The Working Set Model for Program Behavior. Peter J. Denning Massachuse=s Ins?tute of Technology, Cambridge, Massachuse=s

Transcription

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

2 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 2

3 Background: Virtual memory In the 50s ~ 60s System: ATLAS computer Two- level memory hierarchies: main memory + auxiliary storage Demand paging Backbone for mul?programming 3

4 Background: Thrashing 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 4

5 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 5

6 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 6

7 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 7

8 Working Set Model - Example sequences of page references W(t1, τ) = {2, 6, 1, 5, 7} W(t2, τ) = {7, 5, 1} W(t3, τ) = {4, 1, 2, 3} 8

9 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 9

10 Working Set Model - Proper?es 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) 10

11 Working Set Model - Proper?es 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. 11

12 Working Set Model - Proper?es 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 12

13 Working Set Model - Proper?es 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) 13

14 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 14

15 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) 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 15

16 Detec?ng W(t, τ) Page table entries for detec?ng W(t, τ) - M is 1 if and only if page is in main memory - 1- >u 0 each?me a page reference occurs - At end of each sampling interval, pa=ern in use bits shised right one posi?on 16

17 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 17

18 Scheduling Implementa?on with Working Set 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 18

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20 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 20

21 Resource Alloca?on: A Balancing Problem 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(t i ), to predict the amount of process?me to elapse before the next interac?on 21

22 Resource Alloca?on: A Balancing Problem processor demand of process i Where N is the number of processors system demand is defined as D i = (p i, m i ) 22

23 Resource Alloca?on: A Balancing Problem 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 ) ) 23

24 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 24