Slotted ALOHA Protocol

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1. Concept and Motivation

In 1972, Lawrence Roberts proposed Slotted ALOHA as a method to double the capacity of Norman Abramson's Pure ALOHA system.

In Pure ALOHA, a station can transmit at any arbitrary point in time, leading to frequent partial overlaps between frames. Slotted ALOHA imposes discrete time synchronization:

• Time is divided into continuous, uniform intervals called Slots, each equal to one frame transmission duration ($T_{fr}$).
• A central clock or beacon synchronizes all network stations.
• A station is only permitted to begin transmitting at the exact beginning of a time slot.
• If a frame is generated in the middle of a time slot, the station must wait and buffer the frame until the beginning of the next slot.

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2. Vulnerable Time in Slotted ALOHA

Because transmissions are restricted to slot boundaries, frames either completely collide or do not collide at all. Partial overlaps are physically impossible!

• If another station generates a frame during Slot $(t - T_{fr}, t)$, it will transmit at the start of Slot $t$, colliding with Station A's frame.
• Any frame generated after time $t$ will wait for Slot $(t + T_{fr})$ and cannot collide with Station A.
• Vulnerable Time for Slotted ALOHA:

(Exactly half the vulnerable time of Pure ALOHA!)

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3. Mathematical Derivation of Throughput

Assuming a Poisson frame arrival distribution with average rate $G$ frames per frame-time $T_{fr}$:

For a successful transmission in a slot, the probability that zero other frames ($k = 0$) are generated during the vulnerable interval $V_t = T_{fr}$ is:

Throughput Equation ($S$):

The channel throughput $S$ is given by:

Finding Maximum Throughput:

Differentiating $S$ with respect to $G$:

Substituting $G = 1$ into the throughput equation:

Key Takeaway: Slotted ALOHA achieves a maximum channel throughput of $36.8\%$, exactly doubling the capacity of Pure ALOHA ($18.4\%$)!

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4. Comprehensive Comparison: Pure ALOHA vs. Slotted ALOHA

Parameter	Pure ALOHA	Slotted ALOHA
Transmission Timing	Any arbitrary instant	Strictly at the start of a synchronized time slot
Time Synchronization	None (asynchronous)	Required (global master clock or beacon)
Vulnerable Time ($V_t$)	$2 \times T_{fr}$	$1 \times T_{fr}$
Throughput Formula	$S = G \cdot e^{-2G}$	$S = G \cdot e^{-G}$
Optimal Traffic Load ($G$)	$G = 0.5$	$G = 1.0$
Maximum Throughput ($S_{\max}$)	$\frac{1}{2e} \approx 18.4\%$	$\frac{1}{e} \approx 36.8\%$
Collision Type	Partial or complete overlap	Always complete overlap
Implementation Complexity	Simplest	Requires clock synchronization circuitry

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