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clients arriving within the time window of 2
seconds will be admitted this way, it is easy to
see that the average waiting time for statically-admitted clients, denoted by
W
S
(
δ
δ
), is equal
to half of the admission threshold:
W
S
(
δ
)
=
δ
(19.5)
assuming it is equally probable for a request to arrive at any time within the time window.
19.3.2 Waiting Time for Dynamically-Admitted Clients
The second way to admit a new client is through a dynamic multicast channel as shown in
Figure 19.6. Unlike staticmulticast channels, dynamicmulticast channels are allocated in an on-
demand basis according to the admission procedure described in Section 19.1.2. Specifically,
if there are one or more free channels available at the time a request arrives, a free channel will
be allocated to start transmitting video data to the client immediately and the resultant waiting
time will be zero.
On the other hand, if there is no channel available at the time a request arrives, then the
resultant waiting time will depend on when a request arrives and when a free dynamic multicast
channel becomes available. Specifically, requests arriving at the admission controller will be
consolidated using the procedure described in Section 19.1.2 where the admission controller
will send a consolidated
START
request to a service node to initiate video transmission.
Figure 19.8 illustrates this admission process. This example assumes that there is no request
waiting and all dynamic multicast channels are occupied before client request 1 arrives. After
receiving request 1, the admission controller sends a
START
request to a service node to initiate
a new multicast transmission for this request. However, as all channels are occupied, the
transmission will not start until a later time
t
1
when a free channel becomes available. During
Free channel
becomes available
An admission cycle
t
0
t
1
t
2
t
3
1
2
3
x
y
Client Requests:
. . .
. . .
START
Requests:
time in waiting for a free
dynamic multicast channel
time in waiting for a free
dynamic multicast channel
1/
λ
Figure 19.8
Classification of dynamically-admitted users
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