# Slotted ALOHA

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- [x] Step 1: Background knowledge (with text and figures)
* [x] Step 2: System model (I/P parameters, system architecture and timing diagram)
* [x]Step 3a: Specify the constant
* [ ]Step 3b: Draw a timing diagram showing the transmission behavior of a STA
* [x] Step 4: Simulator (Data structure, flowchart)
* [ ]Step 5: Verification of values generated from the simulator and Step 3b
* [x]Step 6: Simulation results
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## Step 1: Background Knowledge
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Summarize the background knowledge (with text and figures)
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- **In slotted ALOHA**, time is assumed to be slotted in timeslots of duration $τ$, and STAs can only start their packet transmissions at the beginning of the next timeslot after the packet has formed
- Each STAs can have two states: ***idle*** or ***backlogged***.
- When a STA has nothing to transmit it is in the idle state.
- If the packet was received successfully the STA enters the idle state again, *otherwise* it goes to backlogged state.
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***Idle State***
- As there are a total of $m$ STAs in the network, each of the $m−n$ nonbacklogged STAs will transmit a packet **immediately** in the given slot if one or more packets arrived at these STAs
- These new arrivals are Poisson distributed with mean $λ$, so probability of no arrivals is $e^{-λ/m}$
- This implies that the probability of an unbacklogged STA transmits packets in a given slot is $P_a = 1-e^{-λ/m}$
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***Backlogged state***
- Each backlogged STAs retransmits with probability $P_r$ in each successive slot until successful transmission happens
- Let $n$ denote the number of backlogged STAs at the beginning of a given slot, each of the STAs will transmit a packet in a given slot independent of the other nodes, with probability $P_r$
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- $G=λτ$ is offered load, and throughput $S=Ge^{-G}$
- Collision Probability $P_c=1-Ge^{-G}-e^{-G}$
- Mean delay $\overline{D_{}}=1-{1/λ}+{m/S}$
## Step 2: System Model
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Define the problem by specifying the system model you considered
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- There are m STAs,
- Time is divided into fixed-length slots
- Packet arrivals are poisson distribution with mean $λ$
- When STAs are in the idle state, probability of new arrival for each STAs is $P_a = 1-e^{-λ/m}$
- When in backlogged state, probability of retransmission is $P_r=P_a = 1-e^{-λ/m}$
- An STA will stay in backlogged state until the packet is successful, when the packet is successful STA will become idle and waiting for a new packet arrival

*Figure 2.1 Timing Diagram*

## Step 3: Draw figures to show the concepts you learned

### 3a. Specify the constants you used in the figures
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specify I/P parameters
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| I/P | Value |
| -------- | -------- |
| number of STAs | 100 |
| $λ$ | [0:0.1:5] |
| simulation Time | $10^5$ timeslots |

### 3b. Draw a timing diagram showing the transmission behavior of a STA
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Draw a timing dirgram showing the concepts you learned
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## Step 4 : Simulator
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Write a simulator to verify the concept
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### 4a. Define the parameters (their ranges need to be specified) and data structures to be used in your simulator

#### STA's Data structure
| datatype | meaning | range |
| -------- | -------- | -------- |
| int[status]| STA status, idle or backlogged | $[0,1]$ |
| float[pa] | packet arrival probability | $[0,1]$ |
| float[pr] | packet retransmission probability | $[0,1]$ |
|int[N] | packet transmitted in a given slot|$[0,100]$ |
| int[totalPacketAt] |total packets attempted| |
| int[totalPacketTr] |total packets successfully transmitted| |

|O/P|
|-|-|
|$p$ : packet collision probability |
|$S$ : throughput |
|$G$ : offered load |
|$\overline{D_{}}$ : mean delay |

### 4b. Draw the flowchart

## Step 5 : Verification
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Implement a simulator. Use the values you generated from the simulator and verified them one-by-one based on Step 3
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>this is the transmission behavior when lambda=1
https://raw.githubusercontent.com/bariqfirmansyah/slottedaloha/master/lambda1.txt
this is also the transmission behavior when lambda=1
https://raw.githubusercontent.com/bariqfirmansyah/slottedaloha/master/lambda1a.txt
this is the transmission behavior when lambda=5
https://raw.githubusercontent.com/bariqfirmansyah/slottedaloha/master/lambda5.txt

>look at how the packet transmission occurs more when lambda=5

## Step 6 : Simulation Result
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Show us the simulation results
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