Streaming Variable Bit-Rate Media Streams - Scalable Continuous Media Streaming Systems - page 132

To reduce the inefficiency due to bandwidth over-allocation, we observe that a video server
often serves many video stream simultaneously. The data for these video streams typically go
through the same backbone network before reaching the access networks. For a network link
carrying more than one video stream, if we can ensure that the aggregate traffic conforms to
the monotonicity property, the delivery of the individual streams is also guaranteed, even with
mixed network traffics. In this case, we are applying the MDR principle to the aggregate traffic
flow instead of individual video streams.
When a video stream with a transmission schedule generated by the MDR scheduler is
admitted to the system, say at round A , we simply add the transmission schedule to the
aggregate bandwidth utilization to obtain the new system utilization:

u i = u i + v i − A , i = A , A + 1 ,..., A + w − 1 (7.25)

The bandwidth reservation schedule will then be set equal to the systemutilization, i.e., s i = u i .

On the other hand, when a video streamwith transmission schedule generated by the Optimal
Smoothing algorithm is admitted to the systemat round A , wewill need to performan additional
step to maintain monotonicity for the aggregated bandwidth reservations. We first compute the
system utilization using equation (7.25). Then we apply a procedure similar to equation (7.24)
to compute a MDR bandwidth reservation schedule by over-allocations:

u i ,

if u i >

u i + 1

s i =

, = + w − , + w − ,...,

i A 2 A 3 A (7.26)

u i + 1 , otherwise

as shown in Figure 7.6. Again, the bandwidth over-allocations only affect the amount of network
resources reserved. The individual video stream's transmission schedule is not affected.

7.5.2 Admission Complexity
The admission complexity of the AMDR scheduler depends on whether the requested video is
delivered using aMDR transmission schedule or an Optimal Smoothing transmission schedule.
For the MDR case, the admission complexity is the same as in the original MDR scheduler,
i.e., one computation for the admission test, and O( w ) computations for updating the system

utilization series.
For the Optimal Smoothing case, the admission complexity is higher than the MDR case
but, interestingly, lower than the original Optimal Smoothing case. This is because in the
AMDR scheduler, the bit-rates in the bandwidth reservation schedule

are non-increasing.
This enables the system to perform the admission test by checking only the initial rate and the
rate-increasing rounds.
Again, assume the client arrives at time slot A , with a transmission schedule

{ s i }

{ v i } . We define

a round i in the transmission schedule as rate increasing if v i >v i − 1 . Let there be g such

rate increasing rounds, with the round number denoted by h i , i = 1 , 2 ,..., g . To simplify

notations, we also define h 0 = 0 to represent the initial round. With these notations we can

then define the admission test as:

s h i + A + v h i ≤ U , for i = 0 , 1 ,..., g (7.27)