Performance evaluation of video transcoding and caching solutions in

mobile networks

Jim Roberts (IRT-SystemX)joint work with Salah Eddine Elayoubi (Orange Labs)

ITC 27September 2015

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

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

Radio conditions

• user position, assumed fixed, determines maximum download rate: class i users can attain rate Ri

• proportional fair scheduling: when n users are active, users of class i receive rate Ri/n

cell centreeg, Ri=15Mb/s

cell edgeeg, Ri=5Mb/s

Traffic mix and congestion avoidance

• 3 types of downlink flows:• type 1 flows: transcodable video downloads, original rate

Co, compressed rate Cc (eg, Cc = Co/4)– on arrival, if Ri/(n+1) < Co, request compressed version

• type 2 flows: non-video downloads– assume TCP realizes fair rate Ri/n

• type 3 flows: adaptive rate video streaming– assume rate adapted to fair rate Ri/n

Ri, max rate for class i users, n, number of active users of all types

A Markov model

• Poisson flow arrivals at rate λit for class i and type t

• exponential duration of mean τ1, τ3 for type 1 and type 3 videos

• exponential size of mean σ2 for type 2 flows• to simplify, assume only 2 radio classes (edge and centre)

with system state: n = (a1o,a2o, a1c,a2c, b1,b2, c1,c2) where– a1o,a2o are numbers of type 1 flows with original video rate

– a1c,a2c are numbers of type 1 flows with compressed video rate

– b1,b2 are numbers of type 2 flows

– c1,c2 are numbers of type 3 flows

• total number of flows– n = a1o + a2o + a1c + a2c + b1 + b2 + c1 + c2

class 1

class 2

First, assume compressed version isalways available

• transition rates determine transition matrix Q• state probabilities π(n) are determined on numerically

solving Q π(n) = 0• non-zero transition rates

– aio → aio+1 : λi1 if Ri/(n+1) ≥ Co

– aio → aio-1 : aio Ri/(nCoτ1)

– aic → aic+1 : λi1 if Ri/(n+1) < Co

– aic → aic-1 : aic Ri/(nCcτ1)

type 1 videos

First, assume compressed version isalways available

• transition rates determine transition matrix Q• state probabilities π(n) are determined on numerically

solving Q π(n) = 0• non-zero transition rates

– aio → aio+1 : λi1 if Ri/(n+1) ≥ Co

– aio → aio-1 : aio Ri/(nCoτ1)

– aic → aic+1 : λi1 if Ri/(n+1) < Co

– aic → aic-1 : aic Ri/(nCcτ1)

– bi → bi+1 : λi2

– bi → bi-1 : bi Ri/(nσ2)type 2 downloads

First, assume compressed version isalways available

• transition rates determine transition matrix Q• state probabilities π(n) are determined on numerically

solving Q π(n) = 0• non-zero transition rates

– aio → aio+1 : λi1 if Ri/(n+1) ≥ Co

– aio → aio-1 : aio Ri/(nCoτ1)

– aic → aic+1 : λi1 if Ri/(n+1) < Co

– aic → aic-1 : aic Ri/(nCcτ1)

– bi → bi+1 : λi2

– bi → bi-1 : bi Ri/(nσ2)

– ci → ci+1 : λi3

– ci → ci-1 : ci /τ3

type 3 adaptive streaming

Performance criteria

• compression probability, pic, the probability a compressed

version is downloaded to users of class i– pi

c = 1 - ∑(n∈Si) π(n) where Si are states such that Ri/(n+1) < Co

• cell utilization, u, proportion of time cell is active– u = 1 - π(0)

• rate deficit probability, pd, the probability an on-going type 1 download proceeds at a rate less than its coding rate, Co or Cc

– pd = ∑n ∑i ( aio/(aio+aic) 1{Ri/n < Co} + aic/(aio+aic) 1{Ri/n < Cc} ) π(n)

• cell sizing such that pic, pd and u meet threshold conditions

– eg, E [pic] < 30%, u < 80%, pd < 10%

Case study

• radio conditions: 2 classes, – cell edge R1 = 5 Mb/s, 50% of flows

– centre R2 = 15 Mb/s, 50% of flows

• traffic mix (flow arrival rates): – transcodable videos 52.5%– adaptive videos 22.5%– other downloads 25%

• coding rates: – original version Co = 1 Mb/s

– compressed version Cc = 250 Kb/s

• performance criteria thresholds– compression proba < 30%, utilization < 80%, deficit proba <

10%

class 1

class 2

video

other

threshold(30%)

Compression probability

.1 .2 .3 .4 .5 .6

.1

0

.2

.3

.4

flow arrival rate

cell edge

cell centre

average

threshold(80%)

Cell utilization

.1 .2 .3 .4 .5 .6

.4

.2

.6

.8

1

flow arrival rate

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

Rate deficit probability

.1 .2 .3 .4 .5 .6

.2

0

.4

.6

.8

flow arrival rate

withcompression

threshold(10%)

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...

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 hc 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– aio → aio+1 : (1 – hc) λi1 if Ri/(n+1) < Co (instead of 0)

– aic → aic+1 : hc λi1 if Ri/(n+1) < Co (instead of λi1)

LRU cache hit rate

0 .25 .5 .75 1

.25

0

.5

.75

1

cache size/catalogue size

Zipf (.8) popularitycache compressed version only

Rate deficit probability: impact of cache size

0 .25 .5 .75 1

cache size/catalogue size

.15

.1

.2

.25

no compression

compressed versionalways available

with LRU cacheof given size

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 aio and aic become

– aio → aio+1 : (1 – h’c) λi1 if Ri/(n+1) < Co (instead of 0)

– aic → aic+1 : h’c λi1 if Ri/(n+1) < Co (instead of λi1)

where h’c = hc + (1 – hc)(1 - f)

• to estimate f, – assume each compressed video flow in progress is being

transcoded with probability (1 – hc)– 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

Rate deficit probability: impact of cache size and transcoding capacity T for 100 cells

0 .25 .5 .75 1

cache size/catalogue size

.15

.1

.2

.25

no compression

compressed versionalways there

with LRU cacheand T = 0

T = 10

T = 20

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

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...