[PPT] - On the Analysis of Caches with Pending Interest Tables Mostafa PowerPoint Presentation

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College of Information and Computer Sciences

On the Analysis of Caches with Pending Interest Tables

Mostafa Dehghan1, Bo Jiang1 Ali Dabirmoghaddam2, Don Towsley1

1University of Massachusetts Amherst 2University of California Santa Cruz

ICN, October 2, 2015

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Overview

Named Data Networking

Data names instead of IP addresses

Data Structures:

Content Store Pending Interest Table Forwarding Information Base

Packets:

Interest packet Data packet

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SLIDE 3

Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1

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SLIDE 4

Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 Interest: /icn/pit.pdf

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SLIDE 5

Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 Interest: /icn/pit.pdf

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SLIDE 6

Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 Interest: /icn/pit.pdf

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SLIDE 7

Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 Interest: /icn/pit.pdf /icn/pit.pdf

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SLIDE 8

Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 Interest: /icn/pit.pdf /icn/pit.pdf

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SLIDE 9

Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 Interest: /icn/pit.pdf /icn/pit.pdf

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SLIDE 10

Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 /icn/pit.pdf Interest: /icn/pit.pdf

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SLIDE 11

Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 /icn/pit.pdf Interest: /icn/pit.pdf

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SLIDE 12

Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 /icn/pit.pdf Interest: /icn/pit.pdf

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SLIDE 13

Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 /icn/pit.pdf Interest: /icn/pit.pdf 0,2

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Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 /icn/pit.pdf 0,2 Data: /icn/pit.pdf

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Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 /icn/pit.pdf 0,2 Data: /icn/pit.pdf

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Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 /icn/pit.pdf 0,2 Data: /icn/pit.pdf /icn/pit.pdf ...

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Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 /icn/pit.pdf 0,2 Data: /icn/pit.pdf /icn/pit.pdf ...

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SLIDE 18

Overview

Face 0 Face 1 Face 2

Content Store Name Data ss Pending Interest Table Name Face ss Forwarding Information Base Prefix Face ss /icn/ 1 /icn/pit.pdf ...

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Pending Interest Table (PIT)

Performs request aggregation

Keep track of Interests forwarded but not yet satisfied

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Pending Interest Table (PIT)

Performs request aggregation

Keep track of Interests forwarded but not yet satisfied

Advantages:

lower bandwidth usage communication without knowledge of source and destination better security . . .

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Pending Interest Table (PIT)

Performs request aggregation

Keep track of Interests forwarded but not yet satisfied

Advantages:

lower bandwidth usage communication without knowledge of source and destination better security . . .

Affects cache behavior

hit probability response time

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Motivation

Need analytical models to predict cache behavior

Better design choices

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Motivation

Need analytical models to predict cache behavior

Better design choices

PIT sizing

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Motivation

Need analytical models to predict cache behavior

Better design choices

PIT sizing State of the art:

Ignores download delay Does not consider PIT

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Motivation

Need analytical models to predict cache behavior

Better design choices

PIT sizing State of the art:

Ignores download delay Does not consider PIT

Goal: Analytically model cache with PIT

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SLIDE 26

Outline

Time-To-Live Caches Model and Analysis Replacement Based Policies Simulation Results

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SLIDE 27

Time-To-Live (TTL) Caches

Content eviction occurs upon timer expiration

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Time-To-Live (TTL) Caches

Content eviction occurs upon timer expiration Cache t

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Time-To-Live (TTL) Caches

Content eviction occurs upon timer expiration Cache T t

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Time-To-Live (TTL) Caches

Content eviction occurs upon timer expiration Cache T t

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Time-To-Live (TTL) Caches

Content eviction occurs upon timer expiration Cache T t Reset TTL cache

reset timer upon each hit

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Time-To-Live (TTL) Caches

Content eviction occurs upon timer expiration Cache T t Reset TTL cache

reset timer upon each hit

Cache T t

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Time-To-Live (TTL) Caches

Content eviction occurs upon timer expiration Cache T t Reset TTL cache

reset timer upon each hit

Cache T t

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Time-To-Live (TTL) Caches

Content eviction occurs upon timer expiration Cache T t Reset TTL cache

reset timer upon each hit

Cache T t

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Time-To-Live (TTL) Caches

Content eviction occurs upon timer expiration Cache T t Reset TTL cache

reset timer upon each hit

Cache T t

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Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT t

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SLIDE 37

Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT t

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Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT t

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Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT D t

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Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT D t

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SLIDE 41

Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT D t

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SLIDE 42

Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT D t

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SLIDE 43

Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t

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SLIDE 44

Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t

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Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t

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Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t

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Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t

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Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t

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Model

Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t

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SLIDE 50

Metrics

D # misses M # hits N L Z t

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Metrics

Cache hit prob h = E[N] E[M] + E[N] D # misses M # hits N L Z t

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Metrics

Cache hit prob h = E[N] E[M] + E[N] Cache response time r = E[w(D)]/(E[M]+E[N]) w(t) = t+ t (t − x)dm(x) m(t): renewal function Poisson: m(t) = λt D # misses M # hits N L Z t

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Metrics

Cache hit prob h = E[N] E[M] + E[N] Cache response time r = E[w(D)]/(E[M]+E[N]) w(t) = t+ t (t − x)dm(x) m(t): renewal function Poisson: m(t) = λt D # misses M # hits N L Z t Cache occupancy prob

= E[L]/E[Z]

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Metrics

Cache hit prob h = E[N] E[M] + E[N] Cache response time r = E[w(D)]/(E[M]+E[N]) w(t) = t+ t (t − x)dm(x) m(t): renewal function Poisson: m(t) = λt D # misses M # hits N L Z t Cache occupancy prob

= E[L]/E[Z]

PIT occupancy prob p = E[D]/E[Z]

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Replacement Based Policies

Characteristic Time Approximation Introduced by Che et al. for LRU policy w/ Poisson arrivals Extended to other policies, e.g. FIFO, Random, . . . Extended to general request arrival processes Characteristic time T solution of

i oi(T) = C
i – cache occupancy probability of file i

C – cache size

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LRU Cache with Poisson Arrivals

Modeled as reset TTL with constant T Cache hit/occupancy probability hi = oi = eλiT − 1 λiEDi + eλiT

λi – arrival rate of requests for file i EDi – expected download delay for file i characteristic time T solution of

i

eλiT − 1 λiEDi + eλiT = C

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LRU Cache with Poisson Arrivals

PIT occupancy probability pi = λiEDi λiEDi + eλiT

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LRU Cache with Poisson Arrivals

PIT occupancy probability pi = λiEDi λiEDi + eλiT PIT size S ∼ N

i

pi,

i

pi(1 − pi)

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LRU Cache with Poisson Arrivals

PIT occupancy probability pi = λiEDi λiEDi + eλiT PIT size S ∼ N

i

pi,

i

pi(1 − pi)

Average cache response time

ri = EDi + 0.5λiED2

i

λiEDi + eλiT

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Simulation

Cache size = 103 # different files = 104 Requests: Poisson process w/ rate λ = 105 per second File popularity: Zipf distribution, λi ∝ i−0.8 Download delay: 100 ms One simulation run: total of 107 requests simulated Base model:

ZDD: Zero-Download Delay

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Result – Cache Hit Probability

Hit probability for individual files (D = 100 ms)

10 10

2

10

4

10

−2

10

−1

10

File index Hit probability

LRU Simulation Model

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Result – Cache Hit Probability

Hit probability for individual files (D = 100 ms)

10 10

2

10

4

10

−2

10

−1

10

File index Hit probability

LRU Simulation ZDD Model

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Result – Cache Hit Probability

Average hit probability vs. download delay

50 100 150 200 250 0.1 0.2 0.3 0.4 0.5

Download delay (ms) Average hit probability

LRU Simulation Model

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Result – Request Aggregation

PIT occupancy probability for individual files (D = 100 ms)

10 10

2

10

4

0.2 0.4 0.6 0.8

Files

Req. aggregation prob.

LRU Simulation Model

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Result – PIT Size

PIT size distribution

2800 2900 3000 3100 3200 0.002 0.004 0.006 0.008 0.01

PIT size Probability density

LRU Simulation Model

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Result – PIT Size

Average PIT size vs. download delay

50 100 150 200 250 1000 2000 3000 4000 5000

Download delay (ms) Average PIT size

LRU Simulation Model

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Result – Cache Response Time

Response time for individual files (D = 100 ms)

10 10

2

10

4

20 40 60 80 100

File index Average response time (ms)

LRU Simulation Model

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Result – Cache Response Time

Response time for individual files (D = 100 ms)

10 10

2

10

4

20 40 60 80 100

File index Average response time (ms)

LRU Simulation ZDD Model

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Result – Cache Response Time

Average response time vs. download delay

50 100 150 200 250 50 100 150

Download delay (ms) Average response time (ms)

LRU Simulation Model

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Numerical Results

Cache size = 104 # different files = 107 Requests: Poisson process w/ rate λ = 105 per second File popularity: Zipf distribution, λi ∝ i−0.8 Download delay: 100 ms Model only – no simulations

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Result – Cache Hit Probability

Average hit probability vs. cache size

10

3

10

4

10

5

10

6

10

7

10

−2

10

−1

10

Cache size Overall hit probability

LRU FIFO

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Result – Cache Hit Probability

Average hit probability vs. download delay

50 100 150 200 250 0.04 0.06 0.08 0.1 0.12

Download delay (ms) Overall hit probability

LRU FIFO

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Result – PIT Size

Average PIT size vs. cache size

10

3

10

4

10

5

10

6

10

7

2000 4000 6000 8000 10000

Cache size Average PIT size

FIFO LRU

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Result – PIT Size

Average PIT size vs. download delay

50 100 150 200 250 0.5 1 1.5 2 2.5x 10

4

Download delay (ms) Average PIT size

FIFO LRU

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Summary

Conclusions:

Modeled cache with PIT and non-zero download delay

Cache hit probability PIT size Cache response time

Analysis based on TTL caches

LRU, FIFO and Random

Characteristic time holds with positive download delay

Future Work:

Requests arriving for chunks of files (e.g. streaming video) Different scales of download delays

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