FEC versus PRT - Scalable Continuous Media Streaming Systems - page 245

with more redundancies as expected. For PRT, a total of 10 curves are plotted, each with a
different setting of K min , ranging from 1 to 10, representing the number of redundancies that
are actively transmitted. There are two observations. First, the systemMTTF of PRT for small
values of K max is similar to that of FEC with K

=

K max . However, beyond a certain number
of redundancies, the system MTTF levels off. This implies that for PRT with a given K min ,
there is an upper limit on the achievable system MTTF even if we increase K max indefinitely.
Beyond that limit any additional redundancies are simply wasted.
Second, the plateau of the curves for PRT is determined by the number of redundancies
actively transmitted - K min , with larger K min resulting in higher achievable system MTTF.
This implies that to achieve a target system MTTF, there is a lower limit on K min below which
the required MTTF can never be achieved, regardless of the total number of redundancies
in the system. The key is that the minimum K min required will still be substantially smaller
than the corresponding number of redundancies K required to achieve the same systemMTTF
in FEC.
For example, FEC with K 7 achieves a system MTTF of 10 15 hours. Now consider the

PRT curve in Figure 13.6 with K min =

=

7 the system MTTF, is only 10 14 hours
which is lower than FEC. To increase the system MTTF, we can either increase K max or
increase K min . In this case, increasing K max does not work because the system MTTF levels
off to a plateau below the required system MTTF. However, increasing K min to 3 does not
work either because the resultant system MTTF is still below 10 15 hours. This is expected as
failure detection in PRT incurs a delay in responding to a server failure. Thus, with the same
number of total redundancies K

2 and K max =

= K max , it must have a lower system MTTF compared to

60%

40%

20%

0 10 20 30 40 50 60 70 80 90 100

Average detection time (s)

MT TF = MTTF = 10 11 10 11 MT TF = MTTF = 10 22 10 22 MT TF = MTTF = 10 32 10 32

MT TF = MTTF = 10 47 10 47 MT TF = MTTF = 10 61 10 61

Figure 13.6 Bandwidth ratio ( K min / K ) versus average detection time for 64 servers