Consider a source and a destination connected by N links (i.e., N-1 packet switc
ID: 3877468 • Letter: C
Question
Consider a source and a destination connected by N links (i.e., N-1 packet switches). Each link has capacity R bps, and propagation delay d seconds. Ignore processing and queueing delays.
1.Give a formula for the end-to-end delay of sending one packet of length L bits.
2.Generalize the formula for sending P packets of L bits each.
3.Now suppose the links (in the order from source to destination) have capacities R1 < R2 < …< RN, and propagation delays d1, d2, …, dN (with arbitrary values). Give formula for the end-to-end delay of sending P packets of L bits each.
4.Repeat c), but assume that R1 > R2 > …> RN (still arbitrary values for d1, d2, …, dN).
Explanation / Answer
1) Formula for end to end delay for given information :
We know that
No of links = N
Packet length = L
Transmission rate = R
So end to end delay is : N(L/R)
2) Formula for P packets of length L :
Consider there are P packets of length L are transmitted over the N links.
The end-to-end delay for transmitting 1st packet of P packets is: N(L/R)
The end-to-end delay for transmitting 2nd packet of P packets is: N(L/R)
Therefore, for pth packet also the delay is N(L/R).
Hence, by adding all the packet delays, the generalized formula of back-to-back delay of sending P packets, each of length L over N links of transmission rate R is: [N(L/R)] * P.
3) For different capacities R1 < R2 < ...<RN
The acket Length = L
The Propagation delay = Di where i lies between 1 < i < N
The Transmission rate = Ri where i lies between 1 < i < N
Let , Length of link i = Si
The first end system requires to transmit the packet onto the first link = L/R1
The first end system requires to transmit the packet onto the second link = L/R2
The first end system requires to transmit the packet onto the N link = L/RN
the packet propagates over the first link = S1/D1
the packet propagates over the second link = S2/D2
the packet propagates over the third link = SN/DN
So end to end delay for these are :
L/R1 + L/R2 + L/RN + S1/D1 + S2/D2 + SN/DN
if there any processing delay or quenig delay then you must add with above formula.
4) For different capacities R1 > R2 > ...>RN
The formula is same as in (3) because there is no mean that the transmission rates R1 ..... RN are less than or greater than others.
So in this case formula is :
L/R1 + L/R2 + L/RN + S1/D1 + S2/D2 + SN/DN.