Multiple stream transmission reduces the delay by offering the opportunity
of accepting and playing out the packets with lower delay. Here we study how
much delay reduction can be obtained compared to using only one stream. To
this end, we define a quantity, average delay reduction, denoted by 
, for stream l. Average delay reduction is calculated as
the trace average of the difference between 
and 
, by only counting packets with 
. It
characterizes how much lower delay can be obtained on average by using
multiple streams instead of stream l only.
In this experiment we vary the propagation delay of links in the simulation
and study its effect on average delay reduction. In Fig. 7,
we have plotted versus the difference in propagation
delay of the two paths, which is defined as the trace average of the
difference between the propagation delay of path 2 and that of path 1. Two
sets of curves are shown in Fig. 7 for a low delay STD of
around 26 ms and a high delay STD of about 40 ms respectively. For either
set, it is observed that the two streams obtain equivalent gain in terms of
delay reduction as they have the same propagation delay. As the difference
in propagation delay increases, stream 2 gets more gain while stream 1 gets
less. This indicates that if the alternative path has much higher
propagation delay in average than the direct path, the benefit from using
multi-path becomes less since the role of the alternative path becomes less
important. However, the direct path does not necessary have lower delay than
the alternative path, according to [13]. Hence, the efficiency of
multi-path depends on the availability a secondary path which has a mean
delay not much higher than the default path. In practice, this is not
difficult to obtain, as what we have got in the experiments in Section 3
(refer to Table 2). In both experiments in Section 3, we have
got very close delay medians from different paths since those paths follow
close geographical routes (with the propagation delay contributing to the
constant part of the total delay), while they traverse through different
service providers (which introduce the varying part of delay).
From Fig. 7, it is also obvious that the gain from multi-path is higher when the delay variation is higher. This can be seen more clearly from Fig. 13. For both steams, the delay reduction increases as the STD of network delay goes up. This is because the higher the variation of network delay each individual path, the more benefit of having and using an alternative path, whose variation is statistically independent of that of the default path.
Figure 12: Average delay reduction vs. difference in propagation delay
Figure 13: Average delay reduction vs. delay STD
