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
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 centre
eg, Ri=15Mb/s
cell edge
eg, 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
class 1
c1,c2 are numbers of type 3 flows
• total number of flows
– n = a1o + a2o + a1c + a2c + b1 + b2 + c1 + c2
class 2
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
–
–
–
–
aio → aio+1
aio → aio-1
aic → aic+1
aic → aic-1
:
:
:
:
λi1 if Ri/(n+1) ≥ Co
aio Ri/(nCoτ1)
λi1 if Ri/(n+1) < Co
aic Ri/(nCcτ1)
type 1 videos
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
–
–
–
–
–
–
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 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
–
–
–
–
–
–
–
–
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
– pic = 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
class 1
• radio conditions: 2 classes,
– cell edge R1 = 5 Mb/s,
– centre
R2 = 15 Mb/s,
50% of flows
50% of flows
– transcodable videos
– adaptive videos
– other downloads
52.5%
22.5%
25%
class 2
• traffic mix (flow arrival rates):
• coding rates:
– original version
– compressed version
Co = 1 Mb/s
Cc = 250 Kb/s
other
video
• performance criteria thresholds
– compression proba < 30%, utilization < 80%, deficit proba < 10%
Compression probability
cell edge
.4
threshold
(30%)
.3
average
.2
.1
cell centre
0
.1
.2
.3
.4
flow arrival rate
.5
.6
Cell utilization
1
threshold
(80%)
.8
.6
.4
.2
.1
.2
.3
.4
flow arrival rate
.5
.6
Rate deficit probability
.8
cell edge
without
compression
.6
.4
average
.2
threshold
(10%)
0
cell centre
.1
.2
.3
.4
flow arrival rate
.5
.6
Rate deficit probability
.8
with
compression
.6
.4
.2
threshold
(10%)
0
.1
.2
.3
.4
flow arrival rate
.5
.6
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
1
.75
.5
.25
0
0
Zipf (.8) popularity
cache compressed version only
.25
.5
.75
cache size/catalogue size
1
Rate deficit probability: impact of cache size
.25
no compression
.2
with LRU cache
of given size
.15
.1
compressed version
always available
0
.25
.5
.75
cache size/catalogue size
1
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
.25
no compression
.2
with LRU cache
and T = 0
.15
T = 10
.1
compressed version
always there
T = 20
0
.25
.5
.75
cache size/catalogue size
1
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...