On the Analysis of Caches with Pending Interest Tables

Transcription

1 On the Analysis of Caches with Pending Interest Tables Mostafa Dehghan 1, Bo Jiang 1 Ali Dabirmoghaddam 2, Don Towsley 1 1 University of Massachusetts Amherst 2 University of California Santa Cruz ICN, October 2, 2015 College of Information and Computer Sciences

2 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 1 / 25

3 Overview Content Store Name ss Data Face 0 Pending Interest Table Name Face ss Face 1 Forwarding Information Base Prefix Face /icn/ ss 1 Face 2 2 / 25

4 Overview Content Store Name Data ss Pending Interest Table Name Face ss Face 0 Interest: /icn/pit.pdf Face 1 Forwarding Information Base Prefix Face /icn/ ss 1 Face 2 2 / 25

5 Overview Content Store Name Data ss Pending Interest Table Name Face ss Face 0 Interest: /icn/pit.pdf Face 1 Forwarding Information Base Prefix Face /icn/ ss 1 Face 2 2 / 25

6 Overview Content Store Name Data ss Pending Interest Table Name Face ss Face 0 Interest: /icn/pit.pdf Face 1 Forwarding Information Base Prefix Face /icn/ ss 1 Face 2 2 / 25

7 Overview Content Store Name Data ss Pending Interest Table Name Face /icn/pit.pdf ss 0 Face 0 Interest: /icn/pit.pdf Face 1 Forwarding Information Base Prefix Face /icn/ ss 1 Face 2 2 / 25

8 Overview Content Store Name Data ss Pending Interest Table Name Face /icn/pit.pdf ss 0 Face 0 Interest: /icn/pit.pdf Face 1 Forwarding Information Base Prefix Face /icn/ ss 1 Face 2 2 / 25

9 Overview Content Store Name Data ss Pending Interest Table Name Face /icn/pit.pdf ss 0 Face 0 Interest: /icn/pit.pdf Face 1 Forwarding Information Base Prefix Face /icn/ ss 1 Face 2 2 / 25

10 Overview Content Store Name ss Data Face 0 Pending Interest Table Name Face /icn/pit.pdf ss 0 Face 1 Forwarding Information Base Prefix Face /icn/ ss 1 Face 2 Interest: /icn/pit.pdf 2 / 25

11 Overview Content Store Name ss Data Face 0 Pending Interest Table Name Face /icn/pit.pdf ss 0 Face 1 Forwarding Information Base Prefix Face /icn/ ss 1 Face 2 Interest: /icn/pit.pdf 2 / 25

12 Overview Content Store Name ss Data Face 0 Pending Interest Table Name Face /icn/pit.pdf ss 0 Face 1 Forwarding Information Base Prefix Face /icn/ ss 1 Face 2 Interest: /icn/pit.pdf 2 / 25

13 Overview Content Store Name ss Data Face 0 Pending Interest Table Name Face /icn/pit.pdf ss 0,2 Face 1 Forwarding Information Base Prefix Face /icn/ ss 1 Face 2 Interest: /icn/pit.pdf 2 / 25

14 Overview Content Store Name ss Data Face 0 Pending Interest Table Name Face /icn/pit.pdf ss 0,2 Forwarding Information Base Prefix Face /icn/ ss 1 Face 1 Data: /icn/pit.pdf Face 2 2 / 25

15 Overview Content Store Name ss Data Face 0 Pending Interest Table Name Face /icn/pit.pdf ss 0,2 Forwarding Information Base Prefix Face /icn/ ss 1 Face 1 Data: /icn/pit.pdf Face 2 2 / 25

16 Overview Content Store Name Data /icn/pit.pdf ss... Pending Interest Table Name Face /icn/pit.pdf ss 0,2 Forwarding Information Base Prefix Face /icn/ ss 1 Face 0 Face 1 Data: /icn/pit.pdf Face 2 2 / 25

17 Overview Content Store Name Data /icn/pit.pdf ss... Pending Interest Table Name Face /icn/pit.pdf ss 0,2 Forwarding Information Base Prefix Face /icn/ ss 1 Face 0 Face 1 Data: /icn/pit.pdf Face 2 2 / 25

18 Overview Content Store Name Data /icn/pit.pdf ss... Pending Interest Table Name Face ss Face 0 Face 1 Forwarding Information Base Prefix Face /icn/ ss 1 Face 2 2 / 25

19 Pending Interest Table (PIT) Performs request aggregation Keep track of Interests forwarded but not yet satisfied 3 / 25

20 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... 3 / 25

21 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 3 / 25

22 Motivation Need analytical models to predict cache behavior Better design choices 4 / 25

23 Motivation Need analytical models to predict cache behavior Better design choices PIT sizing 4 / 25

24 Motivation Need analytical models to predict cache behavior Better design choices PIT sizing State of the art: Ignores download delay Does not consider PIT 4 / 25

25 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 4 / 25

26 Outline Time-To-Live Caches Model and Analysis Replacement Based Policies Simulation Results 5 / 25

27 Time-To-Live (TTL) Caches Content eviction occurs upon timer expiration 6 / 25

28 Time-To-Live (TTL) Caches Content eviction occurs upon timer expiration Cache t 6 / 25

29 Time-To-Live (TTL) Caches Content eviction occurs upon timer expiration T Cache t 6 / 25

30 Time-To-Live (TTL) Caches Content eviction occurs upon timer expiration T Cache t 6 / 25

31 Time-To-Live (TTL) Caches Content eviction occurs upon timer expiration T Cache t Reset TTL cache reset timer upon each hit 6 / 25

32 Time-To-Live (TTL) Caches Content eviction occurs upon timer expiration T Cache t Reset TTL cache reset timer upon each hit T Cache t 6 / 25

33 Time-To-Live (TTL) Caches Content eviction occurs upon timer expiration T Cache t Reset TTL cache reset timer upon each hit T Cache t 6 / 25

34 Time-To-Live (TTL) Caches Content eviction occurs upon timer expiration T Cache t Reset TTL cache reset timer upon each hit T Cache t 6 / 25

35 Time-To-Live (TTL) Caches Content eviction occurs upon timer expiration T Cache t Reset TTL cache reset timer upon each hit T Cache t 6 / 25

36 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT t 7 / 25

37 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT t 7 / 25

38 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT t 7 / 25

39 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT D t 7 / 25

40 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT D t 7 / 25

41 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT D t 7 / 25

42 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT D t 7 / 25

43 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t 7 / 25

44 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t 7 / 25

45 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t 7 / 25

46 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t 7 / 25

47 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t 7 / 25

48 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t 7 / 25

49 Model Requests: renewal arrivals Reset TTL cache with PIT CS PIT D T t 7 / 25

50 Metrics Z D L t # misses M # hits N 8 / 25

51 Metrics Cache hit prob Z h = E[N] E[M] + E[N] D L t # misses M # hits N 8 / 25

52 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 0 (t x)dm(x) m(t): renewal function Poisson: m(t) = λt Z D L # misses M # hits N t 8 / 25

53 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 0 (t x)dm(x) m(t): renewal function Poisson: m(t) = λt Z D L # misses M # hits N Cache occupancy prob o = E[L]/E[Z] t 8 / 25

54 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 0 (t x)dm(x) m(t): renewal function Poisson: m(t) = λt Z D L # misses M # hits N Cache occupancy prob o = E[L]/E[Z] PIT occupancy prob p = E[D]/E[Z] t 8 / 25

55 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 o i(t) = C o i cache occupancy probability of file i C cache size 9 / 25

56 LRU Cache with Poisson Arrivals Modeled as reset TTL with constant T Cache hit/occupancy probability h i = o i = eλ it 1 λ i ED i + e λ it λ i arrival rate of requests for file i ED i expected download delay for file i characteristic time T solution of i e λit 1 λ i ED i + e λit = C 10 / 25

57 LRU Cache with Poisson Arrivals PIT occupancy probability p i = λ i ED i λ i ED i + e λ it 11 / 25

58 LRU Cache with Poisson Arrivals PIT occupancy probability p i = λ i ED i λ i ED i + e λ it PIT size ( S N p i, i i p i (1 p i ) ) 11 / 25

59 LRU Cache with Poisson Arrivals PIT occupancy probability p i = λ i ED i λ i ED i + e λ it PIT size ( S N p i, i i Average cache response time p i (1 p i ) ) r i = ED i + 0.5λ i ED 2 i λ i ED i + e λ it 11 / 25

60 Simulation Cache size = 10 3 # different files = 10 4 Requests: Poisson process w/ rate λ = 10 5 per second File popularity: Zipf distribution, λ i i 0.8 Download delay: 100 ms One simulation run: total of 10 7 requests simulated Base model: ZDD: Zero-Download Delay 12 / 25

61 Result Cache Hit Probability Hit probability for individual files (D = 100 ms) 10 0 LRU Hit probability 10 1 Simulation Model File index 13 / 25

62 Result Cache Hit Probability Hit probability for individual files (D = 100 ms) 10 0 LRU Hit probability 10 1 Simulation ZDD Model File index 13 / 25

63 Result Cache Hit Probability Average hit probability vs. download delay Average hit probability LRU Simulation Model Download delay (ms) 14 / 25

64 Result Request Aggregation PIT occupancy probability for individual files (D = 100 ms) Req. aggregation prob Simulation Model LRU Files 15 / 25

65 Result PIT Size PIT size distribution Probability density Simulation Model LRU PIT size 16 / 25

66 Result PIT Size Average PIT size vs. download delay LRU 5000 Average PIT size Simulation Model Download delay (ms) 17 / 25

67 Result Cache Response Time Response time for individual files (D = 100 ms) Average response time (ms) Simulation Model LRU File index 18 / 25

68 Result Cache Response Time Response time for individual files (D = 100 ms) Average response time (ms) Simulation ZDD Model LRU File index 18 / 25

69 Result Cache Response Time Average response time vs. download delay Average response time (ms) Simulation Model LRU Download delay (ms) 19 / 25

70 Numerical Results Cache size = 10 4 # different files = 10 7 Requests: Poisson process w/ rate λ = 10 5 per second File popularity: Zipf distribution, λ i i 0.8 Download delay: 100 ms Model only no simulations 20 / 25

71 Result Cache Hit Probability Average hit probability vs. cache size Overall hit probability Cache size LRU FIFO 21 / 25

72 Result Cache Hit Probability Average hit probability vs. download delay Overall hit probability Download delay (ms) LRU FIFO 22 / 25

73 Result PIT Size Average PIT size vs. cache size Average PIT size FIFO LRU Cache size 23 / 25

74 Result PIT Size Average PIT size vs. download delay Average PIT size 2.5 x FIFO LRU Download delay (ms) 24 / 25

75 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 25 / 25