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+1 vote

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.

- $p(1-p)^{2(n-1)}$
- $(1-p^{2(n-1)}$
- $p(1-p)^{(n-1)}$
- $(1-p)^{(n-1)}$

+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.

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