Assume you wish to transfer an n-byte file along a path composed ofthe source, d
ID: 3608679 • Letter: A
Question
Assume you wish to transfer an n-byte file along a path composed ofthe source, destination,seven point to point links , and fiveswitches.Suppose each link has a propogation delay of 2ms,bandwidthof 4Mbps,and that the switches support both circuit and packetswitching. Thus you can either break the file up into 1-KBpackets,or set up a circuit through the switches and send thefilesas one contiguous bit stream . Suppose that packets have 24 bytes of packet header information and 1000 bytes of payload,that store- and- forward packet processing at each switch incurs a1 ms delay after packet has been completely received, that packetsmay be be sent continously without waiting for acknowledgementa,and that circuit setup requires a 1KB message to make oneround-trip on the path incurringa 1-ms delay at each switch afterthe message has been completely received.Assume switches introduceno delay to datatraversung a circuit.You may also assume that filesize is a multiple of 1000bytes.a> For what file size n byesis the total number of bytessent across the network less for packets? b> For what file size n bytes is the total latency incurredbefore the entire file arrives at the destination less for circuitsthan for packets? c>How sensitive are these results to the number of switchesalong the path? To the bandwidth of the links? To the ratio ofpacket size to packet header size? d> How do you think this model of the relative merits ofcircuits and packets it? Does it ignoreimportant considerationsthat discredit one or the other approach? if so,what arethey?
a> For what file size n byesis the total number of bytessent across the network less for packets? b> For what file size n bytes is the total latency incurredbefore the entire file arrives at the destination less for circuitsthan for packets? c>How sensitive are these results to the number of switchesalong the path? To the bandwidth of the links? To the ratio ofpacket size to packet header size? d> How do you think this model of the relative merits ofcircuits and packets it? Does it ignoreimportant considerationsthat discredit one or the other approach? if so,what arethey?
Explanation / Answer
(a) Packet Switching:
No. of bytes transferred = no. of packets *packet size
= (n/1000) * 1024
Circuit Switching
No. of bytes transferred = file size +two packets
= n + 2*1024
(n + 2048) < (n/1000)*1024
24*n/1000 > 2048
n >= 86000 bytes
(b) Packet Switching
Latency = Transmission time for allpackets +Transmit delay of one packet at each switch+ Processing delay of one packet at each switch + propogationdelay of all links
=(n/1000)*(1024*8bits/4Mbps) + 3*(1024*8bits/4Mbps) s + 3*1ms +4*2ms
= (n*2*1024/10^6) ms + 6.144+ 11
= (n*2*1024/10^6) ms + 17.144
Circuit Switching:
Latency = Transmission time for the wholefile +propagation delay of all links +
Transfer time of 2packets
= (n*8bits/4Mbps) s + 4*2ms +2*(4*1024*8/4Mbps + 3*1ms+4*2ms)
= n*2*10^3/10^6 ms + 8+ 2*(19.1920)
= 2n/10^3 + 38.3840
For n to meet the condition,
(n*2*1024/10^6) ms + 17.144 > 2n/10^3 +38.3840
Approximately, n > 9500bytes
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