Pure ALOHA Protocol

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1. Origin and Philosophy of ALOHA

The ALOHA protocol was devised in 1970 by Norman Abramson and his colleagues at the University of Hawaii to interconnect computers located on different Hawaiian islands using ground-based UHF radio broadcasting.

ALOHA represents the earliest and simplest Random Access Protocol (Contention-Based):

• Core Rule: A station transmits a frame immediately whenever it has data ready to send.
• There is no central controller and no carrier sensing ("talk before listening").

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2. Collision Mechanism & Vulnerable Time

Because stations transmit completely asynchronously without checking whether the channel is busy, frames frequently overlap in time. Any partial overlap, even by a single bit, corrupts both frames completely and is termed a Collision.

Vulnerable Time ($V_t$) Calculation:

Let all frames have a constant transmission duration of $T_{fr}$.
Suppose Station A begins transmitting a frame at time $t_0$.

• If any other station transmits between $t_0 - T_{fr}$ and $t_0$, the tail of its frame will collide with the start of Station A's frame.
• If any other station transmits between $t_0$ and $t_0 + T_{fr}$, its beginning will collide with the tail of Station A's frame.
• Vulnerable Time for Pure ALOHA:

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3. Mathematical Derivation of Throughput

Assuming frame generation follows a Poisson distribution with an average arrival rate of $G$ frames per frame-time $T_{fr}$ (where $G$ is the channel traffic load):

The probability that $k$ frames are generated during a time interval $T$ is:

For a frame to be successfully transmitted without collision, zero other frames ($k = 0$) must be generated during the entire vulnerable time interval $V_t = 2 T_{fr}$:

Throughput Equation ($S$):

The channel throughput $S$ (average number of successful transmissions per frame-time) is:

Finding Maximum Throughput:

To find the load $G$ that maximizes throughput, differentiate $S$ with respect to $G$ and set to zero:

Substitute $G = 0.5$ into the throughput equation:

Key Takeaway: The maximum channel capacity of Pure ALOHA is only $18.4\%$. Over $81.6\%$ of channel capacity is wasted due to collisions under heavy traffic!

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4. Retransmission and Backoff in Pure ALOHA

• When a collision occurs, stations must not retransmit immediately; doing so would guarantee another immediate collision.
• Each station waits a random Backoff Time $T_B = R \times T_{fr}$ (where $R$ is a random integer chosen from a range) before attempting to retransmit.

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