1. Consider two hosts, A and B, connected by a single link of rate R bps. Suppose that the two hosts are separated by m metres, and suppose the propagation speed along the link is s metres/sec. Host A is to send a packet of size L bits to host B.
a) Express the propagation delay, dprop, in terms of m and s.
b) Determine the transmission time of the packet, dtrans, in terms of L and R.
c) Ignoring processing and queuing delays, obtain an expression for the end-to-end delay.
d) Suppose host A begins to transmit the packet at time t = 0. At time t = dtrans, where is the last bit of the packet?
e) Suppose dprop is greater than dtrans. At time t = dtrans, where is the first bit of the packet?
f) Suppose dprop is less than dtrans. At time t = dtrans, where is the first bit of the packet?
g) Suppose s = 2.5 × 108, L = 100 bits, and R = 28 Kbps. Find the distance m so that dprop equals dtrans.
h) Use a program like Microsoft Excel to explore the interplay of transmission and propagation delay further. Consider three different packet sizes L = 100 bits, 1000 bits and 1,000,000 bits. Further consider three different link bandwidths R = 56 Kbps, 1.5 Mbps and 1.5 Gbps. Also, consider three different distances m = 2.5 metres, 25 Km, and 2500 Km. For each of these 27 combinations, compute dprop, dtrans and the end-to-end delay. Explain your observations in a few sentences.
1. a. dprop = m/s sec
b. dtrans = L/R sec
c. delay = dprop + dtrans = m/s + L/R sec
d. The last bit is just leaving the Host A
e. The first bit still in the link has not reached Host B
f. The first bit still has reached Host B
g. dprop = dtrans => m/s = L/R => m = (L/R)*s = (100/28 × 103) * 2.5 × 108 =
h. Sol: Suppose s = 2.5 * 108, data and observations are summarized below.
|
m |
s |
dprop |
|
2.5 |
250000000 |
0.00000001 |
|
25000 |
250000000 |
0.0001 |
|
2500000 |
250000000 |
0.01 |
As shown in the table above, the value of dprop increases while the physical link becomes longer.
|
L |
R |
dtrans |
|
100 |
56000 |
0.001786 |
|
100 |
1500000 |
0.0000666667 |
|
100 |
1500000000 |
0.0000000667 |
|
1000 |
56000 |
0.017857 |
|
1000 |
1500000 |
0.000667 |
|
1000 |
1500000000 |
0.0000006667 |
|
1000000 |
56000 |
17.85714 |
|
1000000 |
1500000 |
0.666667 |
|
1000000 |
1500000000 |
0.000667 |
As shown in the table above, dtrans decreases when the link bandwidth becomes larger, and increases with the augment of packet length.
|
L |
R |
m |
s |
end-to-end delay |
|
100 |
1500000000 |
2.5 |
250000000 |
7.66667E-08 |
|
1000 |
1500000000 |
2.5 |
250000000 |
6.76667E-07 |
|
100 |
1500000 |
2.5 |
250000000 |
6.66767E-05 |
|
100 |
1500000000 |
25000 |
250000000 |
0.000100067 |
|
1000 |
1500000000 |
25000 |
250000000 |
0.000100667 |
|
100 |
1500000 |
25000 |
250000000 |
0.000166667 |
|
1000 |
1500000 |
2.5 |
250000000 |
0.000666677 |
|
1000000 |
1500000000 |
2.5 |
250000000 |
0.000666677 |
|
1000 |
1500000 |
|