Andrew S. Tanenbaum Edition 5th Exercise 6 Question 39 (Page No. 609)

Question

To get around the problem of sequence numbers wrapping around while old packets
still exist, one could use 64-bit sequence numbers. However, theoretically, an optical
fiber can run at 75 Tbps. What maximum packet lifetime is required to make sure that
future 75-Tbps networks do not have wraparound problems even with 64-bit sequence
numbers? Assume that each byte has its own sequence number, as TCP does.

Answer 1

To avoid getting the same sequence numbered packet at the destination, the Wrap Around Time should be at least the lifetime of the packet, i.e WAT >= LT ,so the max LT can be WAT

Now bandwidth given= 75 Tbps ( I am assuming b means bits)

1s ------------  you can number (75* 2^40)/8 bytes

so time required to assign sequence number for 2^64 bytes is (8* 2^64)/ (75 * 2^40) sec which is 1789569.7 sec

So the maximum life time of the packet can be ~ 498 hours long !!!!!!!!