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 LeeLian-kuan Chen

Outline Introduction MDR (Monotonic-Decreasing Rate) Scheduler –Admission Complexity –Peak Transmission Rate –Client Buffer Requirement Aggregated MDR Scheduler Conclusion

VBR Video

VBR Video Smoothing B(t) = A(t) + b B(t) ≧ S(t) ≧ A(t) Upward Adjustment Downward Adjustment

Optimal Smoothing Method MVBA : minimal bit-rate variance MCBA : minimal change rate

Problem Bandwidth reservation fail : additional bandwidth is not available at upward adjustment Bandwidth reservation processing delay –Network topology –Reservation protocol –Loss of control message

MDR Scheduler Principle : –eliminate upward adjustment and only use downward adjustment. r i > r j, 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

MDR Scheduler {r i, T i | i = 1, 2, …n}

Admission Complexity Notation –U : System capacity –u i : System utilization at time i –w : video length (seconds) –v j : video transmission bit-rate ( j = 0, 1, …,w-1 ) –A : video startup time General Optimal Smoothing u i = u i + v i-A, i = A, A+1,.. A+w-1 (addition computation) u i + v i-A ≦ U, i = A, A+1,.. A+w-1 ( comparison computation ) Need w additions and w comparisons for a successful admission

Admission Complexity MDR Scheduler u A + v 0 ≦ U (only one comparison) u i = u i + v i -A, i = A, A+1,.. A+w-1 (addition computation) u i + v i-A, i = A, A+1, …, A+w-1 ≦ u A + v i-A, ∵ u i is nonincreasing ≦ u A + v 0, ∵ v j ( 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

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 ≦ T 1 (3)Y’(t) ＜ S’(t), for 0 ≦ t ≦ T 1 (4) (5)Y(T 1 ) < S(T 1 ) = A(T 1 ) S(t) A(t) Y(t) T1T1 (Contradiction)

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 t 0 such that S(t 0 ) > X(t 0 ) ≧ A(t 0 ) (3)But S(T i ) = A(T i ), for i=1, 2, …,n (4)so t 0 ≠ T i, for i=1, 2, …, n (5)t 0 not in (Ti-1, Ti), for i=2, 3,..n (6)t 0 not exist S(t) X(t) A(t) T1T1 t0t0 Buffer (Contradiction)

MDR Performance Evaluation Environment –274 different DVD video –Full length( average 5781 s, and 4348 MB) –1-Gb/s backbone network Admission Complexity

MDR Performance Evaluation

Client Buffer Requirement Worst case buffer requirement : 394.5MB

Problem in MDR Client buffer utilization will be low most of time. The worst-case buffer requirement is unbounded.

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 scheduler else use optimal smoothing algorithm with B buffer-constrainted –Because server serves many videos simultaneously, so aggregate traffic conforms to the monotonicity property

Aggregated MDR Scheduler

Admission Complexity Computation complexity –MDR case : need one comparison –Optimal smoothing case transmission schedule {v i } rate-increasing round : v i > v i-1 increasing round point : h i, i=1, 2,.., g s hi+A + v hi ≦ U, for i=0, 1, …g s i+A + v i ≦ U, => s i+A+1 + v i+1 ≦ U need g+1 comparisons

Performance Evaluation Fix buffer size : 32MB

Performance Evaluation

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