Closed-Loop Algorithms - Scalable Continuous Media Streaming Systems - page 302

back media segment D 1 using data received from S d . In Phase 2, client r d continues to receive
media segment D 3 from S c but releases S d and replaces it with S b to receive media segment
D 4 . In Phase 3, client r d continues to receive media segment D 5 from S b but releases S c and
replaces it with S a to receive media segment D 6 . Finally, in Phase 4 the client releases the
remaining P-stream S b and continues playback till the end of the media stream by receiving
data from S a .
Therefore, the additional cost (i.e., excluding the cost of the existing streams) to serve r d is
equal to [(5 t d − 2 t c − 2 t b − t a ) − (3 t c − 2 t b − t a )] R = 5( t d − t c ) R . Compared to the cost of

(3 t d − t b ) R bytes. For

example, if t d equals 260 seconds, the cost of serving r d is 50 R , resulting in 99.31% resource
saving over serving with a new regular stream.
Note that for the example in Figure 17.7, the client caches up to two streams at any time
so the client bandwidth requirement is the same as simple patching and transition patching. In
the recursive patching process, the client caches media data through a total of three P-streams
and one R-stream. In general, a client can cache media data through even more P-streams as
long as there are eligible P-streams that will result in further resource savings.
More generally, if a client caches data from k streams (i.e., one R-stream plus k

2 t c − t b ) R bytes in transition patching, there is a gain of (3 t c − 2 t d −

1P-
streams) to complete the recursive patching process, then we call it k-phase recursive patching
( k P-RP). It is worth noting that simple patching and transition patching are equivalent to 2P-RP
and 3P-RP respectively under this definition. We illustrate the performance differences in the
next section.

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17.3.3 Performance Gains
To illustrate the performance gains of various patching techniques, we developed a simulator to
generate numerical results for comparisons. We assume Poisson client arrivals and all clients
play back the media stream from the beginning to the end without performing interactive
playback operations. For simplicity, we ignore network delays and processing delays in the
simulator. Table 17.1 lists the system parameters used in generating the numerical results.
With the system resources (i.e., number of multicast channels) fixed we use start-up latency -
defined as the time from client arrival to the time playback can begin, as the performance
metric for comparison.
Figure 17.8 plots the start-up latency versus arrival rate ranging from 0.1 to 1 client/second.
There are three curves plotting the start-up delay for 3-phase, 4-phase, and 5-phase recursive
patching respectively.
Compared to transition patching (i.e., with k 3), 4-phase recursive patching can achieve

significantly lower start-up latency under the same system load. For example, the latency is

=

Table 17.1 Parameters used in simulations

Parameter Range of values

Request arrival rate (arrivals/sec) 0.1 - 1.0

Media stream length (seconds) 7,200

Number of server channels 20