Cooperative Caching for Adaptive Bit Rate Streaming in Content Delivery Networks

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1 Cooperative Caching for Adaptive Bit Rate Streaing in Content Delivery Networs Phuong Luu Vo Departent of Coputer Science and Engineering, International University - VNUHCM, Vietna vtlphuong@hciu.edu.vn Seung Il Moon Departent of Coputer oons85@hu.ac.r Tuan-Anh Le Faculty of Inforation Technology, University of Thudauot, Vietna letuanh@tdu.edu.vn Sungwon Lee Departent of Coputer drsungwon@hu.ac.r Choong Seon Hong Departent of Coputer cshong@hu.ac.r Nga Ly Tu Departent of Coputer Science and Engineering, International University - VNUHCM, Vietna ltnga@hciu.edu.vn ABSTRACT This wor proposes a cooperative caching odel which supports adaptive bit-rate streaing in content delivery networs. A linear progra LP) proble is applied to axiize the total user satisfaction. The optial content placeent and content fetching strategies are the solutions to the LP. The LP is a large-scale optiization proble because of the large aount of contents in the networ. We also introduce a technique to decopose the large-scale LP into any subprobles which can be solved in parallel. Each subproble is associated with one content. Categories and Subject Descriptors C.2.2 [Coputer Counication Networs]: Networ Protocols content caching, content delivery networ; G..6 [Nuerical Analysis]: Optiization linear prograing General Ters Theory Keywords content caching, adaptive bit-rate streaing, content delivery networ, linear prograing. INTRODUCTION In content delivery networs CDNs), popular contents are cached in the cache nodes placed in the networ. Thus, the users can obtain the contents at the interediate nodes Perission to ae digital or hard copies of all or part of this wor for personal or classroo use is granted without fee provided that copies are not ade or distributed for profit or coercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific perission and/or a fee. IMCOM 5, January 08-0, 205, BALI, Indonesia. Copyright 205 ACM /5/0 instead of downloading fro the original sources. The perforance of content delivery to the end users is iproved. Ideally, all the contents should be cached in each storage node. However, there is a large nuber of contents in the networ whereas the storage capacity is liited. Hence, intuitively, the storage nodes usually cache only the ost popular contents. When a node receives a request for a particular content, if it already has the content at its storage, the content is directly sent bac to the end user. Otherwise, the content is fetched fro the other nodes in the networ. It has been nown that the cache nodes should cooperate in caching to reduce the aount of traffic transferred inside the networ. Given the deands of the contents, the optial content placeent and fetching strategies are proposed by solving a large-scale integer linear progra LP) that iniizes the total cost of the networ [4, 5, 0]. According to Cisco VNI report [8], videos will soon be a doinant traffic type in the Internet. By 207, video traffic will be accounting for 69% of the internet traffic where nearly a illion inutes of video will be transferred. On the other hand, adaptive bit-rate ABR) streaing is a ain video streaing technique in the Internet nowadays. It can utilize the networ resource and provide a sooth playbac and high quality-of-experience QoE) [2, 9]. With ABR, each content is encoded into different representations corresponding to different playbac rates. For exaple, reference [3] describes the recoended representation set of Apple s HTTP live streaing. Depending on networ condition, an appropriate representation is dynaically chosen. Intuitively, a higher QoE video consues ore bandwidth and also requires a bigger representation size. Considering storage capacity of the nodes as the constraint, the target of this paper is to find an optial content placeent and content delivery strategies such as axiizing the networ perforance. The proble is odelled by a linear progra LP). Solving the LP yields the optial content placeent and fetching strategy. This LP is usually a large-scale proble due to the large nuber of contents in the networ. We introduce a technique to decopose the LP to ultiple subprobles which can be solved in parallel. Each subproble corresponds to a content.

2 requestfor content N2 N N6 N5 Figure : An exaple of cooperative caching in a content delivery networ. To serve the request on content at node which has the x fraction of content already, node receives yi fraction of content fro node i. To the best of our nowledge, there is still a lac of wors in literature proposing a theoretical caching odel specifically for ABR streaing. Few of the are the wors in [] and []. Reference [] odels the caching proble as an optiization proble. Every content has a storage budget and the ai of the algorith is to axiize QoE of each content. The constraint in [] is not flexible since each video content has a liited storage capacity, and this storage budget is equally for every contents. The content request rates are not taen into account in the odel in []. Moreover, reference [] only odel the caching proble on a single node. Our wor addresses cooperative caching proble. The cache nodes cooperate to leverage caching capability of each other. The aount of contents stored on each node depends not only on the storage capacity, but also on the deands of the contents and the lin costs. Reference [] odels the ABR-capable caching by an optiization proble axiizing the nuber of concurrent requests are served while eeting the QoE requireent. The authors propose a heuristic caching algorith called ABR-LRU-P which is a odification fro the traditional eviction algorith least-recently-used LRU). The storage capacity constraint is not considered in this wor. The reain of the paper is organized as follows. Sections II describes the atheatical odel. Section III decoposes the large-scale LP. The nuerical results and conclusions are presented in Sections IV and V, respectively. 2. THE OPTIMIZATION MODEL Consider a CDN cluster with N cache nodes providing the caching service to the users please see the notations given in Table ). Nodes in the networ collaborate in caching to reduce the total lin cost. When a user requests content at node i. Depending on the networ condition, the user receives -th representation of content fro node i if node i has this representation already in its storage, i.e., x i =, or fro node j if x i = 0, yij = see Figure ). In this paper, we assue that the deands for the contents N3 N4 on the nodes are given and reained constants during the tie period of interest. All the contents are assued to be cached in the CDN cluster. The aount of lin cost for serving the deand of content at node i is the total lin cost to transfer content fro other nodes to node i for all levels of representations, i.e., K s d i c ijyij). Hence, the total networ cost for serving its deands will be s d i c ijyij). M i N K On the other hand, when the user that requests content at node i receives -th representation of content, the user satisfaction is U. Thus, the utility when obtaining -th representation of content fro node i is U s d i x i + yij). Therefore, the total utility is U s d i M i N K x i + y ij). Our goal is to axiize the networ perforance, i.e., the total utility after subtracting the bandwidth cost. The optiization odel of the content placeent proble is as follows. Max. s d i U x i + ) U c ij )yij ) M i N K st. s x i B i, i N, 2) M K yij x j, K, i, j N, i j, M, 3) x i + ) yij =, i N, M, 4) K x i, y ij {0, }, K, i, j N, i j, M. 5) Constraint 2) is the storage capacity constraint of each node, i.e., the total storage of all contents for all representations on node i ust be less than its storage capacity B i. Constraint 3) eans that the aount of content fro node j serving the request at node i ust be less than the aount of content stored at node j. Constraint 4) guarantees that the aount of content stored at node i and the total received aount of for all representations ust be equal to the whole content in order to serve the request fro the assuption that all the contents are cached inside the networ). Proble )-5) is an integer linear progra which is solved by a high coplexity algorith. In case the content can be stored fractionally, constraint 5) can be relaxed to 0 x i, 0 yij, K, i, j N, i j, M. 6) The fractional caching proble )-4), and 6) becoes a linear progra and can be solved with polynoial tie. In this proble, x i is the fraction of -th representation of content stored on node i and yij is the fraction of -th representation of content fetched fro node j to serve the request on node i. User satisfaction and quality-of-experience are used interchangeably in this paper.

3 Table : Main notations Paraeters: M set of contents N the set of storage nodes in the considered networ B i storage capacity of node i K axiu nuber of representations of a content U user satisfaction when receiving one unit of content at -th representation s size of content at -th representation d i deand for content at node i c ij cost for one unit of data fro node j to node i Variables: x i decision variable indicating node i has content at -th streaing rate / fraction of content at -th streaing rate stored on node i yij decision variable indicating content at -th streaing rate on node j serves the deand on node i / fraction of content at -th streaing rate fro node j serving the deand on node i There are soe additional rears about the caching optiization forulation )-5):. In case of an additional assuption that if a content is stored on any node up to -level representation, all the lower-level representations are also stored exists, the forulation )-5) reains unchanged except the constraint 2), which will becoe S x i B i, i N, 7) M K where S = s +... s, i.e., the storage size for content. The objective is unchanged because the utility is calculated based on the bit-rate of the highest representation. 2. The proble )-5) can be utilized to odel the cooperative caching aong the clusters at a higher level. For exaple, each cluster which includes several storage nodes is considered as a node in the above forulation. The variable x i is the fraction of -th representation of content stored on cluster i, y ij is the fraction of -th representation of content fetched to cluster i fro cluster j. We introduce a technique to decopose the large-scale fractional caching proble into ultiple subprobles which can be solved in parallel in next section. 3. SOLVING THE LARGE-SCALE LINEAR PROGRAM Although a linear progra can be solved in a polynoial tie, the caching LP is actually a large-scale proble since there is a large nuber of contents in the networ. However, the caching LP has a special structure, the bloc-angular for see Figure 2) which can be decoposed into any subprobles. To solve the proble, we first relax the nonseparable constraint 2). Then, we decopose the relaxed probles into any subprobles according to the contents. Each subproble is a linear progra associated with each content. non-separable constraints separable constraints Figure 2: The bloc-angular structure of the linear progra. Particularly, the relaxed proble of LP has the following for Max. s d i U x i + ) U c ij )yij M i N K ) α i s x,i B i 8) i N M K st. yij x j, K, i, j N, i j, M, x i + ) yij =, i N, M, K 0 x i, y ij, K, i, j N, i j, M, α i 0, i N, where α is the Lagrange ultiplier associated with constraint 2). Therefore, the subproble associated with content is as follows: Max. s d i i N K U αi d i )x i + st. yij x j, K, i, j N, i j, x i + ) yij =, i N, K 0 x i, y ij, K, i, j N, i j. U c ij)y ij Giving α in each iteration, M subprobles the nuber of contents in the networ, M ) are solved parallelly. We apply Dantzig-Wolfe decoposition technique to find the optial ultipliers in each iteration by solving the aster proble as described in [6, chap.2]. The objective of the aster proble onotonically decreases in each iteration and converges to the optial solution of the original LP. In case there is syetry in the networ, we can reduce the size of the proble. Note that a LP can have ultiple solutions. If two variables are syetric in both objective and constraints, there is no guarantee that their optial values have to be the sae. However, if we only focus on finding one solution of the proble, then the syetric solution is one of the optial solutions of the LP. We utilize this feature to reduce the size of the large-scale proble. 4. NUMERICAL RESULTS We assue the deands of the contents follow Zipf - Mandelbrot distribution with shape paraeter a = and shift ) 9)

4 content distribution contents Table 3: The optial content placeent strategy for the toy odel x). Node x ): base-line) add. ain) add. high) Node 2 x 2): base-line) add. ain) add. high) Figure 3: The distribution of 0,000 contents with a = and q = 0 only the populations of first 400 contents are plotted). Table 2: Base-line and additional ain and additional high profile settings recoended by Apple HTTP live Streaing 6:9 aspect ratio), [3]. Representations ) 2 3 Resolutions 6:9 aspect 224p 720p 080p ratio) Bit-rates bps) 240 2,540 25,000 paraeter q = 0 in the experients [7]. The request are uniforly distributed aong the nodes. Hence, the deand of -th popularity content at each node in a considered interval is given by d q + ) a i = r i M, 0) = q + ) a where r i is the nuber of requests to node i per second. For exaple, Figure 3 shows the distribution of first 400 contents in 0,000-content catalog with a =, q = 0, and r =. We consider the recoended representation set of Apple s HTTP live streaing [3]. For siplicity, three levels of representations, which are chosen fro base-line, additional ain, and additional high profile settings, represent low, ediu, and high perforance representations, respectively see Table 2). We assue that every contents are all 0-inute playbac tie. The size of representation is approxiated to s = r T/8/024 MB, where r is the corresponding bit-rate in Kbps) of the representation and T = 600 is the video playbac tie in seconds. Specifically, s = [7.58, 86.04, 83.06] MB corresponding to the baseline, additional ain, and additional high representations. Logarithic utility is used [, 2]. Without loss of generality, we assue that U = logr). Therefore, the utilities of the user corresponding to three type of representations are U = [2.38, 3.4, 4.40]. 4. A toy odel In this siulation, we assue that the networ has 2 nodes with the storages B = 4 GB. There are 6 contents in the net- Table 4: The optial content fetching strategy for the toy odel y). Fro node to node 2 y2): base-line) add. ain) add. high) Fro node 2 to node y2): base-line) add. ain) add. high) wor. The shift paraeter q = 0 and the shape paraeter a =. Nuber of requests per second to nodes# and #2 are and.5 requests per considered interval, respectively. The lin cost between two cache nodes is 4. Node# stores the first and part of third and fourth contents at additional high representation; fifth, sixth, and part of fourth contents at base-line representations. Node#2 with higher request rate stores first, second, and part of third contents at additional high representations see Table 3). Table 4 shows that except the first content, node#2 receives all the content fro node# to serve node#2 s requests. Node# receives the second and part of third contents at baseline fro node#2 to serve node# s requests. 4.2 Trade-off between perforance and bandwidth cost We now consider a the cluster networ includes 0,000 contents stored on 0 cache nodes. Each node has 00 GB of storage for the video contents. The nuber of requests to the cluster of node is 0 request per second and is uniforly distributed aong the nodes r i = request per second). The lin costs between every pair of nodes are all equal, i.e., c. We increase c gradually. Figure 4 shows the tradeoff between the overall perforance, which is calculated by subtracting the networ cost fro the total utility of the networ, and the lin cost c. The higher cost decreases the overall perforance. When c increases gradually, the networ cost also increases. However, if the lin cost is too high, the networ cost decreases since it costs too uch to transfer the representations between the nodes. The local

5 perforance overall perforance user satisfaction networ cost lin cost Figure 4: The perforance of the networ networ utility - bandwidth cost) when the lin cost is gradually increased. node tends to serve the requests by its currently stored representations rather than downloads the better perforance representations fro the other nodes. 5. CONCLUSIONS We have proposed a linear prograing odel for the optial content placeent which supports adaptive bit-rate streaing. The perforance and the bandwidth cost of the networ is optiized. We also propose a technique to decopose the LP to any subprobles which can be solved in parallel. Each subproble corresponds to a content. The siulations deonstrate the content placeent on the cache nodes and the trade-off between the lin cost and the perforance of the networ. 6. ACKNOWLEDGMENTS This research was funded by Vietna National University HoChiMinh City VNU-HCM) in 205 and the MSIPMinistry of Science, ICT & Future Planning), Korea in the ICT R&D Progra 204. Dr. CS Hong is the corresponding author. 7. REFERENCES [] H. Ahlehagh and S. Dey. Adaptive bit rate capable video caching and scheduling. In Proceeding of IEEE Wireless Counications and Networing Conference, WCNC 203, pages , April 203. [2] S. Ahshabi, A. C. Begen, and C. Dovrolis. An experiental evaluation of rate-adaptation algoriths in adaptive streaing over http. In Proceedings of the Second Annual ACM Conference on Multiedia Systes, MMSys, pages 57 68, New Yor, NY, USA, 20. ACM. [3] Apple. Using http live streaing. [Online]. Available: [4] D. Applegate, A. Archer, V. Gopalarishnan, S. Lee, and K. K. Raarishnan. Optial content placeent for a large-scale vod syste. In Proceedings of the 6th International COnference, Co-NEXT 0, pages 4: 4:2, New Yor, NY, USA, 200. ACM. [5] S. Borst, V. Gupta, and A. Walid. Distributed caching algoriths for content distribution networs. In Proceedings of the IEEE Conference on Coputer Counications, INFOCOM 0, pages 9, arch 200. [6] S. P. Bradley, A. C. Hax, and T. L. Magnanti. Applied atheatical prograing. Addison-Wesley, 977. [7] L. Breslau, P. Cao, L. Fan, G. Phillips, and S. Shener. Web caching and zipf-lie distributions: evidence and iplications. Proceedings of the IEEE Conference on Coputer Counications, INFOCOM 99, pages 26 34, vol., Mar 999. [8] Cisco. Cisco visual networing index: Forecast and ethodology, [9] T. Stochaer. Dynaic adaptive streaing over http: Standards and design principles. In the Second Annual ACM Conference on Multiedia Systes, MMSys, pages 33 44, New Yor, NY, USA, 20. ACM. [0] H. Xie, G. Shi, and P. Wang. Tecc: Towards collaborative in-networ caching guided by traffic engineering. In Proceedings of the IEEE Conference on Coputer Counications, INFOCOM 2, pages , arch 202. [] W. Zhang, Y. Wen, Z. Chen, and A. Khisti. Qoe-driven cache anageent for http adaptive bit rate streaing over wireless networs. IEEE Transactions on Multiedia, 56):43 445, Oct 203. [2] P. Reichl, B. Tuffin, and R. Schatz. Logarithic laws in service quality perception: where icroeconoics eets psychophysics and quality of experience. Telecounication Systes, vol. 52, no. 2, pp , 203.