FIND MEAN NUMBER OF FRAME REQUIRED TO ATTEMPT A FRAME IN ALOHA - NETWORKING

 

Let P_k is the probability that exactly K attempts are required to transmit a frame.

P_{k = ( 1- e}-G ₎^k-1 _{. ( e}^-G ₎¹

_{( 1- e}-G ₎^k-1 is Probability of failure

_{( e}^-G ₎¹  is Probability of failure    

Excepted number of attempt

E = e^G

 Where: G is load, E    is exponential load

NOTE: Number of attempt will reduce if load is less.

 

FINITE POPULATION ALOHA  / SLOTTED ALOHA

There are N number of station are compiling for a single channel SLOTTED ALOHA channel.

G_i : It is a load shared by the station I, that means number of frame including new entry transmission transmitted by station is per frame time) / It is probability that station ( I ) will transmit in a particular slot.

S_i : Throughput shared by a station ( I ), that means probability that particular station I will transmit successful.

OR

Mean / average number of successful transmission per frame time by station (i).

S_i = G_i   (1 – G₁) (1 –G₂) ---------- (1 – G_N)        

 Let the channel load is G

G = G_{1 +} G_{2 +} G_{3 + ----------- +} G_N

_{ASSUME :}

G = G_{1 +} G_{2 +} G_{3 + ----------- +} G_N

Load shared by all station are equal than.

G = N . G_i

G_i = G / N

Let the throughput of the channel is S

S = S_{1 +} S_{2 +} S_{3 + ----------- +} S_N

_{ASSUME :}

S₁ = S₂₊ S_{2 +} S_{3 + ----------- +} S_N

S_i = S /N

_than

Put  S_i =  S/N   ,   G_i =  G/N

S/N  =  G/N ( 1 - G/N )^N-1

S =  G ( 1 - G/N )^N-1

For infinite population ALOHA / Infinite slotted ALOHA

If N = infinite

S = G . _e^-G 

For what value of G , S will be  maximum.

If   G = 1 than

S will be maximum.

QUESTION: Consider the delay of PURE ALOHA  and SLOTTED ALOHA.

ANSWER: We can measure ALOHA by two parameters.

1. Delay

2. Throughput / Efficiency / Utilisation             

Delay can be compared in the case of extreme load due to some rules. Such as only one 

can be transmitted.

In PURE ALOHA delay = 0 , because when any sander make their message immediately 

they can able to send the message without waiting at time slot.

In SLOTTED ALOHA   we have to wait for one time slot.  This delay is due to rules

 ( such as only one can be transmit / we cannot transmit until previous are not completed)