Streaming Variable Bit-Rate Media Streams - Scalable Continuous Media Streaming Systems - page 131

7.5.1 Bandwidth Reservation
The large buffer requirement in those rare videos is a result of the MDR scheduler's mono-
tonicity property. However, as we proved in Section 7.3.4, theMDR scheduler already achieves
minimum buffer requirement among all monotonic decreasing rate schedules, implying that
the only way to reduce the buffer requirement is to relax the monotonicity requirement.
Under the AMDR scheduler, the client buffer requirement, say B , is specified by the service
provider as a design parameter. For videos with buffer requirements smaller than or equal to B ,
they are delivered using the original MDR schedules. By contrast, for videos that have buffer
requirements larger than B , they are delivered using buffer-constrained schedules generated
using temporal smoothing algorithms such as Optimal Smoothing.
Now obviously temporal smoothing in general does not guarantee monotonicity and this
implies that we can no longer guarantee video delivery for these videos in a mixed-traffic
network. To tackle this problem, we can over-allocate bandwidth for these video streams
such that the reserved bandwidth allocations are kept monotonic decreasing. For example,
consider the transmission schedule

{

r i , T i |

= , ,..., }

generated by a temporal smoothing
algorithm with buffer constraint B . For the rare videos, there exists i , j such that r i <

i 1 2 n

r j for

i j . We can maintain the monotonicity property by applying the following procedure to the

transmission schedule:

<

r i ,

if r i > r i + 1

s i = , i = n − 2 , n − 3 ,..., 1 (7.24)

r i + 1 , otherwise

{

s i ,

| = , ,..., }

to obtain the bandwidth reservation schedule as shown in Figure

7.5. Note that the transmission schedule is not changed, only the bandwidth reservations are
modified to maintain the monotonicity property, albeit at the expense of some unused network
bandwidth.

T i i 1 2 n

Time

An “exceptional” stream, smoothed using
buffer-constrained temporal smoothing.

r , if r > r

i i i + 1

s = , i = n − 2, n − 3, ,1

…

i

r , otherwise

i + 1

The “relaxed” bandwidth reservation schedule
that maintains the monotonicity property.

Bandwidth over-allocated here
to maintain rate monotonicity.

Time

Figure 7.5 Preserving the monotonicity property by over-allocating bandwidth