Slotted ALOHA

• Step 1: Background knowledge (with text and figures)

• 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
• Step 4: Simulator (Data structure, flowchart)
• [ ]Step 5: Verification of values generated from the simulator and Step 3b
• [x]Step 6: Simulation results

Step 1: Background Knowledge

Summarize the background knowledge (with text and figures)

• In slotted ALOHA, time is assumed to be slotted in timeslots of duration
  $\tau$, 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.

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
  $\lambda$, so probability of no arrivals is
  $e^{-\lambda /m}$
• This implies that the probability of an unbacklogged STA transmits packets in a given slot is
  $P_a=1-e^{-\lambda /m}$

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
  $P_r$

• $G=\lambda \tau$ is offered load, and throughput
  $S=G{e}^{-G}$
• Collision Probability
  $P_c=1-G{e}^{-G}-e^{-G}$
• Mean delay
  $\overline{D_{}}=1-1/\lambda +m/S$

Step 2: System Model

Define the problem by specifying the system model you considered

• There are m STAs,
• Time is divided into fixed-length slots
• Packet arrivals are poisson distribution with mean
  $\lambda$
• When STAs are in the idle state, probability of new arrival for each STAs is
  $P_a=1-e^{-\lambda /m}$
• When in backlogged state, probability of retransmission is
  $P_r=P_a=1-e^{-\lambda /m}$
• 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

specify I/P parameters

I/P	Value
number of STAs	100
$\lambda$	[0:0.1:5]
simulation Time	${10}^5$ timeslots

3b. Draw a timing diagram showing the transmission behavior of a STA

Draw a timing dirgram showing the concepts you learned

Step 4 : Simulator

Write a simulator to verify the concept

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

Implement a simulator. Use the values you generated from the simulator and verified them one-by-one based on Step 3

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

Show us the simulation results