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A.2 Proof of Theorem 10.2
Let the new session request arrive at the admission scheduler at time
t
during group
v
new
=
tG
/
T
F
. Then due to clock jitter, the current group at other servers can range from
. To guarantee that the assigned group has not started in
any of the servers implies assigning a group larger than the largest current group in any of
the servers, i.e.
s
new
=
(
t
−
τ
)
G
/
T
F
to
(
t
+
τ
)
G
/
T
F
(
t
+
τ
)
G
/
T
F
+
1. Applying the inequality
x
+
y
≤
x
+
y
we
have
s
new
≤
tG
/
T
F
+
τ
G
/
T
F
+
1
(10.51)
Substituting into
v
new
we have
s
new
≤
v
new
+
τ
G
/
T
F
+
1 and the results follows.
References
[1] T.C. Chiueh, C. Venkatramani, and M. Vernick,
Design and Implementation of the Stony Brook Video Server
,
Technical Report TR-16, Computer Science Department, State University of New York at Stony Brook, August
1995.
[2] F.A. Tobagi and J. Pang, StarWorks: A Video Applications Server,
IEEE COMPCON Spring'93
, 1993, pp. 4-11.
[3] R. Buck, The OracleMedia Server for nCubeMassively Parallel Systems,
Proceedings of 8th International Parallel
Processing Symposium
, 1994, pp. 670-673.
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IEEE
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IEEE Computer
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IEEE Transactions on Comm
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10, Oct. 1991, pp. 1482-1493.
[7] Z. Yang and T.A. Marsland, (eds)
Global States and Time in Distributed Systems
, IEEE Computer Society Press,
Los Alamitos, CA, USA, 1994.
[8] P.S. Yu, M.S. Chen, and D.D. Kandlur, Grouped Sweeping Scheduling for DASD-based Multimedia Storage
Management,
ACM Multimedia Systems
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[9] J.N. Lloyd and K.S. Samuel,
Urn Models and their Application
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