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Analytical Modeling of End-to-End Delay in OpenFlow Based NetworksAzeem Iqbal
OpenFlow enabled networks split and separate the data and control planes of traditional networks. This design commodifies network switches and enables centralized control of the network. Control decisions are made by an OpenFlow controller, and locally cached by switches, as directed by controllers. Since controllers are not necessarily co-located with switches that can significantly impact the forwarding delay incurred by packets in switches. Only very few studies have been conducted to evaluate the performance of OpenFlow in terms of end-to-end delay. In this work we develop a stochastic model for the end to end delay in OpenFlow switches based on measurements made in Internetscale experiments performed on three different platforms, i.e. Mininet, the GENI testbed and the OF@TEIN testbed.
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3. Motivation
HTTP Adaptive Streaming (HAS) is now the dominant source of data traffic.
• It is projected to reach 82% of the global Internet traffic, by 20221
• OTT services (Netflix, YouTube etc.) account for > 50% of the global ⇓ traffic2
• Cord-cutters and live applications are expedited → rise of low-latency streaming
Some current challenges of bitrate adaptation:
• Channel instability (physical phenomena)
• QoE management
• Reliable low-latency video streaming (1-5 s) . Need for robust, lightweight and
universal solutions ← our contribution
1
Cisco Visual Networking Index, “Forecast and Trends, 2017-2022” - Cisco ’19
2
Global Internet Phenomena - Sandvine 19’
Low-latency adaptive streaming 1 / 11
4. Adaptive streaming media format
Low-latency bitrate adaptation is facilitated by:
• Multiple qualities={resolutions, encoding rates} served from a regular origin.
• By requiring commodity web infrastructure → operational costs ↓
• Fragments - smaller (independently decodable) files
• Independent fragment requests (multiple servers) maintain session state
• Data segmentation → finer granularity of bitrate selection → channel utilization ↑
• A client initially fetches an XML file, which contains content information
• Control logic, a.k.a a bitrate adaptation algorithm→ bitrate indicates quality
• Logic that selects the appropriate encoding bitrate ∀ fragments, given network
conditions
• Essentially matches the streaming rate to the channel rate, via means of adaptation
• CMAF in combination with the supported chunked transfer mechanism of HTTP 1.1
and beyond, have set the stage for low-latency streaming
Low-latency adaptive streaming 2 / 11
6. Motivation
Insights from earlier research (MMSys ’17)3:
• Existing schemes → parameter tuning according to network or app. scenario
• Difficulty in generalizing well beyond a certain scope of usage
• Optimal adaptation over fluctuating channels remains a challenging operation
• Low-latency bitrate adaptation still relies on throughput estimation
To overcome this limitation → resort to learning or control theory
• Practical implementation may be hindered
• by energy-demanding architectures (Deep Learning)
• or by the complexity of exploring the complete optimization space (MDPs)
Proposal: Novel adaptation algorithm based on Online Convex Optimization (OCO)
• OCO emerged in 2003 (Zinkevich) as a very effective online learning framework
• Does not rely on estimations (throughput). Only on historical values.
• “Model-free”, as no assumption for the statistical model of the channel is required
• Independent of any parameter selection concerning the streaming environment
• It provides tractable feasibility and performance guarantees
3
T. Karagkioules et al. A Comparative Case Study of HTTP Adaptive Streaming Algorithms in Mobile Networks
Bitrate adaptation via learning 3 / 11
7. Problem definition
An adaptation algorithm is an optimization solution with the objective of maximizing
the video bitrate, while ensuring stable and continuous low-latency streaming.
However, the application of OCO in HAS is not a straightforward task
• OCO requires convex decision space and constraints
• HAS has a discrete decision space (set of qualities for every fragment)
• Instantaneous state-dependent constraints (finite-sized buffer)
Modelling assumptions:
• We model the adaptive streaming client by a learning agent
• Agent minimizes latency, s.t. scheduling constraints of the buffer
• We model the channel rate evolution by an adversary
• Adversary decides the cost of each decision only after it has been taken
• Adversarial setting is general enough to include any potential time-variant distribution
• Learning agent minimizes an adversarial loss function, unknown at decision time.
We fulfill the OCO requirement (convex decision set and constraints):
1. Agent decides video quality, according to a probability distribution for the
appropriate bitrate, given network and latency conditions
2. Relaxation to unbounded buffer → adheres to time-averaging constraints
Bitrate adaptation via learning 4 / 11
8. Relaxations
Relaxation 1: Convexification of decision set by randomization
∀ fragment t ∈ {1, . . . , T}, the client selects quality xt ∈ X = {1, . . . N}
• upon bitrate indication rxt ∈ {r1, . . . , rN} of the bitrate adaptation algorithm
Consider the probability simplex:
Ω = {ω ∈ RN
: ω ≥ 0 ∧ ∥ω∥1 = 1}
→ Instead of xt, client learns the optimal probability ωt = (ωt,n)n=1,...,N of picking xt ∈ X
Relaxation 2: Convexification of buffer constraints
Buffer evolution:
Bt+1 =
Bt − ρt
Playback rate
Seg. size≈V·rxt
St,xt
Ct
Throughput
⇓ time
+
+ V
Seg. duration
−
Inter-request delay
∆t
keeps Bt+1<Bmax
∈ [0, Bmax]
→ We treat the buffer as an infinite queue, i.e. Bt ∈ (−∞, ∞). ∆t is never imposed
• We allow instantaneous violation of the buffer budget
• But utilize a penalty to maintain 0 < Bt < Bmax on average
Bitrate adaptation via learning 5 / 11
9. Problem formulation
Consider the following functions =⇒ random processes:
˜ft(xt) ≜ V −
ρtSt,xt
Ct
Loss
=⇒ ft(ωt) ≜ E V −
ρtSt,xt
Ct
˜gt(xt)
Underflow
≜
ρtSt,xt
Ct
adversary
− V
Bt>0 on avg.
=⇒ gt(ωt) ≜ E
ρtSt,xt
Ct
− V
Given the loss function and constraints above, we formulate the constrained OCO:
min
ω∈Ω
T
t=1
ft(ω) s.t.
T
t=1
gt(ω) ≤ 0
At every decision epoch t the following events occur in succession:
(a) Agent computes ωt ∈ Ω → xt ∈ arg minx∈X |rx − N
n=1 ωt,nrn|
(b) Adversary decides jointly Ct, ρt, and ˜ft(xt). ˜gt(xt) → actual buffer displacement
(c) Feedback is provided to the agent
Bitrate adaptation via learning 6 / 11
10. OCO solution for adaptation (Learn2Adapt)
Challenge in adversarial problems: gt(ωt) are unknown at decision time
Solution: prediction around ωt−1 evaluated at ωt (Taylor)
ˆgt(ωt) ≜ gt−1(ωt−1) + ⟨∇gt−1(ωt−1), ωt − ωt−1⟩
We combine the objective and the constraint function in a regularized Lagrangian:
Lt(ω, Q(t)) = Q(t)ˆgt(ω)
Buffer deviation
+ VL
ˆft(ω)
Latency
+ α||ωt − ωt−1||2
Smoothness
• VL and α are convergence parameters
• ||ωt − ωt−1||2 is a regularization term that smooths the decisions
• Q(t) is a multiplier → accumulates the constraint deviations:
Q(t + 1) = [Q(t) + ˆgt(ωt)]+
,
→ We have accounted for latency, smoothness, and stalling, in terms of QoE provisions
Bitrate adaptation via learning 7 / 11
11. Learn2Adapt-LowLatency (L2A-LL)
→ Learn2Adapt-LL takes a step in the direction of the sub-gradient of the Lagrangian
Algorithm 1 Learn2Adapt-LowLatency (L2A-LL)
Initialize: Q(1) = 0, ω0 ∈ S
Parameters: cautiousness parameter VL, step size α
1: for all t ∈ {1, 2, . . . , T} do
2: ωt = projΩ ωt−1 −
VL∇ft−1(ωt−1)+Q(t)∇gt−1(ωt−1)
2α
3: Q(t + 1) = [Q(t) + ˆgt(ωt)]+
4: end for
Bitrate adaptation via learning 8 / 11
12. Implementation in dash.js
Open source:
Learn2Adapt-LowLatency (L2A-LL) has been implemented in ‘dash.js’
It is is publicly available for experimentation at Unified Streaming GitHub.
Experimental setup:
5 network profiles: Cascade, Intra-Cascade, Spike, Slow and Fast jitters.
Video sequence (encoded at R = 0.3, 0.6, 1.0 Mbps) organized in fragments
(V = 0.5s)
We allow a variable ‘catch-up’ playback rate pt but left its selection to dash.js.
Implementation location:
Modified dash.js instance now includes L2A-LL + all server and orchestration nodes.
The implemented instance of L2A-LL in dash.js exists in:
‘Learn2Adapt-LowLatency/dash.js/src/streaming/rules/abr/L2ARule.js’
All required player configuration can be found in:
‘Learn2Adapt-LowLatency/dash.js/samples/low-latency/index.html’.
Bitrate adaptation via learning 9 / 11
13. Experimental evaluation
Table 1: Preliminary experimental results for L2A-LL
Network profile Avg Bitrate (Mbps) Avg Buffer length (s) Latency (s) Stall duration (s) Num. Switches
Cascade 0.58 0.46 1.7 28 10
Intra-Cascade 0.35 0.4 2.5 38 7
Spike 0.59 0.4 1.5 6 3
Slow jitter 0.33 0.47 1.3 7 4
Fast jitter 0.33 0.57 1.2 0.7 2
General remarks:
• Our algorithmic approach allows to adjust QoE priorities
• Modular Lagrangian accounts for: latency, stalling and smoothness
• Of course is all a matter of trade-offs
• L2A-LL achieves relatively high avg. bitrate, and low latency (<2 s)
• L2A-LL adheres to theoretical performance guarantees (Theorem 4.14)
• Verified experimentally (also in the paper)
4
T. Karagkioules et al. Online learning for low-latency bitrate adaptation, MMSys ’20 - Challenges
Bitrate adaptation via learning 10 / 11
14. Summary
Learn2Adapt-LowLatency:
• is a novel bitrate adaptation algorithm, based on online learning
• does not require modifications according to application type
• requires no statistical assumptions for the channel
• performs well in a wide spectrum of possible scenarios
• robust, due to design principle; its ability to learn
• allows parameter selection according to QoE prioritization
• facilitates effective bitrate adaptation in low-latency mode when combined with
CMAF and chunked transfer
All these properties are significantly relevant to the field of modern HAS
• where OTT providers and broadcasters are continuously expanding their services
• to include more: diverse user classes, network scenarios and streaming applications
Bitrate adaptation via learning 11 / 11
15. For any questions, feel free to contact me at:
theo@unified-streaming.com
Thank you.
Bitrate adaptation via learning 11 / 11