Consider mesh network connecting n devices : a) The total number of I/O ports us

ID: 3542128 • Letter: C

Question

Consider mesh network connecting n devices :

a) The total number of I/O ports used in all n devices in this mesh network is 30. What is the

number of devices in this network (i.e., what is the value of n)? Note: each I/O port contains

a transmitter and a receiver.

b) A sending device S transmits fixed length packets to a receiving device R over a link in

this mesh network. The transmission speed is 1000 packets/second. The one-way propagation

delay of this link is 0.01 second. Assume the link suffered a sudden failure (e.g., the cable of

the link was cut) after two minutes from the start of transmission. What is the minimum

number and what is the maximum number of packets that can be lost as a result of the link

failure? Note: If the cable is cut, all packets in transit on the link are lost.

If number of devices in the mesh is n

then there will be a total nC2 number of IO ports in this mesh

This is because between each device we need an I/O port

so the toatal number of IO ports is nC2

howver each port contains a transmitter and a receiver

hence the number of IO port is actually double of what we calculated

or 2 nC2 = 30

or nC2 = 15

now n C 2 = n! / (2! (n-2)! ) = n(n-1)/2 = 15

or n^2 - n = 30

or n^2 - n - 30 = 0

=> n = 6 (discard -5 as it not a solution)

So the number of devices is 6

Two minutes from the start of transmission

The propagation error can vary between 0 and 0.01 sec

in case the delay is zero, time available to send data = 120 seconds

So number of packets sent = 2000 * 120 = 240000 packets

If the delay is 0.01 seconds

then packet stream is active only for 120 - 0.01 = 119.99 seconds

then packets sent is 119.99 * 2000 = 239980 packets

So the maximum number of packets sent is 240000 packets and minimum is 239980 packets

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.