Slotted ALOHA

Slotted ALOHA is an improved version of Pure ALOHA. The main purpose of introducing Slotted ALOHA is to reduce the vulnerable time and thereby improve throughput.

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1. Why was Slotted ALOHA introduced?

In Pure ALOHA, a station can transmit at any time.

Suppose Station B starts transmitting at time $t$:

Pure ALOHA

       A can start here
              ↓
──────────────|─────── B starts ──────────|────────
            t-Tfr       t                t+Tfr
                       [ B frame ]

Another station can start:

• just before B starts, or
• while B is transmitting.

Therefore:

$$\boxed{\text{Vulnerable time}=2T_{fr}}$$

This large vulnerable period results in more collisions.

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2. Basic idea of Slotted ALOHA

Slotted ALOHA introduces a simple rule:

A station is allowed to transmit only at the beginning of a time slot.

The entire time is divided into equal-sized slots.

Each slot has a duration equal to the time required to transmit one frame:

$$\boxed{\text{Slot duration}=T_{fr}}$$

For example:

A station cannot start transmitting in the middle of a slot.

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3. How does it work?

Suppose a station has a frame ready.

It waits until the beginning of the next time slot.

Frame ready
     |
     ↓
Wait for beginning of slot
     |
     ↓
Transmit

For example:

             Slot 1        Slot 2        Slot 3
          |------------|------------|------------|
                       ↑
                    Station waits
                    and transmits
                    here

If the station misses the beginning of Slot 2, it cannot start in the middle of Slot 2.

It must wait until Slot 3.

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4. Why does this reduce collisions?

This is the key idea.

Consider Station B transmitting in Slot 2:

             Slot 1       Slot 2       Slot 3
          |------------|------------|------------|
                       [==== B ====]

Another station cannot suddenly start halfway through Slot 2.

It can only start at begining of slot 3

Therefore, a frame transmitted in Slot 2 can collide only with another frame that also starts at the beginning of Slot 2.

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5. Collision in Slotted ALOHA

There can still be collisions.

Suppose Stations 1 and 2 both have frames to send at the beginning of Slot 2:

             Slot 1        Slot 2        Slot 3
          |------------|------------|------------|
                       ↑
                       |
              ┌────────┴────────┐
              │                 │
             S1                S2
              │                 │
              ↓                 ↓
          [ Frame 1 ]      [ Frame 2 ]
               \               /
                \             /
                 \           /
                  COLLISION

Both frames collide because they started at the same slot boundary.

So Slotted ALOHA does not eliminate collisions.

It simply reduces the period during which a collision can occur.

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6. Vulnerable Time

This is the biggest improvement over Pure ALOHA.

Pure ALOHA

$$\boxed{\text{Vulnerable time}=2T_{fr}}$$

Slotted ALOHA

$$\boxed{\text{Vulnerable time}=T_{fr}}$$

So the vulnerable time is reduced by half.

Pure ALOHA

<--------------- 2Tfr --------------->
        Vulnerable period


Slotted ALOHA

<-------- Tfr -------->
   Vulnerable period

Why?

Because stations are allowed to start transmitting only at slot boundaries.

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7. Simple comparison

Suppose Station B transmits for one frame time.

Pure ALOHA

Another station could start:

        Before B       B transmitting
           ↓                ↓
───────────|──────────────[==========]────────
         t-Tfr            t        t+Tfr

          <------ 2Tfr ------->

So there are many opportunities for collision.

Slotted ALOHA

B starts exactly at a slot boundary:

        Slot n                 Slot n+1
     |------------|----------------------------|
                  [======== B ========]
                  ↑
             fixed start

Another station can collide with B only if it also starts at the same beginning of the slot.

Hence:

$$\boxed{T_{vulnerable}=T_{fr}}$$

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8. Throughput of Slotted ALOHA

The throughput equation for Slotted ALOHA is:

$$\boxed{S=Ge^{-G}}$$

where:

• $G$ = average number of frames generated during one frame transmission time
• $S$ = average number of successfully transmitted frames during one frame transmission time.

Compare this with Pure ALOHA:

$$S=Ge^{-2G}$$

The difference is caused by the vulnerable time.

Protocol	Vulnerable time	Throughput
Pure ALOHA	$2T_{fr}$	$S=Ge^{-2G}$
Slotted ALOHA	$T_{fr}$	$S=Ge^{-G}$

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9. Maximum throughput

For Slotted ALOHA, the maximum throughput occurs when:

$$\boxed{G=1}$$

The maximum throughput is:

$$\boxed{S_{max}=\frac{1}{e}}$$

which is approximately:

$$\boxed{S_{max}=0.368=36.8\%}$$

This is twice the maximum throughput of Pure ALOHA, which is 18.4%.

Interpretation

When:

$$G=1$$

it means:

On average, one frame is generated during one frame transmission time.

At this operating point, approximately 36.8% of the generated frames successfully reach their destination.

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10. Why is $G=1$ the optimum?

The vulnerable time of Slotted ALOHA is only:

$$T_{fr}$$

Therefore, if approximately one frame is generated during this vulnerable period, the system reaches its maximum throughput.

Compare:

Pure ALOHA

Vulnerable time = 2Tfr

Maximum:
G = 0.5
S = 18.4%

Slotted ALOHA

Vulnerable time = Tfr

Maximum:
G = 1
S = 36.8%

The reduction in vulnerable time allows the system to handle a higher offered load.

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11. Example 

A slotted ALOHA network transmits 200-bit frames using a shared channel with a 200-kbps bandwidth. Find the throughput if the system (all stations together) produces

a. 1000 frames per second.

b. 500 frames per second.

c. 250 frames per second.

(a) 1000 frames per second

Given:

• Frame size = 200 bits
• Channel bandwidth = 200 kbps

First calculate:

$$T_{fr}=\frac{200}{200,000}$$ $$T_{fr}=1\text{ ms}$$

Therefore:

Slot duration

$$\boxed{1\text{ ms}}$$

Vulnerable time

$$\boxed{1\text{ ms}}$$

Now suppose the system generates 1000 frames per second.

Since one frame takes 1 ms:

$$1000\text{ frames/sec}=1\text{ frame/ms}$$

Therefore:

$$G=1$$

Using:

$$S=Ge^{-G}$$

we get:

$$S=1\times e^{-1}$$ $$S\approx0.368$$

Therefore:

$$\boxed{S=36.8\%}$$

So approximately:

$$1000\times0.368=368$$

frames per second are successfully transmitted.

(b) 500 frames per second

The system produces:

$$500\text{ frames/sec}$$

Since one frame takes 1 ms:

$$500\text{ frames/sec}=0.5\text{ frame/ms}$$

Therefore:

$$G=0.5$$

Now:

$$S=0.5e^{-0.5}$$ $$S\approx0.3033$$

Therefore:

$$\boxed{S\approx30.33\%}$$

Successful frames per second:

$$500\times0.3033\approx151.65$$ ≈152 successful frames/sec

c) 250 frames per second

The system produces:

$$250\text{ frames/sec}$$

Therefore:

$$250\text{ frames/sec}=0.25\text{ frame/ms}$$

So:

$$G=0.25$$

Using the formula:

$$S=0.25e^{-0.25}$$ $$S\approx0.1947$$

Therefore:

$$\boxed{S\approx19.47\%}$$

Successful frames per second:

$$250\times0.1947\approx48.68$$ $$\boxed{\approx49\text{ successful frames/sec}}$$

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Final Answer

Case	Frames/sec generated	$G$	$S=Ge^{-G}$	Throughput	Successful frames/sec
a	1000	1.0	0.3679	36.8%	368
b	500	0.5	0.3033	30.33%	152
c	250	0.25	0.1947	19.47%	49

Important observation

The maximum throughput of Slotted ALOHA is 36.8%, which occurs at:

$$G=1$$

Therefore, case (a) operates exactly at the maximum-throughput point.

​

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12. Pure ALOHA vs Slotted ALOHA

Feature	Pure ALOHA	Slotted ALOHA
Transmission time	Any time	Only at beginning of slot
Slotting	No	Yes
Slot duration	—	$T_{fr}$
Vulnerable time	$2T_{fr}$	$T_{fr}$
Collision possible?	Yes	Yes
Throughput formula	$Ge^{-2G}$	$Ge^{-G}$
Maximum $G$	$0.5$	$1$
Maximum throughput	18.4%	36.8%
Main improvement	—	Vulnerable time reduced by half

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13. The main idea to remember

The entire difference can be summarized in one diagram:

              ALOHA

       PURE ALOHA
       ───────────
       Send anytime
            ↓
     Vulnerable time
          2Tfr
            ↓
     More collisions
            ↓
     Maximum = 18.4%


       SLOTTED ALOHA
       ──────────────
   Send only at slot beginning
            ↓
     Vulnerable time
           Tfr
            ↓
     Fewer collisions
            ↓
     Maximum = 36.8%

Summary

Slotted ALOHA is an improved version of Pure ALOHA in which time is divided into slots of $T_{fr}$ seconds, and a station is allowed to transmit only at the beginning of a time slot. If a station misses the beginning of a slot, it waits for the next slot. Collisions can still occur when two or more stations transmit at the beginning of the same slot, but the vulnerable time is reduced from $2T_{fr}$ to $T_{fr}$. Its throughput is $S=Ge^{-G}$, with a maximum throughput of 0.368 (36.8%) when $G=1$.