1. Performance evaluation of video transcoding and caching solutions in mobile networks Jim Roberts (IRT-SystemX) joint work with Salah Eddine Elayoubi (Orange Labs) ITC 27 September 2015

2. Alleviating wireless congestion wireless video traffic is increasingly heavy can be reduced by sending lower quality video, as necessary –lower quality is preferable to stalling by means of a “video transcoding and caching” (VTC) device –or a virtualized network function... VTC

3. Alleviating wireless congestion what is the saving for given VTC cache and transcoding capacity? we propose models to evaluate this tradeoff eg, a 16% reduction in wireless traffic in a considered application VTC

4. Radio conditions user position, assumed fixed, determines maximum download rate: class i users can attain rate R i proportional fair scheduling: when n users are active, users of class i receive rate R i /n cell centre eg, R i =15Mb/s cell edge eg, R i =5Mb/s

5. Traffic mix and congestion avoidance 3 types of downlink flows: type 1 flows: transcodable video downloads, original rate C o, compressed rate C c (eg, C c = C o /4) –on arrival, if R i /(n+1) < C o, request compressed version type 2 flows: non-video downloads –assume TCP realizes fair rate R i /n type 3 flows: adaptive rate video streaming –assume rate adapted to fair rate R i /n R i, max rate for class i users, n, number of active users of all types

6. A Markov model Poisson flow arrivals at rate λ it for class i and type t exponential duration of mean τ 1, τ 3 for type 1 and type 3 videos exponential size of mean σ 2 for type 2 flows to simplify, assume only 2 radio classes (edge and centre) with system state: n = (a 1o,a 2o, a 1c, a 2c, b 1,b 2, c 1,c 2 ) where –a 1o,a 2o are numbers of type 1 flows with original video rate –a 1c,a 2c are numbers of type 1 flows with compressed video rate –b 1,b 2 are numbers of type 2 flows –c 1,c 2 are numbers of type 3 flows total number of flows –n = a 1o + a 2o + a 1c + a 2c + b 1 + b 2 + c 1 + c 2 class 1 class 2

7. First, assume compressed version is always available transition rates determine transition matrix Q state probabilities π(n) are determined on numerically solving Q π(n) = 0 non-zero transition rates –a io → a io +1 : λ i1 if R i /(n+1) ≥ C o –a io → a io -1 : a io R i /(nC o τ 1 ) –a ic → a ic +1 : λ i1 if R i /(n+1) < C o –a ic → a ic -1 : a ic R i /(nC c τ 1 ) type 1 videos

8. First, assume compressed version is always available transition rates determine transition matrix Q state probabilities π(n) are determined on numerically solving Q π(n) = 0 non-zero transition rates –a io → a io +1 : λ i1 if R i /(n+1) ≥ C o –a io → a io -1 : a io R i /(nC o τ 1 ) –a ic → a ic +1 : λ i1 if R i /(n+1) < C o –a ic → a ic -1 : a ic R i /(nC c τ 1 ) –b i → b i +1 : λ i2 –b i → b i -1 : b i R i /(nσ 2 ) type 2 downloads

9. First, assume compressed version is always available transition rates determine transition matrix Q state probabilities π(n) are determined on numerically solving Q π(n) = 0 non-zero transition rates –a io → a io +1 : λ i1 if R i /(n+1) ≥ C o –a io → a io -1 : a io R i /(nC o τ 1 ) –a ic → a ic +1 : λ i1 if R i /(n+1) < C o –a ic → a ic -1 : a ic R i /(nC c τ 1 ) –b i → b i +1 : λ i2 –b i → b i -1 : b i R i /(nσ 2 ) –c i → c i +1 : λ i3 –c i → c i -1 : c i /τ 3 type 3 adaptive streaming

10. Performance criteria compression probability, p i c, the probability a compressed version is downloaded to users of class i –p i c = 1 - ∑ (n ∈ Si) π(n) where S i are states such that R i /(n+1) < C o cell utilization, u, proportion of time cell is active –u = 1 - π(0) rate deficit probability, p d, the probability an on-going type 1 download proceeds at a rate less than its coding rate, C o or C c –p d = ∑ n ∑ i ( a io /(a io +a ic ) 1{R i /n < C o } + a ic /(a io +a ic ) 1{R i /n < C c } ) π(n) cell sizing such that p i c, p d and u meet threshold conditions –eg, E [p i c ] < 30%, u < 80%, p d < 10%

11. Case study radio conditions: 2 classes, –cell edge R 1 = 5 Mb/s, 50% of flows –centre R 2 = 15 Mb/s, 50% of flows traffic mix (flow arrival rates): –transcodable videos 52.5% –adaptive videos22.5% –other downloads25% coding rates: –original versionC o = 1 Mb/s –compressed versionC c = 250 Kb/s performance criteria thresholds –compression proba < 30%, utilization < 80%, deficit proba < 10% class 1 class 2 video other

12. threshold (30%) Compression probability.1.2.3.4.5.6.1 0.2.3.4 flow arrival rate cell edge cell centre average

13. threshold (80%) Cell utilization.1.2.3.4.5.6.4.2.6.8 1 flow arrival rate

14. threshold (10%) Rate deficit probability.1.2.3.4.5.6.2 0.4.6.8 flow arrival rate cell edge cell centre average without compression

15. Rate deficit probability.1.2.3.4.5.6.2 0.4.6.8 flow arrival rate with compression threshold (10%)

16. Capacity gain assuming the compressed version is always available the most limiting performance criterion is the deficit probability –compression increases admissible flow arrival rate from.31 flows per sec to.36 flows per sec –an increase in capacity of 16% (i.e., roughly 16% less wireless infrastructure for the same demand) the wireless network capacity gain must be offset against the cost of the VTC device –and this depends on its cache and transcoding capacity...

17. Impact of VTC cache capacity (with no transcoding capacity) assumed cache behaviour –only the compressed version is cached –least recently used (LRU) replacement –Zipf(.8) popularity and stationary request process Che approximation yields hit rate h c for cache capacity of c videos under independent reference model (IRM) –a Gaussian approximation (cf. Fricker et al, ITC 25) transition rates are modified as follows –a io → a io +1 : (1 – h c ) λ i1 if R i /(n+1) < C o (instead of 0) –a ic → a ic +1 : h c λ i1 if R i /(n+1) < C o (instead of λ i1 )

18. LRU cache hit rate 0.25.5.751.25 0.5.75 1 cache size/catalogue size Zipf (.8) popularity cache compressed version only

19. Rate deficit probability: impact of cache size 0.25.5.751 cache size/catalogue size.15.1.2.25 no compression compressed version always available with LRU cache of given size

20. Impact of transcoding if the compressed version is requested and not cached, the VTC can compress up to T flows on the fly let f be the probability of T simultaneous transcodings the transition rates for a io and a ic become –a io → a io +1 : (1 – h’ c ) λ i1 if R i /(n+1) < C o (instead of 0) –a ic → a ic +1 : h’ c λ i1 if R i /(n+1) < C o (instead of λ i1 ) where h’ c = h c + (1 – h c )(1 - f) to estimate f, –assume each compressed video flow in progress is being transcoded with probability (1 – h c ) –from π(n) derive mean and variance of number of simultaneous transcodings –a Gaussian approximation for K similar cells yields f –re-evaluate π(n) and iterate till convergence

21. Rate deficit probability: impact of cache size and transcoding capacity T for 100 cells 0.25.5.751 cache size/catalogue size.15.1.2.25 no compression compressed version always there with LRU cache and T = 0 T = 10 T = 20

22. VTC sizing maximum gains obtained with large enough cache or large enough transcoding capacity transcoding is highly effective even without caching –a VTC for 100 cells needs a capacity of T≈11 –a VTC for 1000 cells needs a capacity of T=84 (scale economies) caching is moderately efficient without transcoding –cache of 20% of catalogue size to halve deficit probability

23. Conclusions increasing wireless congestion due to video demand leads operators to envisage use of transcoding and caching we propose a Markovian model to evaluate capacity gains gains in a case study are around 16% to be offset against the cost of transcoding and caching a relatively small transcoding capacity realizes maximal gains; caching improves performance but a large capacity is needed unfortunately, the proportion of transcodable video is diminishing –use of encryption by video content providers and increasing use of adaptive coding though there are lessons for traffic optimization in a future software defined virtualized mobile access network...