Caching Policy Optimization for Video on Demand

Transcription

1 Caching Policy Optimization or Video on Demand Hao Wang, Shengqian Han, and Chenyang Yang School o Electronics and Inormation Engineering, Beihang University, China, {wang.hao, sqhan, cyyang}@buaa.edu.cn Abstract Caching popular contents at the base stations is an eective way to address the challenging data traic demand driven by video-on-demand VoD) service. Initial delay is one o most important actors aecting the quality o experience QoE) o users or VoD service. Existing work has optimized the caching policy to reduce the average delay or ile downloading service. However, considering the act that the QoE or VoD service does not linearly decrease with the initial delay, the caching policy minimizing the average delay is not optimal or VoD service. In this paper we optimize the caching policy to control the initial delay, aimed at maximizing the average QoE o a user with random requests o videos rom a ile library. By properly approximating the non-smooth non-concave QoE unction, we obtain eicient caching policies or VoD service, based on which the impact o ile popularity on the caching policy is analyzed. Simulation results demonstrate the advantages o the proposed caching policy. I. INTRODUCTION The telecommunication industry has been witnessing an explosion o wireless data traic driven by video-on-demand VoD) service [1]. To meet the challenging traic demands and guarantee the quality o experience QoE) o users, ultra dense network has emerged as an candidate solution, where small base stations SBS) are deployed to bring the network close to the users. However, a drawback o this technology is the requirement o high-capacity and low-latency backhaul or each SBS, which leads to prohibitive cost with the increase o the density o SBSs. To overcome this dilemma, a concept o emtocaching was proposed in [2] to use the cheap storage to replace the expensive backhaul. By caching the popular video iles at the SBSs without backhaul link also reerred to as helpers ) and streaming the non-cached iles rom the macro BS, emtocaching is able to dramatically improve the network throughput. Caching at the wireless edge has been extensively studied in the literature, e.g., [3], [4], [5] and reerences therein. Nevertheless, most existing caching policies are designed or ile downloading service, while the optimization o caching policy or VoD service aimed at improving the QoE o users by taking into account the eatures o VoD has received little attention. Considering the adaptation o video rate, the Least Recently Used LRU) based reactive caching policy was studied in [6] and [7], and the proactive caching policy or multi-rate VoD was investigated or a single video ile in [8] and or multiple video iles in [9] and [10]. Except or video rate adaptation, initial delay is another important actor aecting the QoE o VoD service. Existing works have studied the optimal caching policy aimed at minimizing the average delay or ile downloading service [2], [11], and showed that caching the most popular contents at the helper is the optimal policy in the single-helper scenario. However, the minimization o average delay is not equivalent to the maximization o QoE or VoD service, because the QoE has been shown as a non-linear unction o initial delay [12], [13]. A simple example to show the non-optimality o the existing policy designed or ile downloading is given as ollows, where the eature o VoD service allowing a certain initial delay is considered. Let us consider the caching o three video iles, 1, 2, 3, with increasing popularity. Suppose that the three videos have decreasing ile sizes so that the helper with limited storage size can either only cache 1 or cache both 2 and 3. Assume that the three videos respectively require to pre-buer 2B, B, B bits during the initial phase, the downloading rates rom a macro BS and the helper are B and 2B bit/s, respectively, and the maximal acceptable initial delay is 1 second, within which the QoE o users does not degrade. Then, according to the optimal caching policy or ile downloading, the two most popular videos, i.e., 2 and 3, should be cached, which leads to the initial delays or the three iles as 2, 0.5 and 0.5 seconds. Such caching policy reduces the QoE o users requesting 1 because its initial delay exceeds the maximal acceptable initial dealy. An alternative caching policy is to only cache 1, resulting in the initial delay o 1, 1 and 1 second or the three iles, which does not lead to any QoE degradation. In this paper we optimize the caching policy by taking into account the impact o initial delay on the QoE o VoD service. Considering that the QoE is a non-smooth non-concave unction o the initial delay, which is diicult to optimize, we irst propose an approximate QoE unction, based on which eicient caching policies are obtained and the impact o ile popularity on the caching policies is analyzed. Simulation results show that the proposed caching policies can eectively improve the QoE o users compared to the existing policy. II. SYSTEM MODEL Consider a emtocaching system where a macro BS and a helper serve a single user. The macro BS is assumed to have ideal backhaul, connected to the core network to gather the requested video iles without delay. Each helper has no backhaul but is equipped with a cache with the storage size o C bits. Suppose that the user requests the video rom a library o F iles. Let q,, and denote the popularity i.e., request probability), playback rate, and size o the -th video ile, respectively, = 1,..., F. Under the constraint on storage size o the helper, partial caching is allowed in the

2 paper, i.e., the helper may only cache a part o a video ile. This means that a user may stream the cached part o a video rom the helper and the uncached part rom the macro BS via backhaul, respectively. Let x denote the cached portion o the -th video ile. Then, the caching policy is to determine how much portion o which iles should be cached at the helper. A video ile is composed o a sequence o chunks, each o which is encoded and decoded as a stand-alone unit. The duration o a chunk is generally much longer than the coherent time o the small-scale ading channel, i.e., the channel coding can span across a large number o independent ading channels [14]. Thereore, it is sae to assume that the ergodic capacity is achievable. Let and R H denote the ergodic capacity rom the macro BS and the helper to the user, which are reerred to as downloading rates. Moreover, consider R H since the helper is usually closer to the user and can allocate a larger bandwidth to the user compared to the macro BS by noting that the number o users accessing to the helper is smaller. Regarding the impact o initial delay on QoE, the logarithmic relationship between them has been validated by experiment or ile downloading service in [15]. Moreover, it is shown in [12] that there exists a threshold or initial delay blow which the QoE does not degrade. In [13], the impact o page loading delay on the QoE o web browsing service is characterized by the ollowing unction { α 0, 0 τ < τ 0 ητ) = 1) α 1 κ logτ), τ τ 0, where the constants α 0, α 1, and κ satisy α 1 κ logτ 0 ) = α 0 to ensure the unction continuous. We can see that the web browsing service allows a delay less than τ 0 without degrading the QoE, beyond which the QoE degrades in a logarithmic law. According to the analysis in [13], such a QoE unction coincides with the Weber-Fechner Law, a key principle in psychophysics describing the general relationship between the magnitude o a physical stimulus and its perceived intensity within the human sensory system, and thereore can be used to evaluate the impact o the initial delay on the QoE o VoD service. III. DELAY-AWARE VIDEO CACHING In this section we optimize the caching policy by taking into account the impact o the initial delay o VoD service. A. Initial Delay The initial delay, τ, or the user requesting the -th video ile is deined as the minimal pre-buer duration ater which the user can play the whole video without stalling. This requires that at any moment t ater the user starts to play the video, the cumulative bits received by the user should be no less than the cumulative bits required by displaying the video. It is obvious that the initial delay τ depends on how much portion o the -th video is cached, i.e., x. We next show that τ is also aected by which portion o the video is cached given x. To see this, we consider two special cases, where the helper caches the irst or inal x portion o the -th video, respectively, which are denoted by Cache-irst and Cache-inal or notational simplicity. 1) Cache-inal: In this case, the user streams the irst 1 x portion o the -th video rom the macro BS, and streams the remaining x portion rom the helper. Let τ B, and τ H, denote the pre-buer durations rom the macro BS and the helper, respectively. In order to ensure non-stalling or the irst portion o the -th video lasting 1 x ) seconds, which is streamed rom the macro BS, the ollowing condition needs to be satisied or all t [0, 1 x ) ]: min 1 x ), τ B, + t) t. 2) From 2), we can ind that the pre-buer duration τ B, should be long enough so that 2) is satisied when t = 1 x ). Further considering that τ B, 0 and the prebuered data τ B, should be no more than all data included in the irst portion o the video, we can obtain that τ B, is bounded by 1 x ) τ B, 1 x ), 3) where x) + maxx, 0). Moreover, the time required to download the non-pre-buered data o the irst portion can be computed rom 2) as T = 1 x ) τ B,. 4) When the irst portion has been downloaded, the user can start to download the second portion rom the helper. To ensure non-stalling during streaming the second portion, the ollowing condition needs to be satisied or all t [ 1 x ), ]: τ B, + R H τ H, + T + R H t T ) 5) = R H ) 1 x ) +R H τ B, +τ H, )+R H t t, where the equality ollows upon substituting 4). From 5), we can obtain that the pre-buer duration τ B, + τ H, should be long enough so that 5) is satisied when t =, which leads to τ B, +τ H, ) 1 x )+ B ) x. 6) R H Further considering 3) and τ H, 0, ater some manipulations, we can obtain the initial delay τ as τ = min τ B, + τ H, = max B ) 1 x )+ 1 x )) R H ) x, max 1 + 2, 1 ) +). 7)

3 Noting R H so that 2 > 0 leads to 1 > 0, we can obtain τ rom 7) as { 1 ) +, 2 < 0 τ = 8) 1 + 2, 2 > 0 and hence 1 > 0, which can be rewritten in a compact orm as τ = 1 ) ) + = ) + 1 x )+ x. 9) R H 2) Cache-irst: In this case, the user streams the irst portion rom the helper and the second portion rom the macro BS. Similar to the cache-inal case, we can obtain the initial delay as τ = max 1 + 2, 2 ) +) { ) +, 2 < 0 = 1 + 2, 2 > 0 and hence 1 > 0, 10) which can be rewritten as τ = ) + x = + 1 x ). 11) R H We next discuss the initial delay in general cases where the helper arbitrarily selects x portion o the -th video to cache. First, comparing 9) and 11), we can ind that the cacheirst case needs shorter initial delay than the cache-inal case i 1 > 0 and 2 < 0, i.e., < < R H. In this scenario, or the cached portion the downloading time is shorter than the playback time, so that the user can use the time dierence to buer the not-yet-played uncached portion. This reduces the amount o data that are required to be pre-buered and hence leads to the reduction o initial delay. Meanwhile, the beneits o exploiting the high downloading rate rom helper depends on how much uncached data remain, e.g., the cache-inal case beneits nothing because there are no data let to stream within the above mentioned time dierence. This suggests that caching earlier portion o a video can beneit more. Thus, the cache-irst and cache-inal cases provide the lower and upper bounds or the initial delay in general cases, respectively. Second, the cache-irst and cache-inal cases need the same initial delay i 1 0 and 2 0 or 1 0 and 2 0, i.e., and R H or and R H. In the ormer scenario, both the downloading rates are not larger than the playback rate, then the beneits due to high downloading rate described in the last paragraph does not exist. Thus, in this scenario the same initial delay is required no matter which portion is chosen to cache. In the latter scenario, both the downloading rates are not smaller than the playback rate, then pre-buering is not necessary and the initial delay is zero. In summary, the initial delay in general cases is bounded by or equal to those in the cache-inal and cache-irst cases. Thereore, in the ollowing we ocus on the two cases or the optimization o caching policies. Fig. 1. Comparison o two QoE unctions with τ 0 = 10, α 0 = 0, κ = 10, α 1 = 10 log 10, ρ = 10 5, and ξ = log ). B. Approximation o QoE Function We strive to optimize the caching policy aimed at maximizing the average QoE o the user subject to storage size constraint o the helper, where the average is taken over the random request to the F video iles. However, the QoE unction given in 1) is non-smooth and non-concave, which is diicult to optimize. Thus, we introduce a smooth and concave approximate QoE unction or optimization, which is ητ) = ξ log1 + ρe τ ), τ 0, 12) where the parameter ρ is a positive constant with small value, and ξ = log1 + ρ) + α 0 ensures that the approximate QoE unction has the same value as the real one when τ = 0. The comparison o the two QoE unctions is shown in Fig. 1. We can observe that the approximate QoE unction ητ) is able to relect the nonlinear impact o initial delay on QoE, i.e., a small initial delay does not reduce QoE. For small and medium values o τ, the approximation is reasonable in general, but large dierence between the two unctions appears when τ is large. Speciically, ητ) decreases logarithmically or large τ, while ητ) decreases linearly. Fortunately, in practical VoD applications, dierent schemes such as playback rate adaptation, adaptive resource allocation, admission control, can control the initial delay not too long, which makes using ητ) to approximate ητ) reasonable. C. Optimization o Caching Policy The caching policy optimization problem can be ormulated as ollows. max x F =1 q ξ q log1 + ρe τ ) 13a) s.t. F =1 x C 13b) 0 x 1,, 13c) where the objective unction is the approximate average QoE with random video requests, the initial delay τ is given

4 in 9) and 11) or the cache-inal and cache-irst cases, respectively, and 13b) is the constraint o storage size at the helper. We ocus on the scenario where the storage size o the helper is small so that it cannot cache all video iles, i.e., C < F =1 ; otherwise, the optimization problem is trivial. It is obvious that the optimal caching policy must ully use all storage resources, i.e., constraint 13b) holds with equality. We next solve problem 13) in the cache-inal and cacheirst cases, respectively, whose perormance can serve as lower and upper bounds or other general cases as analyzed beore. In the cache-inal case, we can ind rom 9) that τ is a linear unction o x, and hence problem 13) is a convex problem. By analyzing the Karush-Kuhn-Tucker KKT) conditions o the problem, we can obtain the optimal solution o x in closed orm see the Appendix or detailed derivations): 1, 0 ν g 1) ) x = 1 t q Q log Q +ν ) ν, g 1) <ν < g 0) 14) 0, ν g 0), ) + ) + where Q = R H 0, t = ) ρ exp +, R g x) = q t Q e xq, and ν is the Lagrangian multiplier. We can ind that x 1+t e xq is a non-increasing unction o ν, thereore the optimal ν can be easily obtained by using a bisection method to ensure constraint 13b) holding with equality. In the cache-irst case, we can see rom 11) that τ is a convex unction o x. Further considering ητ ) is a concave and non-increasing unction o τ, then based on the composition rule o convex unctions [16], we know that the objective unction 13a) is a concave unction o x. Thereore, problem 13) is convex in this case, whose globally optimal solution can be obtained eiciently with standard convex optimization algorithms [16]. D. Impact o File Popularity In this subsection we analyze the impact o ile popularity q on the optimal caching policy x. Since only the caching-inal case has the closed-orm solution, we ocus on the analysis in this case based on 14). For the caching-irst case, we ind by simulations that the conclusions drawn or the caching-inal case is also valid the simulation result is not presented due to the lack o space). It is easy to see rom 14) that x is lower and upper bounded by 0 and 1, and within the bounds its behavior ) is determined by the term 1 Q log t q Q +ν ) ν x. Thus, we ocus on the analysis o x herein. To see the impact o q, we rewrite x as x = 1 Q log q Q ν ) Q log ρ 1 Q log ν ) Q ) +. 15) Fig. 2. Caching policies designed or VoD and ile downloading, C = 50 MB. When given the size, playback rate, and popularity q o the F video iles, the Lagrangian multiplier ν can be determined accordingly, which is common or all iles. Thus, the inal three terms in 15) are constants, and the cached portion x is determined by the irst term in the right-hand side o 15). Then, we can obtain the ollowing observation. Observation: The cached portion x o the -th video ile logarithmically increases with its popularity q. The logarithm law means that the cached portions or a highly popular video and a medium popular video may have small dierence, which implies that only caching the most popular video iles is no longer optimal or VoD service. IV. SIMULATION RESULTS In this section we evaluate the perormance o the proposed caching policy or VoD service. For comparison, we also simulate the optimal caching policy or ile downloading service proposed in [3] or the single helper scenario as we considered in the paper, i.e., caching the most popular iles until the storage resource is used up. In the simulations, the spectral eiciency o the macro BS and the helper are set as 3 and 5 bps/hz, respectively, as in [11]. Considering that the macro BS covers more users than the helper, the bandwidth allocated by the macro BS and the helper to the user are set as 0.2 and 2 MHz, respectively, which leads to the downloading rates rom the macro BS and the helper as = 0.6 Mbps and R H = 10 Mbps. We consider F = 30 video iles, whose popularity ollows Zip distribution with the parameter o 0.56 [11]. The parameters in the QoE unction are set as τ 0 = 10 seconds, κ = 10, α 0 = 0, and α 1 = 10 log 10. As or the approximate QoE unction, we choose ξ = log ) and ρ = 10 4, which can well approximate the real QoE unction. The ile size and playback rate are set as = 10 MB and = 0.8 Mbps, respectively, = 1,..., F, i.e., the playback duration o each video is 100 seconds.

5 Fig. 3. Average QoE achieved by the proposed and existing caching policies. Fig. 4. QoE o the user when requesting every ile under the proposed and existing caching policies, C = 50 MB. Figure 2 shows the caching results o the existing caching policy or ile downloading and the proposed caching policies or both cache-inal and cache-irst cases, where the storage size o the helper is set as C = 50 MB. The x-axis is the index o the video iles, ranking rom one the most popular) to F the least popular) based on popularity, and y-axis is the cached portion o every video ile. We can observe that in contrast to the cache policy or ile downloading, which only caches the ive most popular videos, the proposed caching policies preer to cache more videos with smaller portion. The cache-irst case can stores more iles than the cache-inal case. This is because the cache-irst case can achieve shorter initial delay than the cache-inal case given the same x as analyzed beore, or inversely, to ensure the same initial delay, the cacheirst case only needs to cache a smaller portion and thereore more videos can be cached. Figure 3 compares the average QoE achieved by the proposed and existing caching policies as a unction o the storage size o the helper, where the y-axis shows the values o the real QoE rather than the approximate one. We consider cache-inal and cache-irst cases or both the proposed caching policy and the policy or ile downloading when a video ile cannot be ully cached due to the limited storage size. We can see that the impact o cache-irst and cache-inal is very small or ile downloading. The proposed policies perorm the same as the policy or ile downloading when the storage size is small so that very ew videos can be cached or when the storage size is very large so that all video iles can be cached. For medium storage size, the proposed policies can achieve higher average QoE, and the gain in the cache-irst case is remarkable because it can reduce the initial delay more eectively than the cacheinal case. Although the proposed polices can improve the average QoE when the user randomly requests the F video iles, it is not clear whether or not the QoE o the user can be improved or every video ile. Figure 4 shows the QoE o the user when requesting every video ile, where both the proposed and existing caching policies in cache-irst and cache-inal cases are considered, and C = 50 MB. The x-axis is the index o the video iles and y-axis is the QoE o the user. It can be observed that compared to the ile downloading policy, the proposed caching policy in the cache-inal case can largely improve the QoE or the sixth and seventh video iles with a small QoE degradation o the ith video ile, while in the cache-irst case the improvement o QoE is dramatic or most video iles. V. CONCLUSIONS In this paper we optimized the caching policy or VoD service by taking into account the impact o initial delay on the QoE. We analyzed the initial delays or the cache-inal and cache-irst cases, and introduced an approximate QoE unction to overcome the diiculty or caching policy optimization caused by the original non-smooth non-concave QoE unction. We obtained the optimal caching policy or the caching-inal case in closed orm and or the caching-irst case numerically, and then analyzed the impact o ile popularity on the caching policy. Simulation results show the perormance gain o the proposed caching policies. VI. ACKNOWLEDGEMENT This work was supported in part by National High Technology Research and Development Program o China No. 2014AA01A705) and by National Natural Science Foundation o China No ). APPENDIX OPTIMAL SOLUTION TO 13) IN CACHE-FINAL CASE By deining t = ρ exp R H ) + and Q = ) + ) +, we can write the KKT condi-

6 tions o problem 13) as ollows: 0 x 1, λ 0, µ 0, ν 0, 16a) F ) ν =1 x C = 0 16b) q t Q e x Q 1 + t e x Q λ x = 0, 16c) µ x 1) = 0, 16d) λ + µ + ν = 0,, 16e) where λ, µ, and ν are Lagrangian multipliers, and x denotes the optimal solution. Deine g x ) = q t Q e x Q, which is a monotonically 1+t e x Q increasing unction o x. Then, we can obtain rom 16e) that λ = g x ) + µ + ν. 17) Substitute 17) into 16c) and considering λ 0, we can obtain g x ) ) + µ + ν = 0, 18) x µ g x ) ν. 19) 1) I ν g 0), i.e., g 0) + ν 0, then g 0) + µ + ν < 0 will not hold because µ 0 according to 16a). Thus, we have g 0) + µ + ν 0, then g x ) + µ + ν 0 since x 0 and g x ) is an increasing unction. I x > 0, then g x ) + µ + ν > 0, which makes 18) ineasible. Thereore, we have x = 0 in this case. 2) I ν < g 0), i.e., g 0) + ν < 0, we can show that g 0) + µ + ν 0 will not hold because this inequality leads to µ > 0 and x = 0 as analyzed in the above case, which does not satisy 16d). Thus, in this case we have g 0)+µ +ν < 0. Since g x ) is an increasing unction and x 0, we know that 19) holds only when x > 0. Then, rom 18) we have g x ) + µ + ν = 0. 20) We have µ = g x ) ν rom 20). By substituting it into 16d) and considering µ 0, we obtain g x ) + ν )x 1) = 0, 21) ν g x ). 22) i) I 0 ν g 1), i.e., g 1) + ν 0, then g x ) + ν 0 since x 1 and g x ) increases with x. I x < 1, then g x )+ν < 0, which makes 21) ineasible. Thus, we have x = 1 in this case. ii) I ν > g 1), i.e., g 1) + ν > 0, 22) holds only when x < 1 considering that g x ) is an increasing unction. Then, we can obtain rom 21) that rom which x can be solved as x = 1 ) t q Q + ν ) log hν). 24) Q ν Based on the above analysis, we obtain x as 1, 0 ν g 1) x = hν), g 1) < ν < g 0) 25) 0, ν g 0) which gives rise to 14). REFERENCES [1] N. Golrezaei, A. F. Molisch, A. G. Dimakis, and G. Caire, Femtocaching and device-to-device collaboration: A new architecture or wireless video distribution, IEEE Communications Magazine, vol. 51, no. 4, pp , Apr [2] N. Golrezaei, K. Shanmugam, A. G. Dimakis, A. F. Molisch, and G. Caire, Femtocaching: Wireless video content delivery through distributed caching helpers, in Proc. IEEE INFOCOM, [3] D. Liu, B. Chen, C. Yang, and A. F. Molisch, Caching at the wireless edge: Design aspects, challenges, and uture directions, IEEE Communications Magazine, vol. 54, no. 9, pp , Sep [4] X. Wang, M. Chen, T. Taleb, A. Ksentini, and V. C. Leung, Cache in the air: exploiting content caching and delivery techniques or 5G systems, IEEE Communications Magazine, vol. 52, no. 2, pp , Feb [5] C. Yang, Y. Yao, Z. Chen, and B. Xia, Analysis on cache-enabled wireless heterogeneous networks, IEEE Trans. on Wireless Communications, vol. 15, no. 1, pp , Jan [6] H. Ahlehagh and S. Dey, Adaptive bit rate capable video caching and scheduling, in Proc. IEEE WCNC, [7], Video-aware scheduling and caching in the radio access network, IEEE/ACM Trans. on Networking, vol. 22, no. 5, pp , Oct [8] W. Zhang, Y. Wen, Z. Chen, and A. Khisti, QoE-driven cache management or HTTP adaptive bit rate streaming over wireless networks, IEEE Transactions on Multimedia, vol. 15, no. 6, pp , Oct [9] Y. Wang, X. Zhou, M. Sun, L. Zhang, and X. Wu, A new QoE-driven video cache management scheme with wireless cloud computing in cellular networks, Mobile Networks and Applications, Feb [Online]. Available: [10] H. Su, S. Han, and C. Yang, Caching policy optimization or rate adaptive video streaming, in Proc. IEEE Globalsip, [11] K. Shanmugam, N. Golrezaei, A. G. Dimakis, A. F. Molisch, and G. Caire, Femtocaching: Wireless content delivery through distributed caching helpers, IEEE Trans. on Inormation Theory, vol. 59, no. 12, pp , Dec [12] C. Quadros, A. Santos, M. Gerla, and E. Cerqueira, QoE-driven dissemination o real-time videos over vehicular networks, Computer Communications, vol. 91, pp , [13] P. Reichl, B. Tuin, and R. Schatz, Logarithmic laws in service quality perception: Where microeconomics meets psychophysics and quality o experience, Telecommun. Syst., pp. 1 14, [14] D. Bethanabhotla, G. Caire, and M. J. Neely, Adaptive video streaming or wireless networks with multiple users and helpers, IEEE Transactions on Communications, vol. 63, no. 1, pp , Jan [15] S. Egger, P. Reichl, T. Hoßeld, and R. Schatz, Time is bandwidth? narrowing the gap between subjective time perception and quality o experience, in Proc. IEEE ICC, [16] S. Boyd and L. Vandenberghe, Convex optimization. Cambridge university press, g x ) + ν = 0, 23)