ECE $534/$ CSC $424-$ Fall $2024$

Due Date: Fri. Sep. ${20}^{th}$

Q$1$: $$

How long does it take a packet of length $1,000$ bytes to propagate over a link of distance $2,500km,$

propagation speed $2\mathrm{.}5*{10}^8$ mis, and transmission rate $2$ Mbps$?$ More generally, how long does it take a

packet of length $L$ to propagate over a link of distanced, propagation speeds, and transmission rate $R$ bps$?$

Does this delay depend on packet length? Does this delay depend on transmission rate?

Q$2$:

Suppose Host A wants to send a large file to Host B$.$ The path from Host A to Host $B$ has three links, of rates $R_1$

$=500kbps,R_2=2Mbps,$ and $R_3=1Mbps.$

a$.$ Assuming no other traffic in the network, what is the throughput for the file transfer.

b$.$ Suppose the file is $4$ million bytes. Dividing the file size by the through put, roughly how long will it

take to transfer the file to Host B$?$

c$.$ Repeat $($a$)$ and $($b$),$ but now with ${?}_R$; reduced to $100$ kbps $.$

Q$3$:

Suppose users share a $2$ Mbps link. Also suppose each user transmits continuously at $1$ Mbps when transmitting,

but each user transmits only $20$ percent of the time. When circuit switching is used, how many users can be

supported?

a$.$ For the remainder of this problem, suppose packet switching is used. Why will there be essentially no

queuing delay before the link if two or fewer users transmit at the same time? Why will there be a

queuing delay if three users transmit at the same time?

b$.$ Find the probability that a given user is transmitting.

c$.$ Suppose now there are three users. Find the probability that at any given time, all three users are

transmitting simultaneously. Find the fraction of time during which the queue grows.

Q$4$:

Consider a packet of length $L$ which begins at end system A and travel over three links to a destination end system.

These three link are connected by two packet switches. Let di$,$ si$,$ and Ri denote the length, propagation speed, and

the transmission rate of link $i,$ for $i=1,2,3.$ The packet switch delays each packet by dproc. Assuming no queuing

delays, in terms of $di,$ si$,$ Ri$,$