Question

Let a cluster of stations share 48 Kbps of pure Aloha channel. Every station outputs frames of length 1024 bits on an average of every 50 seconds. Then what is the maximum value of number of stations?

Answer 1

Since its pure aloha. So max Bandwidth utilization is 18% of 48Kbps.

And its given

Each station transmits 1024 bits ----> 50 seconds

                                    (1024/50)bits-----> 1 second

Lets say there are N stations.

So N*(1024/50)=18% of 48*1024

N=432

Comments

ans comes out to be 431..not 421...

Answer 2

Bandwidth of Pure Aloha = 48 Kbps

Effective bandwidth will be Max throughput possible for given bandwidth.

So Effective bandwidth = 48 * 0.184 Kbps

= 8.832 Kbps.

In 50 sec = 1024 bit (1 frame) is genrated.

So in 1 sec = 1024/50 bit = 20.48 bit generated by each station.

So to achive effective bandwidth rate No. Of Stations that can genrate this amount of frame size per sec will be

= 8.832 Kbps/20.48 bps = 431.25 i.e 431 (floor value) stations possible.

Answer 3

Pure ALOHA

Bandwidth = 0.184 * 48kbps = 8.832 kbps

transmission rate = 1024/50 = 20.48 bps

N = Bandwidth / Frame rate

N = 8.832*1000/20.48

N = 431.25

N = 431 stations.