Adaptive Media Streaming - Scalable Continuous Media Streaming Systems - page 146

B i = ( B i −1 + T i −1 ) − T i + 1/ G

T i −1 T i

B i

t

T i

Period when
buffer is empty

t

Frame i

B i −1

B i = 1/ G

Figure 8.3 Two ways to estimate B i when i > K + B p × G − 1

Case 1 ( i 1): In this case, frame i belongs to the initial prefetch part of

the video or the rebuffering period, i.e., the player has not yet started/resumed decoding the
received video data. Thus the buffer occupancy is simply equal to:

≤ K + B p × G −

B i = ( i − K + 1) / G (8.3)

Case 2 ( i 1): In this case, the way to estimate B i depends on whether or

not frame i has arrived before all the data in the client buffer is consumed as illustrated in
Figure 8.3. If ( T i − 1 +

> K + B p × G −

0, that means frame i has arrived before the client buffer
becomes empty, then B i is estimated as:

B i − 1 ) − T i ≥

B i = ( B i − 1 + T i − 1 ) − T i + 1 / G (8.4)

Otherwise, if ( T i − 1 + 0, that means the client buffer has been empty for a period

of time before frame i arrived, then B i is simply equal to the time value of a frame, i.e.:

B i − 1 ) − T i ≥

B i = 1 / G (8.5)

where K is set to i .
The previous derivations enable us to estimate B i at the instant frame i arrives at the client.
However, a subtle complication arises due to buffering inside the server. Specifically, in order
to determine the bit-rate for frame i

+

1, we need to estimate the client buffer occupancy when
frame i arrives at the client. However, due to buffering inside the server, some previous frames
including frame i may not have been transmitted yet so we will need to estimate the arrival
times of these frames inside the server buffer.
Let n i be the index of the last frame of segment i , we have to predict B n i at time t n i while
frame f n i to frame n i are still in the server buffer and then use the predicted B n i to perform
adaptation of segment i 1. Assuming the remaining data in the server buffer at time t n i will

arrive at the client at a constant rate of D i + 1 , which is also the estimated TCP throughput for
sending the segment i

+

+ 1, the arrival times of the remaining frames are estimated as follows:

k

∈ f n i , n i

1
D i + 1

T k = t n i + F j ( t n i ) ∀ k (8.6)

j = f n i