Propagation Delay vs Transmission delay

Recall that propagation delay d/s is the time to transmit one bit over a link

And transmission delay is the time to transmit a whole packet over a link

Then, why isn't packet length * propagation delay = transmission delay?

Because they're measuring different things.

Propagation delay is how long it takes one bit to travel from one end of the "wire" to the other (it's proportional to the length of the wire, crudely).

Transmission delay is how long it takes to get all the bits into the wire in the first place (it's packet_length/data_rate).

The transmission delay is the amount of time required for the router to push out the packet.

The propagation delay, is the time it takes a bit to propagate from one router to the next.

the transmission and propagation delay are completely different! if denote the length of the packet by L bits, and denote the transmission rate of the link from first router to second router by R bits/sec. then transmission delay will be L/R. and this is depended to transmission rate of link and the length of packet.

then if denote the distance between two routers d and denote the propagation speed s, the propagation delay will be d/s. it is a function of the Distance between the two routers, but has no dependence to the packet's length or the transmission rate of the link.

Obviously , packet length * propagation delay = trasmission delay is wrong.

Let us assume that you have a packet which has 4 bits 1010.You have to send it from A to B.

For this scenario,Transmission delay is the time taken by the sender to place the packet on the link(Transmission medium).Because the bits(1010) has to be converted in to signals.So it takes some time.Note that here only the packet is placed.It is not moving to receiver.

Propagation delay is the time taken by a bit(Mostly MSB ,Here 1) to reach from sender(A) to receiver(B).

Transmission Delay : Amount of time required to pump all bits/packets into the electric wire/optic fibre.

Propagation delay : It's the amount of time needed for a packet to reach the destination.

If propagation delay is very high than transmission delay the chance of losing the packet is high.

Transmission Delay:

This is the amount of time required to transmit all of the packet's bits into the link. Transmission delays are typically on the order of microseconds or less in practice. 

> L: packet length (bits)
R: link bandwidth (bps)
so transmission delay is = L/R

Propagation Delay:

Is the time it takes a bit to propagate over the transmission medium from the source router to the destination router; it is a function of the distance between the two routers, but has nothing to do with the packet's length or the transmission rate of the link. 

> d: length of physical link
> S: propagation speed in medium (~2x10⁸m/sec, for copper wires & ~3x10⁸m/sec, for wireless media)
> so propagation delay is = d/s

The transmission delay is the amount of time required for the router to push out the packet, it has nothing to do with the distance between the two routers. The propagation delay is the time taken by a bit to to propagate form one router to the next