## Properties of the Working-Set model (1972)

Venue: | Communications of the ACM |

Citations: | 43 - 0 self |

### BibTeX

@ARTICLE{Denning72propertiesof,

author = {Peter J. Denning and Stuart C. Schwartz},

title = {Properties of the Working-Set model},

journal = {Communications of the ACM},

year = {1972},

volume = {15},

pages = {191--198}

}

### Years of Citing Articles

### OpenURL

### Abstract

A program's working set W(t, T) at time t is the set of distinct pages among the T most recently referenced pages. Relations between the average working-set size, the missing-page rate, and the interreference-interval distribution may be derived both from time-average definitions and from ensemble-average (statistical) definitions. An efficient algorithm for estimating these quantities is given. The relation to LRU (least recently used) paging is characterized. The independent-reference model, in which page references are statistically independent, is used to assess the effects of interpage dependencies on working-set size observations. Under general assumptions, working-set size is shown to be normally distributed. Key Words and Phrases: working-set model, paging, paging algorithms, program behavior, program

### Citations

492 |
A study of replacement algorithms for a virtual-storage computer
- Belady
- 1966
(Show Context)
Citation Context ...ons in algorithm strategy and data organization can magnify the manifestations of this effect manyfold [3, 14]. Third, programs may be run efficiently with only a subset of their pages in main memory =-=[2, 11, 14]-=-. According to the above, we may picture a program as making transitions from time to time among "localities," a locality being some subset of its pages. The pages in the "current locality" are refere... |

324 |
Evaluation techniques for storage hierarchies
- Mattson, Gecsei, et al.
- 1970
(Show Context)
Citation Context ...one-pass algorithm that estimates the functions f, F, m, and s for a given reference string rlr2 ... rk. (This algorithm is analogous to one suggested by Mattson et al. for measuring page fault rates =-=[12]-=-.) Let (cl, ..., CL+I) be a vector of integer variables, initially all 0; after the tth iteration of the algorithm (1 < t < k), G' (1 < j < L) will count the number of interference intervals of length... |

219 |
The Working Set Model for Program Behavior
- Denning
- 1968
(Show Context)
Citation Context ...ands of programs running in them--has stimulated interest in analytic program-behavior models from which adaptive memory management policies can be derived. The working-set model for program behavior =-=[6, 7]-=- has proved to be a useful starting point. A program's working set is, intuitively, the smalle stsubset of its pages that must reside in main memory in order that the program operate at some desired l... |

114 | Virtual memory - Denning - 1970 |

105 | Acentral limit theorem and a strong mixing condition - Rosenblatt - 1956 |

66 | Principles of optimal page replacement - Aho, Denning, et al. - 1971 |

19 |
Estimates of distributions of random variables for certain computer communications traffic models
- Fuchs, Jackson
- 1970
(Show Context)
Citation Context ...ffect of increasing the missing-page rate. Communications March 1972 of Volume 15 the ACM Number 3slnterarrival distributions and densities encountered in practice frequently have nonincreasing tails =-=[4, 10]-=-. Assuming f(x) is such a density, there exists an x0 (relatively small compared to ~) such that f(x) is nonincreasing for x >_ x0. By P5, m (T) would be concave up for T > x0 and (3.10) would hold. 4... |

7 |
Program behavior in a paging environment
- Brawn, Gustavson
- 1968
(Show Context)
Citation Context ...nd to concentrate on small parts of large problems for moderately long intervals; simple alterations in algorithm strategy and data organization can magnify the manifestations of this effect manyfold =-=[3, 14]-=-. Third, programs may be run efficiently with only a subset of their pages in main memory [2, 11, 14]. According to the above, we may picture a program as making transitions from time to time among "l... |

7 |
Is automatic folding of programs efficient enough to displace manual
- Sayre
- 1969
(Show Context)
Citation Context ...nd to concentrate on small parts of large problems for moderately long intervals; simple alterations in algorithm strategy and data organization can magnify the manifestations of this effect manyfold =-=[3, 14]-=-. Third, programs may be run efficiently with only a subset of their pages in main memory [2, 11, 14]. According to the above, we may picture a program as making transitions from time to time among "l... |

6 |
A study of storage partitioning using a mathematical model of locality
- Coffman, Ryan
- 1972
(Show Context)
Citation Context ...tribution of w(t, T) as expressed in (5.8) converges to a normal distribution with mean s(T) and standard deviation ~r(T) as given by (5.6). These conclusions are corroborated by experiments cited in =-=[5]-=-. 6. The Independent Reference Model According to the independent reference model [1], a program's reference string rlr2 • • • rt • • • is a sequence of independent random variables with stationary pr... |

5 |
Interarrival statistics for time sharing systems
- Wood
- 1966
(Show Context)
Citation Context ...ffect of increasing the missing-page rate. Communications March 1972 of Volume 15 the ACM Number 3slnterarrival distributions and densities encountered in practice frequently have nonincreasing tails =-=[4, 10]-=-. Assuming f(x) is such a density, there exists an x0 (relatively small compared to ~) such that f(x) is nonincreasing for x >_ x0. By P5, m (T) would be concave up for T > x0 and (3.10) would hold. 4... |

2 |
Resource Allocation in Multiprocess or Computer Systems , " (Ph
- Denning
- 1968
(Show Context)
Citation Context ...ands of programs running in them--has stimulated interest in analytic program-behavior models from which adaptive memory management policies can be derived. The working-set model for program behavior =-=[6, 7]-=- has proved to be a useful starting point. A program's working set is, intuitively, the smalle stsubset of its pages that must reside in main memory in order that the program operate at some desired l... |

2 |
Scheduling TSS/360 for responsiveness
- Doherty
- 1970
(Show Context)
Citation Context ...memory, and that no working-set page of an active program may be considered for removal from main memory. Simulation results on the RCA Spectra 70/46 [16] and experimental observations of raM TSS/360 =-=[9]-=- provide evidence that this principle is viable. Programs, to one degree or another, obey the principle of locality which asserts: (I) during any interval of time, a program distributes its references... |

1 |
The cache, lBMSyst
- Liptay
- 1968
(Show Context)
Citation Context ...ons in algorithm strategy and data organization can magnify the manifestations of this effect manyfold [3, 14]. Third, programs may be run efficiently with only a subset of their pages in main memory =-=[2, 11, 14]-=-. According to the above, we may picture a program as making transitions from time to time among "localities," a locality being some subset of its pages. The pages in the "current locality" are refere... |

1 | Stationary Random Functions - Yaglom - 1962 |

1 |
Virtual memory management in a paging environment
- Weizer, Oppenheimer
(Show Context)
Citation Context ...se a processor only if its working set is in main memory, and that no working-set page of an active program may be considered for removal from main memory. Simulation results on the RCA Spectra 70/46 =-=[16]-=- and experimental observations of raM TSS/360 [9] provide evidence that this principle is viable. Programs, to one degree or another, obey the principle of locality which asserts: (I) during any inter... |