Derive the efficiency of Pure ALOHA protocol

The word ALOHA originally means "hello" in Hawaiian. ALOHA is a random access protocol that operates at the MAC (Medium Access Control) layer of the OSI model. It allows multiple stations to transmit data over a shared communication channel without requiring coordination or scheduling.

When multiple devices need to communicate over a single transmission medium, data collisions can occur if two or more stations transmit simultaneously. ALOHA protocols provide a mechanism to handle such situations and improve transmission efficiency despite the inherent collision problems.

How ALOHA Works

In ALOHA protocol, stations transmit data frames whenever they have data to send, without checking if the channel is busy. If a collision occurs (when two or more frames overlap), the involved stations detect the failure through lack of acknowledgment and retransmit after a random delay period.

Types of ALOHA

Pure ALOHA

In Pure ALOHA, stations can transmit at any time without synchronization. After transmission, the station waits for an acknowledgment. If no acknowledgment is received within a timeout period, the station assumes a collision occurred and retransmits after a random backoff time.

Slotted ALOHA

In Slotted ALOHA, time is divided into discrete slots, and stations can only begin transmission at the start of a time slot. This synchronization reduces the vulnerable time and improves efficiency.

Key Parameters of Pure ALOHA

Vulnerable Time: The time period during which a collision can occur. For Pure ALOHA, if a frame transmission starts at time t, any other frame starting between (t - T) and (t + T) will cause a collision, where T is the frame transmission time.

Vulnerable Time = 2T (twice the frame transmission time)

Backoff Time: The random waiting time before retransmission after a collision.

Backoff Time = k × RTT (where k is a randomly chosen integer)

Efficiency Derivation of Pure ALOHA

Let G be the average number of transmission attempts per frame time. The probability that a frame is successfully transmitted (no collision) follows a Poisson distribution:

P(success) = e^(-2G)

The throughput S (successful transmissions per frame time) is:

S = G × e^(-2G)

To find maximum efficiency, we differentiate S with respect to G and set it to zero:

dS/dG = e^(-2G) + G × (-2) × e^(-2G) = 0
dS/dG = e^(-2G) × (1 - 2G) = 0

Since e^(-2G) ? 0, we have: 1 - 2G = 0, therefore G = 1/2

Substituting G = 1/2 into the throughput equation:

S_max = (1/2) × e^(-2×1/2)
S_max = (1/2) × e^(-1)
S_max = (1/2) × 0.368
S_max = 0.184 or 18.4%

Comparison of ALOHA Types

Conclusion

Pure ALOHA achieves a maximum efficiency of 18.4% when the offered load G = 0.5. While this efficiency is relatively low due to collisions, Pure ALOHA remains important for its simplicity and serves as the foundation for understanding more advanced random access protocols.