Streaming Variable Bit-Rate Media Streams - Scalable Continuous Media Streaming Systems - page 123

7.3.1 Computing the MDR Schedules
Compared to existing smoothing algorithms, the MDR property introduces an additional con-
straint - only downward rate adjustments can be used. Note that although this reduces the
set of possible schedules within the feasible region, it still does not uniquely determine the
transmission schedule for a given video. In fact, there are still an infinite number of possible
MDR schedules within the feasible region.
To select a MDR schedule, we need to consider the resultant resource requirements. The
choice of the MDR schedule can affect the peak transmission rate and the client buffer re-
quirement, both of which should be minimized. Interestingly, it turns out that we can always
compute a MDR schedule that has minimum peak rate and minimum client buffer requirement,
among all possible MDR schedules.
We define a MDR transmission schedule with the set of rate-time tuples: { r i , T i | i =

1 , where r i and T i are the transmission rate and commencing time for the i th

segment in the transmission schedule as depicted in Figure 7.2; and n is the total number of
segments in the MDR transmission schedule. For a MDR transmission schedule, the rates will
be monotonic decreasing, i.e., r i >

, 2 ,..., n }

1.
To compute the schedule, we begin from the origin as depicted in Figure 7.2, and assign the
first segment with the highest transmission rate, i.e.,

r j , for all i , j where n ≥ j > i ≥

∀

max A ( t ) 0

− A (0)

r 1 = t > (7.5)

t

and mark the time, denoted by T 1 , at which the rate is maximized. The tuple then

represents the first segment of the MDR transmission schedule. Next, we repeat this process
with T 1 as the starting point to obtain

{ r 1 , T 1 }

r 2 , T 2 } , and so on. In general, the transmission rate for

{

the next segment can be computed from

∀

max A ( t ) T i

− A ( T i )

r i + 1 = t > (7.6)

t − T i

r i : transmission rate for segment i

r 3

r 2

MDR schedule S ( t )

Second bit-rate reduction point: T 2

First bit-rate reduction point: T 1

r 1

A ( t )

Time

Figure 7.2 A monotonic decreasing rate schedule generated by the MDR scheduler