The$Working$SetModel$for$ Program$Behavior$ · The$Working$SetModel$for$ Program$Behavior$ Peter$J.$Denning$ Massachuse=s$Ins?tute$of$Technology,$ Cambridge,$Massachuse=s$ 1

The Working Set Model for Program Behavior

Peter J. Denning Massachuse=s Ins?tute of Technology,

Cambridge, Massachuse=s

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About the paper

•  Published in 1968, 1st ACM Symposium on Opera?on Systems Principles (SOSP)

•  2005, SIGOPS Hall of Fame Award “This paper introduced the working set model, which has became a key concept in understanding of locality of memory references and for implemen:ng virtual memory. Most paging algorithms can trace their roots back to this work”

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Background: Virtual memory

•  In the 50s ~ 60s – System: ATLAS computer – Two-‐level memory hierarchies: main memory + auxiliary storage – Demand paging – Backbone for mul?programming

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Background: Thrashing

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“When it was first observed in the 1960s, thrashing was an unexpected, sudden drop in throughput of a mul:programmed system … I explained the phenomenon in 1968 and showed that a working-‐set memory controller would stabilize the system ...” – Peter D. Denning

Mo?va?on

•  Develop a unified approach to tackle the resource alloca?on problem: process scheduling and memory management

•  However, such unified approach is absent, because there is no adequate model for program behavior – Program behavior: a program’s system demand, including processor and memory demand

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Working Set Model -‐ Overview

•  Intended to model the behavior of programs, specifically the programs’ memory demand

•  What is the working set of a program? – Programmer’s standpoint: the smallest collec?on of informa?on must be present in main memory to assure efficient execu?on of the program

– System’s standpoint: the set of most recently referenced pages

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Working Set Model -‐ Defini?on

•  Working set informa?on of a process at ?me t is defined as

collec?on of memory pages referenced by the process during the ?me interval (t -‐ τ, t), τ is the working set parameter

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Working Set Model -‐ Example

sequences of page references 2 6 1 5 7 7 7 7 7 5 1 6 2 3 4 1 2 3 4 4 4 2 6 1 5 7 7 7 7 7 5 1 6 2 3 4 1 2 3 4 4 4 2 6 1 5 7 7 7 7 7 5 1 6 2 3 4 1 2 3 4 4 4

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W(t1, τ) = {2, 6, 1, 5, 7}

W(t2, τ) = {7, 5, 1}

W(t3, τ) = {4, 1, 2, 3}

Working Set Model -‐ Proper?es

•  P1. Size of working set – w(t, τ): number of pages in working set W(t, τ) – w(t, 0) is 0 – w(t, τ) is a monotonically increasing func?on of τ

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•  P2. Predic?on – For small &me separa&on α, the set W(t, τ) is a good predictor for the set W(t + α, τ), because references to the same page tend to cluster in ?me, the probability (below) is small

– On the other hand, for large &me separa&on α (say, α >> τ), W(t, τ) is a not good predictor for the set W(t + α, τ)

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•  P3. Reentry Rate – The rate at which memory page reenters a working set – Important property for analyzing page traffic – Highly related to the value of τ.

•  E.g. as τ is reduced, size of working set decreases, the probability that needed pages are not in W(t, τ) increases.

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•  P3. Reentry Rate (con?nued) – Process-‐&me reentry rate λ(τ) = 1/m(τ), where m(τ) is the mean ?me between reentries – Real-‐&me reentry rate ϕ(τ) = λ(τ) / (1 + λ(τ)T ), where T is the traverse ?me for fetching a page – Total return traffic rate βMϕ(τ)

•  βM is the average number of pages for all working sets •  It es?mates the number of pages per unit ?me returning to main memory

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•  P4. τ – Sensi?vity – Measures how sensi?ve is the reentry rate λ(τ) to changes in τ

if τ is decreased by dτ, λ(τ) increases by dτ σ(τ)

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Choice of τ

•  If τ is “too small”, it may result in high traffic of returning pages

•  If τ is “too large”, it may result in wasted main memory

•  Recommended τ: a value comparable to the memory traverse ?me T

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Detec?ng W(t, τ)

•  A hardware-‐based approach is described, but not prac?cal

•  Need a sosware-‐based approach •  The paper proposes sampling the page table entries at intervals of σ seconds, where σ = τ / K (K an integer constant)

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“The idea of sampling for used pages was not new …… What was new was that the window was defined in the virtual :me of the program …”

Detec?ng W(t, τ)

•  Page table entries for detec?ng W(t, τ)

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-‐  M is 1 if and only if page is in main memory

-‐  1-‐>u0 each ?me a page reference occurs

-‐  At end of each sampling interval, pa=ern in use bits shised right one posi?on

Memory Alloca?on

•  A program will not be run unless there is space in memory for its working set

•  Knowledge of working set size w(t, τ) with demand paging suffices to mange memory well

•  Before running a process, insure that there are enough pages of memory to contain its working set

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Scheduling Implementa?on with Working Set

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•  Required proper?es – Memory management and process scheduling be closely related ac?vi?es

– Sampling of page tables, only on changing working sets, and as infrequently as possible

– Provide measurements of current working set sizes and processor ?me consump?on for each process

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Resource Alloca?on: A Balancing Problem

•  Formulate the resource alloca?on as a problem of balancing processor and memory demands against available resources

•  “memory demand” of process I where M is number of pages of main memory

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•  But how to define the “processor demand” •  Idea: define “processor demand” to be the frac?on of a standard interval a process is expected to use before it blocks – Standard interval A, chosen to reflect the maximum tolerable response ?me to a user – Condi?onal expecta?on func?on Q(ti), to predict the amount of process ?me to elapse before the next interac?on

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•  “processor demand” of process i

Where N is the number of processors

•  “system demand” is defined as Di = (pi, mi)

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•  Then, a system is balanced if S is dynamically maintained, and measures the

total demand of current running list α, β are constants chose to achieve desired

frac?on of resource to cons?tute balance •  To keep the computer system in balance, a “balance policy” can be designed to minimize ( S – (α, β ) )

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Conclusion

•  Define the working set model for program behavior

•  Working set model provides an convenient way to determine what informa?on is in use by a computa?on and which is not

•  Working set model enables simple determina?on of memory demands

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The$Working$SetModel$for$ Program$Behavior$ · The$Working$SetModel$for$ Program$Behavior$ Peter$J.$Denning$ Massachuse=s$Ins?tute$of$Technology,$ Cambridge,$Massachuse=s$ 1