Adaptive Caching Algorithms with Optimality Guarantees for NDN Networks. Stratis Ioannidis and Edmund Yeh

Transcription

1 Adaptive Caching Algorithms with Optimality Guarantees for NDN Networks Stratis Ioannidis and Edmund Yeh

2 A Caching Network Nodes in the network store content items (e.g., files, file chunks) 1

3 A Caching Network? Nodes generate requests for content items 2

4 A Caching Network? Requests are routed towards a content source 3

5 A Caching Network Responses routed over reverse path 4

6 A Caching Network? Nodes have caches with finite capacities 5

7 A Caching Network? Nodes have caches with finite capacities 6

8 A Caching Network? Requests terminate early upon a cache hit 7

9 Example: Named Data Networks Webserver? cache-enabled routers User 8

10 Optimal Content Allocation Q: How should items be allocated to caches so that routing costs are minimized? 9

11 Optimal Content Allocation Challenge: Caching algorithm should be adaptive, and distributed. 10

12 A Simple Algorithm: Path-Replication [Cohen and Shenker 2002] [Jacobson et al. 2009]? Distributed Adaptive Popular! Cache item on every node in the reverse path Evict using a simple policy, e.g., LRU, LFU, FIFO etc. 11

13 But Path Replication combined with traditional eviction policies (LRU, LFU, FIFO, etc.) is arbitrarily suboptimal. 12

14 Path Replication + LRU is Arbitrarily Suboptimal Cost when caching : Cost of PR+LRU: When M is large, PR+LRU is arbitrarily suboptimal!?? requests per sec True for any strategy (LRU,LFU,FIFO,RR) that ignores upstream costs 13

15 Our Contributions Formal statement of offline problem NP-Hard [Shanmugam et al. IT 2013] Path Replication +LRU, LFU, FIFO, etc. is arbitrarily suboptimal Distributed, adaptive algorithm, within a constant approximation from optimal offline allocation Path Replication+novel eviction policy Great performance under 20+ network topologies 14

16 Overview Problem Formulation Distributed Adaptive Algorithms Evaluation 15

17 Overview Problem Formulation Distributed Adaptive Algorithms Evaluation 16

18 Model: Network Network represented as a directed, bi-directional graph 17

19 Model: Edge Costs Edge costs: 5 Each edge has a cost/weight 18

20 Model: Node Caches Edge costs: Node capacities: Node has a cache with capacity 19

21 Model: Cache Contents Edge costs: Node capacities: Items stored and requested form the item catalog 20

22 Model: Cache Contents Edge costs: Node capacities: For and, let if o.w. stores Then, for all, 21

23 Model: Designated Sources Edge costs: Node capacities:, for all For each and, there exists a set of nodes (the designated sources of ) that permanently store. I.e., if then 22

24 Model: Demand Edge costs: Node capacities:, for all? A request is a pair such that: Requests are always satisfied! is an item in is a simple path in such that. 23

25 Model: Demand Edge costs: Node capacities:, for all : demand Request rates:? Demand : set of all requests Request arrival process is Poisson with rate 24

26 Model: Routing Costs & Caching Gain Edge costs: Node capacities:, for all : demand 6 Request rates: Request? Worst case routing cost: 25

27 Model: Routing Costs & Caching Gain Edge costs: Node capacities:, for all : demand 6 Request rates: Request? Worst case routing cost: Cost due to intermediate caching: 26

28 Model: Routing Costs & Caching Gain Edge costs: Node capacities:, for all : demand 6 Request rates: Request? Worst case routing cost: Cost due to intermediate caching: Caching Gain: 27

29 Caching Gain Maximization Edge costs: : demand?? Node capacities: Request rates: Caching Gain:, for all The global allocation strategy is the binary matrix 28

30 Caching Gain Maximization Edge costs: : demand? Node capacities: Request rates: Caching Gain:, for all Maximize: Subject to:, for all, for all and, for all and 29

31 Offline Problem Maximize: Subject to:, for all, for all and, for all and Shanmugam, Golrezaei, Dimakis, Molisch, and Caire. Femtocaching: Wireless Content Delivery Through Distributed Caching Helpers. IT, 2013 NP-hard Submodular objective, matroid constraints Greedy algorithm gives ½-approximation ratio 1-1/e ratio can be achieved through pipage rounding method [Ageev and Sviridenko, J. of Comb. Opt., 2004] 30

32 Pipage Rounding [Ageev & Sviridenko 2004] Maximize: Subject to:, for all, for all and, for all and 31

33 Pipage Rounding [Ageev & Sviridenko 2004] Maximize: Subject to: Satisfied in expectation Think: All for all, for all and, for all and are independent Bernoulli random variables. Expected CG 32

34 Pipage Rounding [Ageev & Sviridenko 2004] Maximize: Subject to: for all, for all and, for all and Key idea: There exists a concave function such that 33

35 Pipage Rounding [Ageev & Sviridenko 2004] Maximize: Subject to: for all, for all and, for all and Key idea: There exists a concave function such that Algorithm Sketch: Maximize ; round solution to obtain discrete solution. 34

36 Overview Problem Formulation Distributed Adaptive Algorithms Evaluation 35

37 Projected Gradient Ascent Time is divided into slots 36

38 Projected Gradient Ascent Each node keeps track of its own marginal distribution 37

39 Projected Gradient Ascent During a slot, estimates by collecting measurements through passing packets. 38

40 Projected Gradient Ascent At the conclusion of the -th slot, updates its marginals through: 39

41 Projected Gradient Ascent After updating, node places random items in its cache, independently of other nodes, so that:, for all 40

42 Gradient Estimation How can estimate in a distributed fashion? 41

43 Gradient Estimation ? When request is generated, create a new control message 42

44 Gradient Estimation ? Forward control message over path until: 43

45 Gradient Estimation Forward until: ? +8 Send control message over reverse path, collecting sum of edge costs. Each node on reverse path, sniffs upstream costs, and maintains average per item. Average at end of slot is estimate of 44

46 Randomized Placement How can place exactly items in its cache, so that marginals are satisfied? 45

47 Randomized Placement = 0.82 = 0.77 = 0.64 = 0.77 Suppose that I give you a such that. Is there a way to select exactly that item is selected is? items at random, so that the probability 46

48 Randomized Placement: Sketch of Algorithm Triplets: 47

49 Convergence Theorem: For leads to an allocation, Projected Gradient Ascent such that where an optimal solution to the offline problem. 48

50 Projected Gradient Ascent (vs. Path Replication) Distributed Adaptive Constant Approximation to Optimal? Overhead for control traffic Overhead to retrieve content at end of timeslot Not so simple 49

51 Path-Replication + Greedy Eviction Policy Each node maintains an estimate for the (sub)gradient At any point in time, caches top items, with highest gradients 50

52 Path-Replication + Greedy Eviction Intuition: Greedily cache item with best upstream gain Frank-Wolfe Algorithm, PSEPHOS Algorithm [I.,Chaintreau, Massoulie,SIGMETRICS 2010] 6? A response carrying the item adds weights on the reverse path, and reports them to intermediate nodes. Weights are used to update estimate of. Greedy Eviction: if becomes one of the top items, evict item with smallest gradient, and cache. 51

53 Overview Problem Formulation Distributed Algorithms Evaluation 52

54 Multiple Topologies y-axis: ratio to offline solution 53

55 Open Questions Joint caching & routing PR+Greedy Eviction guarantees Delay vs. Throughput Optimality Broader resource management applications 54

56 Reference S. Ioannidis and E. Yeh, Adaptive Caching Networks with Optimality Guarantees. Proc. ACM SIGMETRICS, Antibes Juan-les-Pins, June 14-18, 2016, pp

57 Thank you!