+1 vote
164 views

A multiple access network with a large number of stations can be analyzed using the Poisson distribution. When there is a limited number of stations in a network, we need to use another approach for this analysis. In a network with N stations, we assume that each station has a frame to send during the frame transmission time ($T_{fr}$) with probability p. In such a network, a station is successful in sending its frame if the station has a frame to send during the vulnerable time and no other station has a frame to send during this period of time.

The probability that a station in a pure Aloha network can successfully send a frame during the vulnerable time.

1. $p(1-p)^{2(n-1)}$
2. $(1-p^{2(n-1)}$
3. $p(1-p)^{(n-1)}$
4. $(1-p)^{(n-1)}$
edited | 164 views
+1
it is A as per tenenbaum...read pure aloha from it
+5
@sandygate-Please provide a clear step-by-step explaination

+1 vote

At any given time, the probability that a node is transmitting a frame is p.

suppose this frame begins transmission at time t0. In order for this frame to be successfully transmitted, no other nodes can begin their transmission in the interval of time [t0 – 1, t0]. Such a transmission would overlap with the beginning of the transmission of node i’s frame.

The probability that all other nodes do not begin a transmission in this interval is $(1 – p)^{N-1}$. Similarly, no other node can begin a transmission while node i is transmitting, as such a transmission would overlap with the latter part of node i’s transmission.
The probability that all other nodes do not begin a transmission in this interval is also $(1 – p)^{N-1}$. So,

the probability that a given node has a successful transmission is $p (1 – p)^{2(N-1)}$. Hence, (A) is the correct option.

0

As there won't be any carrier sensing for Aloha we have to consider below statement

"The probability that all other nodes do not begin a transmission in this interval is also $(1-p)^{N-1}$"

1
+1 vote
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