computer programs. Our main results are explicit formulas for the mean and variance of the search-cost, the number of accesses required to ÿnd a given list element. By adjusting the number of modes, one can use the MMR methodology to trade o the quality of an approximation with the computational e ort it requires. Thus, our results provide a useful new tool for evaluating the MTF rule in linear-search applications with correlated request sequences. We illustrate the computations with several examples.

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Section: Mean and Variance Of The Search Costmentioning

confidence: 99%

“…If requests are generated by an aperiodic, irreducible, ÿnite-state Markov chain, R, then the stationary expected search cost is given by [10] …”

Section: Mean and Variance Of The Search Costmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Performance of the move-to-front algorithm with Markov-modulated request sequences

Coffman¹,

Jelenković

1999

Operations Research Letters

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show abstract

“…However, it was shown in [1] that this conjecture is not true in general. Except for the papers mentioned above, the probabilistic analysis of the transposition rule is either limited to the case of simplistic distributions [10,15] or numerical studies [2,12]. The reader is referred to [14] for a combinatorial (amortized) analysis of the transposition rule.…”

Section: Introductionmentioning

confidence: 99%

A Transposition Rule Analysis Based on a Particle Process

Gamarnik¹,

Momčilović

2005

Journal of Applied Probability

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A linear list is a collection of items that can be accessed sequentially. The cost of a request is the number of items that need to be examined before the desired item is located, i.e., the distance of the requested item from the beginning of the list. The transposition rule is one of the algorithms designed to reduce the search cost by organizing the list. In particular, upon a request for a given item, the item is transposed with the preceding one. We develop a new approach for analyzing the algorithm. The approach is based on a coupling with a certain constrained asymmetric exclusion process. This allows us to establish an asymptotic optimality of the rule for two families of request distributions.

show abstract

“…However, it was 236 D. GAMARNIK AND P. MOMČILOVIĆ shown in [1] that this conjecture is not true, in general. Except for the papers mentioned above, the probabilistic analysis of the transposition rule is either limited to the case of simplistic distributions [10], [15] or to numerical studies [2], [12]. The reader is referred to [14] for a combinatorial (amortized) analysis of the transposition rule.…”

Section: Introductionmentioning

confidence: 99%

A Transposition Rule Analysis Based on a Particle Process

Gamarnik¹,

Momčilović

2005

J. Appl. Probab.

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A linear list is a collection of items that can be accessed sequentially. The cost of a request is the number of items that need to be examined before the desired item is located, i.e. the distance of the requested item from the beginning of the list. The transposition rule is one of the algorithms designed to reduce the search cost by organizing the list. In particular, upon a request for a given item, the item is transposed with the preceding one. We develop a new approach for analyzing the algorithm, based on a coupling to a certain constrained asymmetric exclusion process. This allows us to establish an asymptotic optimality of the rule for two families of request distributions.

show abstract

Self-organizing files with dependent accesses

Cited by 35 publications

References 18 publications

Performance of the move-to-front algorithm with Markov-modulated request sequences

Performance of the move-to-front algorithm with Markov-modulated request sequences

A Transposition Rule Analysis Based on a Particle Process

A Transposition Rule Analysis Based on a Particle Process

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