Slotted ALOHA Concepts and Stability

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Questions and Answers

What is the probability of a packet being collision-free in Slotted ALOHA?

$e^{-λ}$ (correct)

$λ^2e^{-λ}$

$λe^{-λ}$

$1 - e^{λ}$

What is the maximum throughput for Slotted ALOHA defined at optimum load?

0.3679 (correct)

0.25

0.5

0.3

What effect does synchronizing users have on throughput in Slotted ALOHA?

Increases throughput by a factor of 2 (correct)

Decreases throughput by half

No effect on throughput

Increases throughput by a factor of 1.5

At what average load does the asymptotic aggregate throughput of Slotted ALOHA peak?

1 Signup and view all the answers

What does the efficiency function ρ(L) of Slotted ALOHA depend on?

The average number of packets in a time slot Signup and view all the answers

What is the average throughput of Slotted ALOHA described as approximated by?

A Poisson random variable with variable rate Signup and view all the answers

At what point is the throughput considered stable according to the described analysis?

k = 2 Signup and view all the answers

What happens to the drift when the number of backlogged nodes is less than 2?

The drift is positive. Signup and view all the answers

What is the effect of a load greater than k = 12 on the network performance?

It pushes the network towards an undesired equilibrium point. Signup and view all the answers

What is indicated by the distance between stable throughput and unstable equilibrium points?

Possibly large delays in re-establishing equilibrium. Signup and view all the answers

What is the approximate aggregate throughput when the load reaches k = 21?

0.05 packets per slot Signup and view all the answers

When the load is between 2 and 12, what does the drift indicate?

It is negative, suggesting a likelihood of serving backlogged nodes. Signup and view all the answers

What occurs when the load reaches the unstable equilibrium point?

The average queue length increases significantly. Signup and view all the answers

What does the drift Dk represent in the context of Slotted ALOHA?

The difference between the blue line and the black curve Signup and view all the answers

What is the impact of increasing pb to 0.3 on drift delay?

It reduces drift delay, but decreases stability Signup and view all the answers

At what value of pe does the network fail to achieve stable throughput?

0.0175 Signup and view all the answers

What factor primarily influences the stability of throughput in Slotted ALOHA?

The probability of new arrivals pe Signup and view all the answers

What happens to aggregate throughput as the load k increases beyond a certain point?

It may decrease if the network cannot handle the load Signup and view all the answers

What effect does a reduction in drift delay have on network performance?

It may cause decreased stability despite better throughput Signup and view all the answers

How does an increase in load k affect drift in Slotted ALOHA?

It generally increases drift due to congestion Signup and view all the answers

When can the drift Dk be calculated in Slotted ALOHA?

Under specific parameters N, pe, and pb Signup and view all the answers

Study Notes

Slotted ALOHA

The probability that a packet is collision-free is calculated with the Poisson distribution, resulting in e^-λ, where λ represents the average number of packets per slot.
The asymptotic aggregate throughput of Slotted ALOHA is ρ(L) = Le^-L where L is the average load.
The optimal load for Slotted ALOHA is L = 1/e, resulting in a maximum throughput of approximately 0.3679.
Synchronizing users in Slotted ALOHA can potentially double the throughput.
Slotted ALOHA has a higher aggregate throughput compared to asynchronous ALOHA.

Stability Conditions

In slotted ALOHA, stability is influenced by the load and likelihood of packets being served.
When the queue has a small number of backlogged nodes (k < 2), the drift is positive, causing an increase in backlogging.
When the load falls between 2 and 12, the drift is negative, which increases the likelihood that backlogged nodes will be served.
A stable throughput point exists around k = 2.
A load exceeding k = 12 leads to an unstable equilibrium point with a high average queue length (k = 21) and very low throughput (around 0.05 packets per slot).
Large delays are possible during re-establishment of equilibrium after an off-balance event.
The stability of Slotted ALOHA can be adjusted.
Increasing the probability of a node transmitting a backlogged packet (pb) reduces drift delay but also decreases stability.
A slightly higher probability of new arrivals (pe) can cause a network to be unable to achieve stable throughput.

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Description

Dive into the principles of Slotted ALOHA, including packet collision probabilities, throughput equations, and stability conditions. Learn about optimal load scenarios and how synchronization can enhance performance. Test your understanding of these key networking concepts.