A Monotonic-Decreasing Rate Scheduler for Variable-Bit-Rate Video Streaming
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A Monotonic-Decreasing Rate Scheduler for
Variable-Bit-Rate Video Streaming
Hin-lun Lai
IEEE Transactions on Circuits and System for Video Technology, February 2005
Yiu-bun Lee Lian-kuan Chen
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Outline
Introduction MDR (Monotonic-Decreasing Rate)
Scheduler– Admission Complexity– Peak Transmission Rate– Client Buffer Requirement
Aggregated MDR Scheduler Conclusion
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VBR Video
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VBR Video Smoothing
B(t) = A(t) + b
B(t) ≧ S(t) ≧ A(t)
Upward Adjustment
Downward Adjustment
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Optimal Smoothing Method
MVBA : minimal bit-rate variance MCBA : minimal change rate
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Problem
Bandwidth reservation fail : additional bandwidth is not available at upward adjustment
Bandwidth reservation processing delay– Network topology– Reservation protocol – Loss of control message
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MDR Scheduler
Principle : – eliminate upward adjustment and only use
downward adjustment.
ri > rj , for j > I
– Provide guaranteed video delivery Advantage : solve previous two problems
– Have sufficient system bandwidth– Adjustment processing time will not be critical
Disadvantage : need more client buffer
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MDR Scheduler
{ri , Ti | i = 1, 2, …n}
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Admission Complexity
Notation
– U : System capacity
– ui : System utilization at time i
– w : video length (seconds)
– vj : video transmission bit-rate ( j = 0, 1, …,w-1 )
– A : video startup time
•General Optimal Smoothing
•ui = ui + vi-A , i = A, A+1, .. A+w-1 (addition computation)
•ui + vi-A U , i≦ = A, A+1, .. A+w-1 ( comparison computation )
Need w additions and w comparisons for a successful admission
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Admission Complexity
•MDR Scheduler
• uA + v0 ≦ U (only one comparison)
•ui = ui + vi-A , i = A, A+1, .. A+w-1 (addition computation)
ui + vi-A , i = A, A+1, …, A+w-1 ≦ uA + vi-A, ∵ ui is nonincreasing ≦ uA + v0 , ∵ vj ( j = 0, 1, …, w-1) is nonincreasing ≦ U
For a unsuccessful admission, client will have to wait until the next round to repeat the admission test
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Peak Transmission Rate
MDR Scheduler has the minimum peak rate among all feasible schedules with zero startup delay.
(1) Y(t) ≧ A(t)
(2) Y’(t) ≦ S’(t) , for 0 ≦t ≦T1
(3) Y’(t) < S’(t) , for 0 ≦t ≦T1
(4)
(5) Y(T1) < S(T1) = A(T1)
S(t)
A(t)
Y(t)
T1
(Contradiction)
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Client Buffer Requirement
MDR scheduler generates schedules with the minimum buffer requirement among all feasible monotonic decreasing rate schedules
(1) X(t) ≧ A(t)
(2) Exist t0 such that S(t0) > X(t0) ≧A(t0)
(3) But S(Ti) = A(Ti), for i=1, 2, …,n
(4) so t0 ≠ Ti, for i=1, 2, …, n
(5) t0 not in (Ti-1, Ti), for i=2, 3,..n
(6) t0 not exist
S(t)
X(t)
A(t)
T1
t0
Buffer(Contradiction)
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MDR Performance Evaluation Environment
– 274 different DVD video– Full length( average 5781 s , and 4348 MB)– 1-Gb/s backbone network
Admission Complexity
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MDR Performance Evaluation
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Client Buffer Requirement
Worst case buffer requirement : 394.5MB
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Problem in MDR
Client buffer utilization will be low most of time.
The worst-case buffer requirement is unbounded.
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Aggregated MDR Scheduler
Principle : apply the MDR principle to aggregated network flows.
Method : – Give a fixed client buffer B
– If B video buffer requirement ≧ use MDR schedulerelse use optimal smoothing algorithm with B buffer-constrainted
– Because server serves many videos simultaneously, so aggregate traffic conforms to the monotonicity property
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Aggregated MDR Scheduler
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Admission Complexity
Computation complexity– MDR case : need one comparison– Optimal smoothing case
transmission schedule {vi} rate-increasing round : vi > vi-1
increasing round point : hi , i=1, 2, .., g
shi+A + vhi ≦ U, for i=0, 1, …g
si+A + vi ≦ U, => si+A+1 + vi+1 ≦ U need g+1 comparisons
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Performance Evaluation
Fix buffer size : 32MB
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Performance Evaluation
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Performance Evaluation
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Conclusion
MDR is able to guarantee video delivery with tradeoff in client buffer requirement
The result of AMDR scheduler show that performance is nearly identical to optimal smoothing even for a buffer size as small as 32 MB