Question

Consider the delay of pure ALOHA versus slotted ALOHA at low load. Which one is less? explain your answer.

Short answer

At low load, slotted ALOHA has less delay than pure ALOHA due to reduced collision probability and synchronization of transmissions.

Step-by-step solution

Understanding ALOHA Protocols

Pure ALOHA and slotted ALOHA are two methods of accessing shared communication channels. Pure ALOHA allows a station to transmit whenever it has data, while slotted ALOHA divides time into discrete slots, and stations can only begin transmission at the start of a slot.

Characteristics at Low Load

At a low load, few devices are trying to access the channel simultaneously. In pure ALOHA, the chance of collision is higher since transmissions can begin at any time, leading to potential overlaps. In slotted ALOHA, the structure of slots reduces the possibility of overlaps, as transmissions are synchronized to begin at the start of a slot.

Collision Probability

The probability of collision in pure ALOHA is higher due to the lack of time synchronization, leading to more retransmissions. Slotted ALOHA reduces the collision probability by restricting transmission to the beginning of slots, thus lowering the likelihood of overlap at low load.

Effective Transmission Time

Effective transmission time is crucial to understanding the average delay. Because slotted ALOHA lowers collisions, it ensures that more packets are successfully transmitted without delay, leading to a lower average delay compared to pure ALOHA.

Key concepts

Pure ALOHA

Pure ALOHA is a simple communication method used in networks where devices share a common channel. It allows any transmitting device to send data whenever it senses the need.
This flexibility, however, comes with the challenge of higher collision probabilities. Since devices can transmit at any time without synchronization, their transmissions are more likely to overlap. This overlap leads to data packets colliding and having to be retransmitted.
The nature of Pure ALOHA means that at any given time, if two or more devices decide to send data, they might choose overlapping time slots leading to a collision. Every packet takes the risk of being lost if another device transmits at the same time.
In simple words, without planned coordination, the line can get congested quickly. Thus, Pure ALOHA, while straightforward, is prone to higher transmission delays due to more frequent retransmissions.

Slotted ALOHA

Slotted ALOHA improves upon the concept of Pure ALOHA by introducing time slots. These time slots are specific time intervals during which devices can start transmitting data. Devices need to wait for the beginning of a slot before they can send their packet.
This method ensures better coordination between devices. By aligning transmissions to these predefined slots, Slotted ALOHA reduces the chance of collisions. The structure facilitates organized data transfer, leading to fewer retransmits.
Compared to Pure ALOHA, this method is more efficient in utilizing the shared channel, especially when the network load is low. Less overlap in time means fewer collisions and, hence, fewer delays in transmission. This makes Slotted ALOHA more efficient in terms of data transmission and generally more reliable in environments with sporadic, low-channel use.

Collision Probability

The probability of collision in both ALOHA systems depends on how they manage the timing of packet transmissions. In Pure ALOHA, the probability of a collision is significantly higher. Since packets can be sent at any moment, the chances of overlapping transmissions are greater.
Mathematically, the probability of no collision in Pure ALOHA is given by the formula: \[ P_{ ext{no collision}} = e^{-2G} \] where \( G \) is the average number of packets generated by the system.
In contrast, the probability of causing a collision in Slotted ALOHA decreases because all transmissions are constrained to happen exactly at the beginning of a timeslot. This reduces the chance of overlap, and its no-collision probability is: \[ P_{ ext{no collision}} = e^{-G} \]
As shown by these formulas, as \( G \) increases, the collision probability remains less in Slotted ALOHA, making it particularly useful for environments where minimizing delays and retransmissions is critical.

Effective Transmission Time

Effective Transmission Time is a measure of how quickly and efficiently data is successfully sent from one point to another within a network.
In Pure ALOHA, the lack of structure often results in many collisions. This increases the time needed to retransmit data, thus, extending the effective transmission time, especially noticeable when multiple devices attempt to utilize the network at random yet simultaneous intervals.
Conversely, Slotted ALOHA, with its organized slots, minimizes these collisions, which directly affects its effective transmission time positively. Less time is spent retransmitting, and more data is sent successfully in the first attempt, lowering the average delay.
This efficiency at low loads makes Slotted ALOHA advantageous for environments focusing on reducing wait times and improving the reliability of transmissions.