Consider a network using the pure ALOHA medium access control protocol, where each frame is of length 1,000 bits. The channel transmission rate is 1 Mbps ($= 10^6$ bits per second). The aggregate number of transmissions across all the nodes (including new frame transmissions and retransmitted frames due to collisions) is modelled as a Poisson process with a rate of 1,000 frames per second. Throughput is defined as the average number of frames successfully transmitted per second. The throughput of the network (rounded to the nearest integer) is \underline{$\hspace{1.5cm}$}.

Given:

• Frame length, $L = 1000\text{ bits}$

• Channel transmission rate, $R = 1\text{ Mbps} = 10^6\text{ bps}$

• Frame transmission time, $T_{\text{fr}} = \frac{L}{R} = \frac{1000}{10^6} = 10^{-3}\text{ s} = 1\text{ ms}$

• Aggregate arrival rate, $\lambda = 1000\text{ frames/second}$

The offered load $G$ per frame transmission time is:

For Pure ALOHA, the probability of a successful transmission is given by:

The throughput in frames per second ($S^{\prime}$) is:

Rounding to the nearest integer gives 135 (acceptable range: 130 to 140).