Delay Comparison: Pure ALOHA vs Slotted ALOHA at Low Load

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Nov 4, 2026

In ALOHA-style random access, a packet is successfully received only if no collision occurs during the relevant vulnerable period. For pure ALOHA, a new transmission can start at any instant, so the vulnerable period is longer. For slotted ALOHA, transmissions are aligned to time slots, reducing overlap and thus collisions.

Key performance quantities include offered load, throughput, and collision probability. At low offered load $G$ , collisions are rare, so the dominant effect is the probability mass of possible overlaps in the vulnerable window.

A standard result for ALOHA throughput under Poisson arrivals and idealized conditions is:

Pure ALOHA: $S_{\text{pure}}(G)=G e^{-2G}$
Slotted ALOHA: $S_{\text{slot}}(G)=G e^{-G}$

These imply that for the same $G$ , slotted ALOHA has a higher success probability because collisions require overlap within a shorter vulnerable period. Intuitively: slotted ALOHA “cuts the vulnerable window in half,” so collision probability drops.

At low load, delay is largely governed by how quickly a packet finds an attempt that does not collide. If fewer collisions occur, the expected number of retransmissions decreases, hence expected access delay decreases.

Mermaid intuition (vulnerable window overlaps):

type="tip" title="Pro Tip" At low $G$ , compare the success probabilities (or equivalently the exponent terms). Since $e^{-2G}$ decays faster than $e^{-G}$ , slotted ALOHA retains a higher fraction of successful attempts, which translates to lower average retransmission delay.

Reasoning Path: why slotted ALOHA has less delay at low load

1
Step 1
Pure ALOHA has overlap risk across a longer time window (a transmission can start at any instant), while slotted ALOHA restricts starts to slot boundaries, shrinking the vulnerable period.
2
Step 2
Under the common Poisson model, the probability of no other transmissions in the vulnerable window yields the exponential terms in the success/throughput formulas: pure uses $e^{-2G}$ , slotted uses $e^{-G}.
3
Step 3
For small $G$ , both $e^{-2G}$ and $e^{-G}$ are near 1, but $e^{-2G}$ is smaller. Hence the success probability per attempt is higher in slotted ALOHA.
4
Step 4
If each attempt succeeds with probability $p$ , then the expected number of attempts is about $1/p$ (geometric retries). Higher $p$ at low $G$ means fewer retries and thus lower expected delay.
5
Step 5
Because slotted ALOHA has higher success probability ( $e^{-G}$ vs $e^{-2G}$ ), slotted ALOHA has less delay than pure ALOHA at low load.

Quantitative comparison at low load (success probability perspective)

For ALOHA under the standard model:

$S_{\text{pure}}(G)=G e^{-2G}$
$S_{\text{slot}}(G)=G e^{-G}$

Since both share the multiplicative factor $G$ , compare the exponentials:

Pure success fraction $\propto e^{-2G}$
Slotted success fraction $\propto e^{-G}$

For small $G$ :

$e^{-2G} \approx 1-2G$
$e^{-G} \approx 1-G$

Thus, the relative reduction in successful attempts is about twice as large for pure ALOHA. With fewer successful attempts, packets require more retransmissions, increasing expected delay. Therefore, slotted ALOHA yields lower delay at low offered load.

How delays arise in ALOHA

Transmit

Attempt

A packet transmits immediately (pure) or at next slot boundary (slotted)."

Overlap check

Collision window

If any other packet overlaps during the vulnerable period, the transmission fails."

Detect failure

Feedback

If failure occurs, the packet is queued for retransmission."

Retry

Retransmission

Higher success probability reduces the expected number of retries → lower delay."

FAQ: What exactly does “delay” mean here?

Knowledge Check

Question 1 of 3

Q1Single choice

At low offered load $G$ , which scheme yields lower average access delay and why?

Slotted ALOHA, because its collision exponent is $e^{-G}$ rather than $e^{-2G}$

Pure ALOHA, because continuous transmission avoids extra waiting for slots

They are equal, because both have success probability near 1 for small $G$

Slotted ALOHA always has higher delay because slotting reduces attempt frequency

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