A Concurrent-Push Parallel Server Architecture - Scalable Continuous Media Streaming Systems - page 182

jitter, the admission scheduler adds an extra delay to the assignment, stated in the following
theorem:

Theorem 10.2. If the admission scheduler delays the start of a new video session by

τ

G
T F

= + 1 (10.25)

groups, then it guarantees that the assigned group has not started in any of the N S servers.
Proof. Please refer to the Appendix.

Note that if the assigned group is full, the admission scheduler will sequentially check the
subsequent groups until an available group is found.

10.4.3 Client Buffer Requirement
As the admission scheduler already guarantees that a new video session will be assigned to
the same group in all servers, the scenario in Figure 10.5 could not occur and the transmission
jitter will be the same as the clock jitter. Hence, the client buffer requirement derived in Section
10.3 becomes

1 N S

f + − f − −

+ τ +

T E

Y = (10.26)

T F

1 N S

f + − f − +

+ τ +

T L

Z = (10.27)

T F

10.4.4 System Response Time
The scheduling delay under the AGSS algorithm depends on the occupancy of the AGSS
groups. Specifically, if a group as calculated from Theorem 10.2 is fully occupied, the new
video session must be delayed until the next available group. In the worst case, the transmission
of the first video block is delayed for ( N S + ) groups:

N S + τ

1 Q
R V

G
T F

D S = + (10.28)

To better evaluate the scheduling delay, we derive the average scheduling delay under a given
system load. Assume that video sessions start independently and with equal likelihood at any
time. Then a video session can be assigned to any one of the G groups with equal probability.
Let there be n active video sessions and G groups, then the number of ways to distribute these
n video sessions among G groups is a variant of the urn-occupancy distribution problem [9]
and is given by

1) j G
j

G

G

+ n − j ( + 1) − 1

N ( n , G , ) = ( − (10.29)

G − 1

j = 0

To obtain the probability of having m fully-occupied groups, we first notice that there are m
possible combinations of picking m fully-occupied groups among G groups. Given that there